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All that we must do to defeat the Tarski Undefinability Theorem:
We define the notion of formal system as an extended
version of Prolog's Facts and Rules. This new system
can handle arbitrary orders of logic. Encodes Facts
in formalized natural language.
The Rules only allow semantic logical entailment from
Facts. When we do this Tarski's Liar Paradox basis is
simply rejected as untrue and
Boolean True(Language L, Expression E) becomes definable.
All that we must do to defeat the Tarski Undefinability Theorem:
We define the notion of formal system as an extended
version of Prolog's Facts and Rules. This new system
can handle arbitrary orders of logic.
Encodes Facts
in formalized natural language.
The Rules only allow semantic logical entailment from
Facts.
When we do this Tarski's Liar Paradox basis is
simply rejected as untrue and
Boolean True(Language L, Expression E) becomes definable.
On 2025-08-25 17:54:02 +0000, olcott said:
All that we must do to defeat the Tarski Undefinability Theorem:
Bad luck if you must but can't.
We define the notion of formal system as an extended
version of Prolog's Facts and Rules. This new system
can handle arbitrary orders of logic.
Prolog's system already can. But it cannot handle negations.
Encodes Facts
in formalized natural language.
The Rules only allow semantic logical entailment from
Facts.
You can't encode "semantic logical entailment" in the rules.
Without a formal definition those words are formally nonsense.
When we do this Tarski's Liar Paradox basis is
simply rejected as untrue and
Boolean True(Language L, Expression E) becomes definable.
As Tarski proved, if True(Language L, Expression E) is definable
then Liar Paradox is provably true (therefore not rejectable as
untrue) and provably false, so true is the same as false.
On 8/26/2025 5:11 AM, Mikko wrote:
On 2025-08-25 17:54:02 +0000, olcott said:
All that we must do to defeat the Tarski Undefinability Theorem:
Bad luck if you must but can't.
I create the basic architecture and others implement it.
We define the notion of formal system as an extended
version of Prolog's Facts and Rules. This new system
can handle arbitrary orders of logic.
Prolog's system already can. But it cannot handle negations.
It not that it can't handle negations.
It handles them differently.
https://en.wikipedia.org/wiki/Negation_as_failure
That is the key to avoiding self-referential paradoxes.
They simply are not derived in the system making them
untrue in the system.
LP = "this sentence is not true"
Boolean True("English", LP)==FALSE
Boolean True("English", ~LP)==FALSE
Encodes Facts
in formalized natural language.
The Rules only allow semantic logical entailment from
Facts.
You can't encode "semantic logical entailment" in the rules.
Without a formal definition those words are formally nonsense.
https://plato.stanford.edu/entries/montague-semantics/
Formalizes natural language semantics syntactically.
When we do this Tarski's Liar Paradox basis is
simply rejected as untrue and
Boolean True(Language L, Expression E) becomes definable.
As Tarski proved, if True(Language L, Expression E) is definable
then Liar Paradox is provably true (therefore not rejectable as
untrue) and provably false, so true is the same as false.
Not at all. Tarski got confused by this.
This sentence is not true: "This sentence is not true" is true.
He never noticed that the Liar Paradox is not a bearer of truth
and must be rejected on that basis as not an member of any
logic system. Prolog does notice that:
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
On 2025-08-26 15:16:31 +0000, olcott said:
On 8/26/2025 5:11 AM, Mikko wrote:
On 2025-08-25 17:54:02 +0000, olcott said:
All that we must do to defeat the Tarski Undefinability Theorem:
Bad luck if you must but can't.
I create the basic architecture and others implement it.
Post again when you have the basic architecture on a web site.
We define the notion of formal system as an extended
version of Prolog's Facts and Rules. This new system
can handle arbitrary orders of logic.
Prolog's system already can. But it cannot handle negations.
It not that it can't handle negations.
It is.
It handles them differently.
It handles a different thing.
https://en.wikipedia.org/wiki/Negation_as_failure
That is the key to avoiding self-referential paradoxes.
They simply are not derived in the system making them
untrue in the system.
You can define a self-reference. You cant refer to the
negation of self.
LP =-a "this sentence is not true"
Boolean True("English", LP)==FALSE
Boolean True("English", ~LP)==FALSE
There is nothing in Prolog that means '~'.
Encodes Facts
in formalized natural language.
The Rules only allow semantic logical entailment from
Facts.
You can't encode "semantic logical entailment" in the rules.
Without a formal definition those words are formally nonsense.
https://plato.stanford.edu/entries/montague-semantics/
Formalizes natural language semantics syntactically.
You can't formalize all of natural language semantics.
When we do this Tarski's Liar Paradox basis is
simply rejected as untrue and
Boolean True(Language L, Expression E) becomes definable.
It doesn't be come definable if it isn't already.
As Tarski proved, if True(Language L, Expression E) is definable
then Liar Paradox is provably true (therefore not rejectable as
untrue) and provably false, so true is the same as false.
Not at all. Tarski got confused by this.
This sentence is not true: "This sentence is not true" is true.
No, Tarski got it right when he said that "This sentence is not true"
is not true.
You can't prove that "This sentence is not true" is true.
He never noticed that the Liar Paradox is not a bearer of truth
and must be rejected on that basis as not an member of any
logic system. Prolog does notice that:
What he used in place of the Liar paradox is a valid sentence that
can be used in proofs, either as a sentence or as a part of a larger sentence.
?- LP = not(true(LP)).
LP = not(true(LP)).
Note that the word "not" above does not mean the logical negation.
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Note that the word "not" above does not mean the logical negation.
That unify_with_occurs_check fails does not prove that the two
expressions do not mean the same.
?- unify_with_occurs_check(LP, true(LP)).
false.
On 8/27/2025 3:28 AM, Mikko wrote:
On 2025-08-26 15:16:31 +0000, olcott said:
On 8/26/2025 5:11 AM, Mikko wrote:
On 2025-08-25 17:54:02 +0000, olcott said:
All that we must do to defeat the Tarski Undefinability Theorem:
Bad luck if you must but can't.
I create the basic architecture and others implement it.
Post again when you have the basic architecture on a web site.
No.
On 2025-08-27 15:27:26 +0000, olcott said:
On 8/27/2025 3:28 AM, Mikko wrote:
On 2025-08-26 15:16:31 +0000, olcott said:
On 8/26/2025 5:11 AM, Mikko wrote:
On 2025-08-25 17:54:02 +0000, olcott said:
All that we must do to defeat the Tarski Undefinability Theorem:
Bad luck if you must but can't.
I create the basic architecture and others implement it.
Post again when you have the basic architecture on a web site.
No.
OK, but then we can't discuss it.
On 8/28/2025 2:50 AM, Mikko wrote:
On 2025-08-27 15:27:26 +0000, olcott said:
On 8/27/2025 3:28 AM, Mikko wrote:
On 2025-08-26 15:16:31 +0000, olcott said:
On 8/26/2025 5:11 AM, Mikko wrote:
On 2025-08-25 17:54:02 +0000, olcott said:
All that we must do to defeat the Tarski Undefinability Theorem:
Bad luck if you must but can't.
I create the basic architecture and others implement it.
Post again when you have the basic architecture on a web site.
No.
OK, but then we can't discuss it.
Prolog already knows to reject the Liar Paradox
as not a truth-bearer.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
On 2025-08-28 15:31:28 +0000, olcott said:
On 8/28/2025 2:50 AM, Mikko wrote:
On 2025-08-27 15:27:26 +0000, olcott said:
On 8/27/2025 3:28 AM, Mikko wrote:
On 2025-08-26 15:16:31 +0000, olcott said:
On 8/26/2025 5:11 AM, Mikko wrote:
On 2025-08-25 17:54:02 +0000, olcott said:
All that we must do to defeat the Tarski Undefinability Theorem: >>>>>>>Bad luck if you must but can't.
I create the basic architecture and others implement it.
Post again when you have the basic architecture on a web site.
No.
OK, but then we can't discuss it.
Prolog already knows to reject the Liar Paradox
as not a truth-bearer.
No, it does not. Prolog doesn't identify anything as a "truth-bearer"
or "non-truth-bearer".
?- LP = not(true(LP)).
The Prolog standard allows an implementation to accept or reject that.
Most implementations accept.
LP = not(true(LP)).
This time the implementation accepted and assigned a value to LP.
?- unify_with_occurs_check(LP, not(true(LP))).
In this case an implementation is required to reject as the result
of unification would be an expression that contains itself. Whether
anything is a truth-bearer or not is not checked.
false.
Implementation rejected as required.
On 8/29/2025 1:42 AM, Mikko wrote:
On 2025-08-28 15:31:28 +0000, olcott said:
On 8/28/2025 2:50 AM, Mikko wrote:
On 2025-08-27 15:27:26 +0000, olcott said:
On 8/27/2025 3:28 AM, Mikko wrote:
On 2025-08-26 15:16:31 +0000, olcott said:
On 8/26/2025 5:11 AM, Mikko wrote:
On 2025-08-25 17:54:02 +0000, olcott said:
All that we must do to defeat the Tarski Undefinability Theorem: >>>>>>>>Bad luck if you must but can't.
I create the basic architecture and others implement it.
Post again when you have the basic architecture on a web site.
No.
OK, but then we can't discuss it.
Prolog already knows to reject the Liar Paradox
as not a truth-bearer.
No, it does not. Prolog doesn't identify anything as a "truth-bearer"
or "non-truth-bearer".
The code below proves that LP is not a truth
bearer even if Prolog were to call it an ice
cream sundae with a cherry on top.
LP cannot be resolved to a truth value because
it specifies infinite recursion.
?- LP = not(true(LP)).
The Prolog standard allows an implementation to accept or reject that.
Most implementations accept.
LP = not(true(LP)).
This time the implementation accepted and assigned a value to LP.
?- unify_with_occurs_check(LP, not(true(LP))).
In this case an implementation is required to reject as the result
of unification would be an expression that contains itself. Whether
anything is a truth-bearer or not is not checked.
false.
Implementation rejected as required.
Because it specifies infinite recursion.
Other systems might just get stuck in infinite recursion.
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value.
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it would
be if the two arguments were bound to incompatible values.
Other systems might just get stuck in infinite recursion.
That is possible. In such systems a program that produces a recursive structure is often defiend as erroneous even if the system is not
required to detect the error.
On 8/30/2025 2:51 AM, Mikko wrote:
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value.
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it would
be if the two arguments were bound to incompatible values.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem
It would then be possible to reconstruct the
antinomy of the liar in the metalanguage, by
forming in the language itself a sentence x
such that the sentence of the metalanguage
which is correlated with x asserts that x is
not a true sentence.
https://liarparadox.org/Tarski_247_248.pdf
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value.
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it would
be if the two arguments were bound to incompatible values.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem
Prolog does not say anyathing about an infinite recursion.
The result is the same for
-a?- unify_with_occurs_check(true(not(LP)), not(true(LP))).
which does not contain any infinite recursion.
-a-a It would then be possible to reconstruct the
-a-a antinomy of the liar in the metalanguage, by
-a-a forming in the language itself a sentence x
-a-a such that the sentence of the metalanguage
-a-a which is correlated with x asserts that x is
-a-a not a true sentence.
-a-a https://liarparadox.org/Tarski_247_248.pdf
Your quote omits essential context. In particular the meanng of "then"
is not clear from the quote. From the omitted context it is clear that
the meaning is 'if a truth predicate could be defined'.
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value.
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it would >>>> be if the two arguments were bound to incompatible values.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem
Prolog does not say anyathing about an infinite recursion.
The result is the same for
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the unification used in Resolution. Most Prolog systems will allow you to satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an uninstantiated subterm of itself. In this example, foo(Y) is matched against Y, which appears within it. As a result, Y will stand for foo(Y), which is foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))),
and so on. So Y ends up standing for some kind of infinite structure. END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth Edition, 254. Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value.
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it would >>>>> be if the two arguments were bound to incompatible values.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem
Prolog does not say anyathing about an infinite recursion.
The result is the same for
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the
unification used in Resolution. Most Prolog systems will allow you to
satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an uninstantiated
subterm of itself. In this example, foo(Y) is matched against Y, which
appears within it. As a result, Y will stand for foo(Y), which is
foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))),
and so on. So Y ends up standing for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth Edition, 254.
Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim that
Prolog say anything about an infinite recursion.
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value.
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it would >>>>>> be if the two arguments were bound to incompatible values.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem
Prolog does not say anyathing about an infinite recursion.
The result is the same for
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the
unification used in Resolution. Most Prolog systems will allow you to
satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an uninstantiated
subterm of itself. In this example, foo(Y) is matched against Y, which
appears within it. As a result, Y will stand for foo(Y), which is
foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))),
and so on. So Y ends up standing for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth Edition, 254.
Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim that
Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value.
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it >>>>>>> would
be if the two arguments were bound to incompatible values.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem
Prolog does not say anyathing about an infinite recursion.
The result is the same for
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the
unification used in Resolution. Most Prolog systems will allow you
to satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an
uninstantiated subterm of itself. In this example, foo(Y) is matched
against Y, which appears within it. As a result, Y will stand for
foo(Y), which is foo(foo(Y)) (because of what Y stands for), which
is foo(foo(foo(Y))), and so on. So Y ends up standing for some kind
of infinite structure.
END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth Edition,
254. Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim that
Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value.
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it >>>>>>> would
be if the two arguments were bound to incompatible values.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem
Prolog does not say anyathing about an infinite recursion.
The result is the same for
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the
unification used in Resolution. Most Prolog systems will allow you
to satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an
uninstantiated subterm of itself. In this example, foo(Y) is matched
against Y, which appears within it. As a result, Y will stand for
foo(Y), which is foo(foo(Y)) (because of what Y stands for), which
is foo(foo(foo(Y))), and so on. So Y ends up standing for some kind
of infinite structure.
END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth Edition,
254. Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim that
Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value.
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it would >>>>>>>> be if the two arguments were bound to incompatible values.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem
Prolog does not say anyathing about an infinite recursion.
The result is the same for
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the >>>>> unification used in Resolution. Most Prolog systems will allow you to >>>>> satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an uninstantiated >>>>> subterm of itself. In this example, foo(Y) is matched against Y, which >>>>> appears within it. As a result, Y will stand for foo(Y), which is
foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))), >>>>> and so on. So Y ends up standing for some kind of infinite structure. >>>>> END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth Edition, 254. >>>>> Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim that >>>> Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
That you fail to understand that Prolog proves
that the Liar Paradox has an infinitely recursive
structure that cannot be resolved to a truth value
is far far less that no rebuttal what-so-ever.
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value.
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it would >>>>>>>> be if the two arguments were bound to incompatible values.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem
Prolog does not say anyathing about an infinite recursion.
The result is the same for
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the >>>>> unification used in Resolution. Most Prolog systems will allow you to >>>>> satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an uninstantiated >>>>> subterm of itself. In this example, foo(Y) is matched against Y, which >>>>> appears within it. As a result, Y will stand for foo(Y), which is
foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))), >>>>> and so on. So Y ends up standing for some kind of infinite structure. >>>>> END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth Edition, 254. >>>>> Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim that >>>> Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
"This sentence is not true"
What is it not true about?
It is not true about being not true.
What is it is not true about being not true about?
It is not true about being not true about being not true.
On 2025-09-02 12:11:14 +0000, olcott said:
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value.
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as >>>>>>>>> it would
be if the two arguments were bound to incompatible values.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem
Prolog does not say anyathing about an infinite recursion.
The result is the same for
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from
the unification used in Resolution. Most Prolog systems will allow >>>>>> you to satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an
uninstantiated subterm of itself. In this example, foo(Y) is
matched against Y, which appears within it. As a result, Y will
stand for foo(Y), which is foo(foo(Y)) (because of what Y stands
for), which is foo(foo(foo(Y))), and so on. So Y ends up standing >>>>>> for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth Edition, >>>>>> 254. Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim that >>>>> Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
That you fail to understand that Prolog proves
that the Liar Paradox has an infinitely recursive
structure that cannot be resolved to a truth value
is far far less that no rebuttal what-so-ever.
That you fail to understand that whatever Prolog does id irrelevant
to what Tarski proved does not make it relevant.
On 2025-09-02 12:13:23 +0000, olcott said:
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value.
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as >>>>>>>>> it would
be if the two arguments were bound to incompatible values.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem
Prolog does not say anyathing about an infinite recursion.
The result is the same for
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from
the unification used in Resolution. Most Prolog systems will allow >>>>>> you to satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an
uninstantiated subterm of itself. In this example, foo(Y) is
matched against Y, which appears within it. As a result, Y will
stand for foo(Y), which is foo(foo(Y)) (because of what Y stands
for), which is foo(foo(foo(Y))), and so on. So Y ends up standing >>>>>> for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth Edition, >>>>>> 254. Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim that >>>>> Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
"This sentence is not true"
What is it not true about?
It is not true about being not true.
What is it is not true about being not true about?
It is not true about being not true about being not true.
Tarski thought that "This sentence is not true" must be unprovable.
On 9/3/2025 2:39 AM, Mikko wrote:What? Nobody says it does.
On 2025-09-02 12:11:14 +0000, olcott said:
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:
On 2025-08-29 13:56:47 +0000, olcott said:?- LP = not(true(LP)).
LP cannot be resolved to a truth value because it specifies >>>>>>>>>>> infinite recursion.Prolog does not even try to resolve LP to a truth value.
Because it specifies infinite recursion.Yes, but the cause is not reported. The result is the same as >>>>>>>>>> it would be if the two arguments were bound to incompatible >>>>>>>>>> values.
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion thus
rejecting the basis of the Tarski Undefinability Theorem
Prolog does not say anyathing about an infinite recursion.
The result is the same for
*Yes it does, you just deleted this*
Clocksin & Mellish merely say what I said above. They don't claim
that Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for some kind of
infinite structure.
Irrelevanto to your false claims about Prolog, which are irrelevant
to the topic specified on the subjec ||ine.
That you fail to understand that Prolog proves that the Liar Paradox
has an infinitely recursive structure that cannot be resolved to a
truth value is far far less that no rebuttal what-so-ever.
That you fail to understand that whatever Prolog does id irrelevant to
what Tarski proved does not make it relevant.
The first step of this proof requires understanding that "this sentence
is not true" does not have a truth value. So far no one else in the
world has gotten this far.
Am Wed, 03 Sep 2025 09:29:07 -0500 schrieb olcott:
On 9/3/2025 2:39 AM, Mikko wrote:
On 2025-09-02 12:11:14 +0000, olcott said:
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:
On 2025-08-29 13:56:47 +0000, olcott said:?- LP = not(true(LP)).
LP cannot be resolved to a truth value because it specifies >>>>>>>>>>>> infinite recursion.Prolog does not even try to resolve LP to a truth value. >>>>>>>>>>>
Because it specifies infinite recursion.Yes, but the cause is not reported. The result is the same as >>>>>>>>>>> it would be if the two arguments were bound to incompatible >>>>>>>>>>> values.
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion thus
rejecting the basis of the Tarski Undefinability Theorem
Prolog does not say anyathing about an infinite recursion.
The result is the same for
*Yes it does, you just deleted this*
Clocksin & Mellish merely say what I said above. They don't claim >>>>>>> that Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for some kind of >>>>>> infinite structure.
Irrelevanto to your false claims about Prolog, which are irrelevant
to the topic specified on the subjec ||ine.
That you fail to understand that Prolog proves that the Liar Paradox
has an infinitely recursive structure that cannot be resolved to a
truth value is far far less that no rebuttal what-so-ever.
That you fail to understand that whatever Prolog does id irrelevant to
what Tarski proved does not make it relevant.
The first step of this proof requires understanding that "this sentenceWhat? Nobody says it does.
is not true" does not have a truth value. So far no one else in the
world has gotten this far.
On 9/3/2025 10:10 AM, joes wrote:
Am Wed, 03 Sep 2025 09:29:07 -0500 schrieb olcott:
On 9/3/2025 2:39 AM, Mikko wrote:What? Nobody says it does.
On 2025-09-02 12:11:14 +0000, olcott said:
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:
On 2025-08-29 13:56:47 +0000, olcott said:?- LP = not(true(LP)).
LP cannot be resolved to a truth value because it specifies >>>>>>>>>>>>> infinite recursion.Prolog does not even try to resolve LP to a truth value. >>>>>>>>>>>>
Because it specifies infinite recursion.Yes, but the cause is not reported. The result is the same as >>>>>>>>>>>> it would be if the two arguments were bound to incompatible >>>>>>>>>>>> values.
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion thus
rejecting the basis of the Tarski Undefinability Theorem
Prolog does not say anyathing about an infinite recursion. >>>>>>>>>> The result is the same for
*Yes it does, you just deleted this*
Clocksin & Mellish merely say what I said above. They don't claim >>>>>>>> that Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for some kind of >>>>>>> infinite structure.
Irrelevanto to your false claims about Prolog, which are irrelevant >>>>>> to the topic specified on the subjec ||ine.
That you fail to understand that Prolog proves that the Liar Paradox >>>>> has an infinitely recursive structure that cannot be resolved to a
truth value is far far less that no rebuttal what-so-ever.
That you fail to understand that whatever Prolog does id irrelevant to >>>> what Tarski proved does not make it relevant.
The first step of this proof requires understanding that "this sentence
is not true" does not have a truth value. So far no one else in the
world has gotten this far.
*The best expert that I found in the whole world says this*
I do not mean to commit myself to the claim that
denying that the Liar expresses a proposition is
the best solution to the Liar paradox, nor do I
want to commit Truthmaker Maximalism to that claim. https://philarchive.org/archive/RODTMD
Truthmaker Maximalism is the appropriate sub-field
of philosophy of logic. Logic only says what the
rules are. Philosophy of logic examines why the
rules are what they are and examines alternative
possibilities.
On 9/3/2025 2:39 AM, Mikko wrote:
On 2025-09-02 12:11:14 +0000, olcott said:
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:Prolog does not say anyathing about an infinite recursion.
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value.
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it would
be if the two arguments were bound to incompatible values. >>>>>>>>>>
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem >>>>>>>>
The result is the same for
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the >>>>>>> unification used in Resolution. Most Prolog systems will allow you to >>>>>>> satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an uninstantiated >>>>>>> subterm of itself. In this example, foo(Y) is matched against Y, which >>>>>>> appears within it. As a result, Y will stand for foo(Y), which is >>>>>>> foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))), >>>>>>> and so on. So Y ends up standing for some kind of infinite structure. >>>>>>> END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth Edition, 254. >>>>>>> Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim that >>>>>> Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
That you fail to understand that Prolog proves
that the Liar Paradox has an infinitely recursive
structure that cannot be resolved to a truth value
is far far less that no rebuttal what-so-ever.
That you fail to understand that whatever Prolog does id irrelevant
to what Tarski proved does not make it relevant.
Whenever I make a proof it is standard procedure
of all of my reviewers to make sure to totally dodge
the first step of this proof and then falsely claim
that I did not prove my point.
The first step of this proof requires understanding
that "this sentence is not true" does not have a
truth value. So far no one else in the world has
gotten this far.
On 9/3/2025 2:43 AM, Mikko wrote:
On 2025-09-02 12:13:23 +0000, olcott said:
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:Prolog does not say anyathing about an infinite recursion.
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value.
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it would
be if the two arguments were bound to incompatible values. >>>>>>>>>>
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem >>>>>>>>
The result is the same for
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the >>>>>>> unification used in Resolution. Most Prolog systems will allow you to >>>>>>> satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an uninstantiated >>>>>>> subterm of itself. In this example, foo(Y) is matched against Y, which >>>>>>> appears within it. As a result, Y will stand for foo(Y), which is >>>>>>> foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))), >>>>>>> and so on. So Y ends up standing for some kind of infinite structure. >>>>>>> END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth Edition, 254. >>>>>>> Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim that >>>>>> Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
"This sentence is not true"
What is it not true about?
It is not true about being not true.
What is it is not true about being not true about?
It is not true about being not true about being not true.
Tarski thought that "This sentence is not true" must be unprovable.
Likewise: "What time is it?" is equally unprovable
for the same reason. When making lunch house bricks
cannot be the main ingredient. When defining formal
systems of logic one must exclude expressions of
language having no truth value.
On 2025-09-03 14:29:07 +0000, olcott said:
On 9/3/2025 2:39 AM, Mikko wrote:
On 2025-09-02 12:11:14 +0000, olcott said:
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:Prolog does not say anyathing about an infinite recursion.
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value. >>>>>>>>>>>
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as >>>>>>>>>>> it would
be if the two arguments were bound to incompatible values. >>>>>>>>>>>
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem >>>>>>>>>
The result is the same for
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from >>>>>>>> the unification used in Resolution. Most Prolog systems will
allow you to satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an
uninstantiated subterm of itself. In this example, foo(Y) is
matched against Y, which appears within it. As a result, Y will >>>>>>>> stand for foo(Y), which is foo(foo(Y)) (because of what Y stands >>>>>>>> for), which is foo(foo(foo(Y))), and so on. So Y ends up
standing for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth
Edition, 254. Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim >>>>>>> that
Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
That you fail to understand that Prolog proves
that the Liar Paradox has an infinitely recursive
structure that cannot be resolved to a truth value
is far far less that no rebuttal what-so-ever.
That you fail to understand that whatever Prolog does id irrelevant
to what Tarski proved does not make it relevant.
Whenever I make a proof it is standard procedure
of all of my reviewers to make sure to totally dodge
the first step of this proof and then falsely claim
that I did not prove my point.
You have never presented any proofs. Apparently you don't even
know what the word means.
The first step of this proof requires understanding
that "this sentence is not true" does not have a
truth value. So far no one else in the world has
gotten this far.
Above you disagreed with the sentnece "The liar parac-|dox has
no truth value". If you don't think so anymore you should
go back to that point in the discussion and try again from there.
On 2025-09-03 14:32:11 +0000, olcott said:
On 9/3/2025 2:43 AM, Mikko wrote:
On 2025-09-02 12:13:23 +0000, olcott said:
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:Prolog does not say anyathing about an infinite recursion.
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value. >>>>>>>>>>>
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as >>>>>>>>>>> it would
be if the two arguments were bound to incompatible values. >>>>>>>>>>>
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem >>>>>>>>>
The result is the same for
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from >>>>>>>> the unification used in Resolution. Most Prolog systems will
allow you to satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an
uninstantiated subterm of itself. In this example, foo(Y) is
matched against Y, which appears within it. As a result, Y will >>>>>>>> stand for foo(Y), which is foo(foo(Y)) (because of what Y stands >>>>>>>> for), which is foo(foo(foo(Y))), and so on. So Y ends up
standing for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth
Edition, 254. Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim >>>>>>> that
Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
"This sentence is not true"
What is it not true about?
It is not true about being not true.
What is it is not true about being not true about?
It is not true about being not true about being not true.
Tarski thought that "This sentence is not true" must be unprovable.
Likewise: "What time is it?" is equally unprovable
for the same reason.-a When making lunch house bricks
cannot be the main ingredient. When defining formal
systems of logic one must exclude expressions of
language having no truth value.
No, the reason is not the same. "What time is it?" does not claim
anything, so there is nothing to prove. "This sentence is not true"
does claim but the sentence is not semantically well founded.
On 9/4/2025 1:31 AM, Mikko wrote:
On 2025-09-03 14:29:07 +0000, olcott said:
On 9/3/2025 2:39 AM, Mikko wrote:
On 2025-09-02 12:11:14 +0000, olcott said:
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:Prolog does not say anyathing about an infinite recursion. >>>>>>>>>> The result is the same for
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value. >>>>>>>>>>>>
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it would
be if the two arguments were bound to incompatible values. >>>>>>>>>>>>
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem >>>>>>>>>>
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the >>>>>>>>> unification used in Resolution. Most Prolog systems will allow you to
satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an uninstantiated
subterm of itself. In this example, foo(Y) is matched against Y, which
appears within it. As a result, Y will stand for foo(Y), which is >>>>>>>>> foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))),
and so on. So Y ends up standing for some kind of infinite structure. >>>>>>>>> END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth Edition, 254.
Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim that >>>>>>>> Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
That you fail to understand that Prolog proves
that the Liar Paradox has an infinitely recursive
structure that cannot be resolved to a truth value
is far far less that no rebuttal what-so-ever.
That you fail to understand that whatever Prolog does id irrelevant
to what Tarski proved does not make it relevant.
Whenever I make a proof it is standard procedure
of all of my reviewers to make sure to totally dodge
the first step of this proof and then falsely claim
that I did not prove my point.
You have never presented any proofs. Apparently you don't even
know what the word means.
When I present the first step of my proof it is
rejected out-of-hand without review.
The first step of this proof requires understanding
that "this sentence is not true" does not have a
truth value. So far no one else in the world has
gotten this far.
Above you disagreed with the sentnece "The liar parac-|dox has
no truth value". If you don't think so anymore you should
go back to that point in the discussion and try again from there.
The Liar Paradox has no truth value thus must be
rejected as the basis of any formal proof.
Tarski did not know this.
On 9/4/2025 1:37 AM, Mikko wrote:
On 2025-09-03 14:32:11 +0000, olcott said:
On 9/3/2025 2:43 AM, Mikko wrote:
On 2025-09-02 12:13:23 +0000, olcott said:
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:Prolog does not say anyathing about an infinite recursion. >>>>>>>>>> The result is the same for
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value. >>>>>>>>>>>>
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it would
be if the two arguments were bound to incompatible values. >>>>>>>>>>>>
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem >>>>>>>>>>
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the >>>>>>>>> unification used in Resolution. Most Prolog systems will allow you to
satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an uninstantiated
subterm of itself. In this example, foo(Y) is matched against Y, which
appears within it. As a result, Y will stand for foo(Y), which is >>>>>>>>> foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))),
and so on. So Y ends up standing for some kind of infinite structure. >>>>>>>>> END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth Edition, 254.
Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim that >>>>>>>> Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
"This sentence is not true"
What is it not true about?
It is not true about being not true.
What is it is not true about being not true about?
It is not true about being not true about being not true.
Tarski thought that "This sentence is not true" must be unprovable.
Likewise: "What time is it?" is equally unprovable
for the same reason.-a When making lunch house bricks
cannot be the main ingredient. When defining formal
systems of logic one must exclude expressions of
language having no truth value.
No, the reason is not the same. "What time is it?" does not claim
anything, so there is nothing to prove. "This sentence is not true"
does claim but the sentence is not semantically well founded.
So both equally have no truth value.
On 2025-09-04 23:38:16 +0000, olcott said:
On 9/4/2025 1:31 AM, Mikko wrote:
On 2025-09-03 14:29:07 +0000, olcott said:
On 9/3/2025 2:39 AM, Mikko wrote:
On 2025-09-02 12:11:14 +0000, olcott said:
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:Prolog does not say anyathing about an infinite recursion. >>>>>>>>>>> The result is the same for
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value. >>>>>>>>>>>>>
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same >>>>>>>>>>>>> as it would
be if the two arguments were bound to incompatible values. >>>>>>>>>>>>>
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem >>>>>>>>>>>
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs >>>>>>>>>> from the unification used in Resolution. Most Prolog systems >>>>>>>>>> will allow you to satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an
uninstantiated subterm of itself. In this example, foo(Y) is >>>>>>>>>> matched against Y, which appears within it. As a result, Y >>>>>>>>>> will stand for foo(Y), which is foo(foo(Y)) (because of what Y >>>>>>>>>> stands for), which is foo(foo(foo(Y))), and so on. So Y ends >>>>>>>>>> up standing for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth
Edition, 254. Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't >>>>>>>>> claim that
Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
That you fail to understand that Prolog proves
that the Liar Paradox has an infinitely recursive
structure that cannot be resolved to a truth value
is far far less that no rebuttal what-so-ever.
That you fail to understand that whatever Prolog does id irrelevant
to what Tarski proved does not make it relevant.
Whenever I make a proof it is standard procedure
of all of my reviewers to make sure to totally dodge
the first step of this proof and then falsely claim
that I did not prove my point.
You have never presented any proofs. Apparently you don't even
know what the word means.
When I present the first step of my proof it is
rejected out-of-hand without review.
The first step of a proof is usually a definition.
If you try to
define a term that is alredy in use differently from its usual
meaning that is sufficient to reject it without further review.
If your first step is a premiss then reviewers must consdier
whether it is acceptable or should be proven or can be rejected
as false.
The first step of this proof requires understanding
that "this sentence is not true" does not have a
truth value. So far no one else in the world has
gotten this far.
Above you disagreed with the sentnece "The liar parac-|dox has
no truth value". If you don't think so anymore you should
go back to that point in the discussion and try again from there.
The Liar Paradox has no truth value thus must be
rejected as the basis of any formal proof.
The why is the sentence "The liar paradox has no truth value"
unacceptable as a basis of proof?
Tarski did not know this.
Then how could he say that the liar paradox cannot be true?
On 2025-09-04 23:39:24 +0000, olcott said:
On 9/4/2025 1:37 AM, Mikko wrote:
On 2025-09-03 14:32:11 +0000, olcott said:
On 9/3/2025 2:43 AM, Mikko wrote:
On 2025-09-02 12:13:23 +0000, olcott said:
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:Prolog does not say anyathing about an infinite recursion. >>>>>>>>>>> The result is the same for
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value. >>>>>>>>>>>>>
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same >>>>>>>>>>>>> as it would
be if the two arguments were bound to incompatible values. >>>>>>>>>>>>>
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem >>>>>>>>>>>
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs >>>>>>>>>> from the unification used in Resolution. Most Prolog systems >>>>>>>>>> will allow you to satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an
uninstantiated subterm of itself. In this example, foo(Y) is >>>>>>>>>> matched against Y, which appears within it. As a result, Y >>>>>>>>>> will stand for foo(Y), which is foo(foo(Y)) (because of what Y >>>>>>>>>> stands for), which is foo(foo(foo(Y))), and so on. So Y ends >>>>>>>>>> up standing for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth
Edition, 254. Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't >>>>>>>>> claim that
Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
"This sentence is not true"
What is it not true about?
It is not true about being not true.
What is it is not true about being not true about?
It is not true about being not true about being not true.
Tarski thought that "This sentence is not true" must be unprovable.
Likewise: "What time is it?" is equally unprovable
for the same reason.-a When making lunch house bricks
cannot be the main ingredient. When defining formal
systems of logic one must exclude expressions of
language having no truth value.
No, the reason is not the same. "What time is it?" does not claim
anything, so there is nothing to prove. "This sentence is not true"
does claim but the sentence is not semantically well founded.
So both equally have no truth value.
Yes, but they are different enough that only one of them is useful
for Tarski's purposes.
On 9/5/2025 2:31 AM, Mikko wrote:
On 2025-09-04 23:38:16 +0000, olcott said:
On 9/4/2025 1:31 AM, Mikko wrote:
On 2025-09-03 14:29:07 +0000, olcott said:
On 9/3/2025 2:39 AM, Mikko wrote:
On 2025-09-02 12:11:14 +0000, olcott said:
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:Prolog does not say anyathing about an infinite recursion. >>>>>>>>>>>> The result is the same for
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value. >>>>>>>>>>>>>>
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it would
be if the two arguments were bound to incompatible values. >>>>>>>>>>>>>>
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem >>>>>>>>>>>>
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the
unification used in Resolution. Most Prolog systems will allow you to
satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an uninstantiated
subterm of itself. In this example, foo(Y) is matched against Y, which
appears within it. As a result, Y will stand for foo(Y), which is >>>>>>>>>>> foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))),
and so on. So Y ends up standing for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth Edition, 254.
Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim that
Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
That you fail to understand that Prolog proves
that the Liar Paradox has an infinitely recursive
structure that cannot be resolved to a truth value
is far far less that no rebuttal what-so-ever.
That you fail to understand that whatever Prolog does id irrelevant >>>>>> to what Tarski proved does not make it relevant.
Whenever I make a proof it is standard procedure
of all of my reviewers to make sure to totally dodge
the first step of this proof and then falsely claim
that I did not prove my point.
You have never presented any proofs. Apparently you don't even
know what the word means.
When I present the first step of my proof it is
rejected out-of-hand without review.
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value.
If you try to
define a term that is alredy in use differently from its usual
meaning that is sufficient to reject it without further review.
The above definition is conventional. It is also a standard
convention that when there is no word for a meaning that
the word with the closest existing meaning is used and becomes
a term of the art by adapting this meaning.
If your first step is a premiss then reviewers must consdier
whether it is acceptable or should be proven or can be rejected
as false.
That the Liar Paradox is not a truth bearer is proven
completely true by the meaning is these words.
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
Here is my own Minimal Type Theory
https://philarchive.org/archive/PETMTT-4 https://philpapers.org/archive/OLCPWM.pdf
I created this before I knew that Prolog does the same thing
The first step of this proof requires understanding
that "this sentence is not true" does not have a
truth value. So far no one else in the world has
gotten this far.
Above you disagreed with the sentnece "The liar parac-|dox has
no truth value". If you don't think so anymore you should
go back to that point in the discussion and try again from there.
The Liar Paradox has no truth value thus must be
rejected as the basis of any formal proof.
The why is the sentence "The liar paradox has no truth value"
unacceptable as a basis of proof?
That is not the way it works.
Tarski incorrectly used "this sentence is not true"
as the basis of his proof, when we reject that as
not a truth bearer then Tarski's proof has no basis.
On 9/5/2025 2:32 AM, Mikko wrote:
On 2025-09-04 23:39:24 +0000, olcott said:
On 9/4/2025 1:37 AM, Mikko wrote:
On 2025-09-03 14:32:11 +0000, olcott said:
On 9/3/2025 2:43 AM, Mikko wrote:
On 2025-09-02 12:13:23 +0000, olcott said:Likewise: "What time is it?" is equally unprovable
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:Prolog does not say anyathing about an infinite recursion. >>>>>>>>>>>> The result is the same for
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because
it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value. >>>>>>>>>>>>>>
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it would
be if the two arguments were bound to incompatible values. >>>>>>>>>>>>>>
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion
thus rejecting the basis of the Tarski Undefinability Theorem >>>>>>>>>>>>
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the
unification used in Resolution. Most Prolog systems will allow you to
satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an uninstantiated
subterm of itself. In this example, foo(Y) is matched against Y, which
appears within it. As a result, Y will stand for foo(Y), which is >>>>>>>>>>> foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))),
and so on. So Y ends up standing for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth Edition, 254.
Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim that
Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
"This sentence is not true"
What is it not true about?
It is not true about being not true.
What is it is not true about being not true about?
It is not true about being not true about being not true.
Tarski thought that "This sentence is not true" must be unprovable. >>>>>
for the same reason.-a When making lunch house bricks
cannot be the main ingredient. When defining formal
systems of logic one must exclude expressions of
language having no truth value.
No, the reason is not the same. "What time is it?" does not claim
anything, so there is nothing to prove. "This sentence is not true"
does claim but the sentence is not semantically well founded.
So both equally have no truth value.
Yes, but they are different enough that only one of them is useful
for Tarski's purposes.
I only used the other example so that you could
totally understand what "not a truth bearer" means.
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value.
That is not a definition but could be a valid starting point for
a proof. One could also state that because it is not a truth-bearer
it cannot be provable in a consistent system.
If you try to
define a term that is alredy in use differently from its usual
meaning that is sufficient to reject it without further review.
The above definition is conventional. It is also a standard
convention that when there is no word for a meaning that
the word with the closest existing meaning is used and becomes
a term of the art by adapting this meaning.
It is not always the word with the closest meaning. Sometimes a
word with a meaning far from the needed meaning is chosen.
In
any case one must be sure that the word is not needed for any
other meaning in the same context.
An important rule with the defined words is that they must not
be used before the definition. Unless the definition is already
well known
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the word.
If your first step is a premiss then reviewers must consdier
whether it is acceptable or should be proven or can be rejected
as false.
That the Liar Paradox is not a truth bearer is proven
completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to
do that only after the defintions, in particular the definition
of "the Liar Paradox".
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
It doesn't prove anything. Prolog merely executes the instructions
according to their standard semantics and implementation choices.
In particular,
?- LP = not(true_(LP)).
false.
would also be correct.
Here is my own Minimal Type Theory
https://philarchive.org/archive/PETMTT-4
https://philpapers.org/archive/OLCPWM.pdf
I created this before I knew that Prolog does the same thing
Apparently you don't know what Prolog does.
The first step of this proof requires understanding
that "this sentence is not true" does not have a
truth value. So far no one else in the world has
gotten this far.
Above you disagreed with the sentnece "The liar parac-|dox has
no truth value". If you don't think so anymore you should
go back to that point in the discussion and try again from there.
The Liar Paradox has no truth value thus must be
rejected as the basis of any formal proof.
The why is the sentence "The liar paradox has no truth value"
unacceptable as a basis of proof?
That is not the way it works.
Tarski incorrectly used "this sentence is not true"
as the basis of his proof, when we reject that as
not a truth bearer then Tarski's proof has no basis.
The statement "The liar paradox has no truth value" is true and therefore
a valid basis for a proof.
On 2025-09-05 14:47:56 +0000, olcott said:
On 9/5/2025 2:32 AM, Mikko wrote:
On 2025-09-04 23:39:24 +0000, olcott said:
On 9/4/2025 1:37 AM, Mikko wrote:
On 2025-09-03 14:32:11 +0000, olcott said:
On 9/3/2025 2:43 AM, Mikko wrote:
On 2025-09-02 12:13:23 +0000, olcott said:Likewise: "What time is it?" is equally unprovable
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:Prolog does not say anyathing about an infinite recursion. >>>>>>>>>>>>> The result is the same for
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because >>>>>>>>>>>>>>>> it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value. >>>>>>>>>>>>>>>
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the >>>>>>>>>>>>>>> same as it would
be if the two arguments were bound to incompatible values. >>>>>>>>>>>>>>>
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion >>>>>>>>>>>>>> thus rejecting the basis of the Tarski Undefinability Theorem >>>>>>>>>>>>>
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs >>>>>>>>>>>> from the unification used in Resolution. Most Prolog systems >>>>>>>>>>>> will allow you to satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an >>>>>>>>>>>> uninstantiated subterm of itself. In this example, foo(Y) is >>>>>>>>>>>> matched against Y, which appears within it. As a result, Y >>>>>>>>>>>> will stand for foo(Y), which is foo(foo(Y)) (because of what >>>>>>>>>>>> Y stands for), which is foo(foo(foo(Y))), and so on. So Y >>>>>>>>>>>> ends up standing for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth >>>>>>>>>>>> Edition, 254. Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't >>>>>>>>>>> claim that
Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
"This sentence is not true"
What is it not true about?
It is not true about being not true.
What is it is not true about being not true about?
It is not true about being not true about being not true.
Tarski thought that "This sentence is not true" must be unprovable. >>>>>>
for the same reason.-a When making lunch house bricks
cannot be the main ingredient. When defining formal
systems of logic one must exclude expressions of
language having no truth value.
No, the reason is not the same. "What time is it?" does not claim
anything, so there is nothing to prove. "This sentence is not true"
does claim but the sentence is not semantically well founded.
So both equally have no truth value.
Yes, but they are different enough that only one of them is useful
for Tarski's purposes.
I only used the other example so that you could
totally understand what "not a truth bearer" means.
Thanx but I knew already.
It means that the statement "Liar's paradox is not true" is true
because only a truth-bearer can be true.
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value.
That is not a definition but could be a valid starting point for
a proof. One could also state that because it is not a truth-bearer
it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes
English declarative sentences and logical propositions.
"This sentence is not true"
Cannot possibly be resolved to a truth value.
If you try to
define a term that is alredy in use differently from its usual
meaning that is sufficient to reject it without further review.
The above definition is conventional. It is also a standard
convention that when there is no word for a meaning that
the word with the closest existing meaning is used and becomes
a term of the art by adapting this meaning.
It is not always the word with the closest meaning. Sometimes a
word with a meaning far from the needed meaning is chosen.
That makes communication very misleading rather than
effective. The best way to do this in natural language
is to choose an existing term with the closest meaning
and then specify the exact divergence from this conventional
meaning.
In
any case one must be sure that the word is not needed for any
other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings
that correspond to sense meanings of words or term-of-the-art
meanings of terms.
An important rule with the defined words is that they must not
be used before the definition. Unless the definition is already
well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the word.
If your first step is a premiss then reviewers must consdier
whether it is acceptable or should be proven or can be rejected
as false.
That the Liar Paradox is not a truth bearer is proven
completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to
do that only after the defintions, in particular the definition
of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not true"
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
It doesn't prove anything. Prolog merely executes the instructions
according to their standard semantics and implementation choices.
In particular,
Not at all.
On 2025-09-06 15:23:58 +0000, olcott said:
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value.
That is not a definition but could be a valid starting point for
a proof. One could also state that because it is not a truth-bearer
it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes
English declarative sentences and logical propositions.
"This sentence is not true"
Cannot possibly be resolved to a truth value.
If you try to
define a term that is alredy in use differently from its usual
meaning that is sufficient to reject it without further review.
The above definition is conventional. It is also a standard
convention that when there is no word for a meaning that
the word with the closest existing meaning is used and becomes
a term of the art by adapting this meaning.
It is not always the word with the closest meaning. Sometimes a
word with a meaning far from the needed meaning is chosen.
That makes communication very misleading rather than
effective. The best way to do this in natural language
is to choose an existing term with the closest meaning
and then specify the exact divergence from this conventional
meaning.
In
any case one must be sure that the word is not needed for any
other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings
that correspond to sense meanings of words or term-of-the-art
meanings of terms.
An important rule with the defined words is that they must not
be used before the definition. Unless the definition is already
well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the word.
If your first step is a premiss then reviewers must consdier
whether it is acceptable or should be proven or can be rejected
as false.
That the Liar Paradox is not a truth bearer is proven
completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to
do that only after the defintions, in particular the definition
of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not true"
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
It doesn't prove anything. Prolog merely executes the instructions
according to their standard semantics and implementation choices.
In particular,
Not at all.
What not at all? What is that intended to refer to?
On 9/7/2025 3:27 AM, Mikko wrote:
On 2025-09-06 15:23:58 +0000, olcott said:
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value.
That is not a definition but could be a valid starting point for
a proof. One could also state that because it is not a truth-bearer
it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes
English declarative sentences and logical propositions.
"This sentence is not true"
Cannot possibly be resolved to a truth value.
If you try to
define a term that is alredy in use differently from its usual
meaning that is sufficient to reject it without further review.
The above definition is conventional. It is also a standard
convention that when there is no word for a meaning that
the word with the closest existing meaning is used and becomes
a term of the art by adapting this meaning.
It is not always the word with the closest meaning. Sometimes a
word with a meaning far from the needed meaning is chosen.
That makes communication very misleading rather than
effective. The best way to do this in natural language
is to choose an existing term with the closest meaning
and then specify the exact divergence from this conventional
meaning.
In
any case one must be sure that the word is not needed for any
other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings
that correspond to sense meanings of words or term-of-the-art
meanings of terms.
An important rule with the defined words is that they must not
be used before the definition. Unless the definition is already
well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the word.
If your first step is a premiss then reviewers must consdier
whether it is acceptable or should be proven or can be rejected
as false.
That the Liar Paradox is not a truth bearer is proven
completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to
do that only after the defintions, in particular the definition
of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not true"
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
It doesn't prove anything. Prolog merely executes the instructions
according to their standard semantics and implementation choices.
In particular,
Not at all.
What not at all? What is that intended to refer to?
That is all extensively elaborated in the whole
paragraph that you completely ignored.
On 2025-09-07 17:26:36 +0000, olcott said:
On 9/7/2025 3:27 AM, Mikko wrote:
On 2025-09-06 15:23:58 +0000, olcott said:
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value.
That is not a definition but could be a valid starting point for
a proof. One could also state that because it is not a truth-bearer
it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes
English declarative sentences and logical propositions.
"This sentence is not true"
Cannot possibly be resolved to a truth value.
If you try to
define a term that is alredy in use differently from its usual
meaning that is sufficient to reject it without further review.
The above definition is conventional. It is also a standard
convention that when there is no word for a meaning that
the word with the closest existing meaning is used and becomes
a term of the art by adapting this meaning.
It is not always the word with the closest meaning. Sometimes a
word with a meaning far from the needed meaning is chosen.
That makes communication very misleading rather than
effective. The best way to do this in natural language
is to choose an existing term with the closest meaning
and then specify the exact divergence from this conventional
meaning.
In
any case one must be sure that the word is not needed for any
other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings
that correspond to sense meanings of words or term-of-the-art
meanings of terms.
An important rule with the defined words is that they must not
be used before the definition. Unless the definition is already
well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the word.
If your first step is a premiss then reviewers must consdier
whether it is acceptable or should be proven or can be rejected
as false.
That the Liar Paradox is not a truth bearer is proven
completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to
do that only after the defintions, in particular the definition
of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not true"
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
It doesn't prove anything. Prolog merely executes the instructions
according to their standard semantics and implementation choices.
In particular,
Not at all.
What not at all? What is that intended to refer to?
That is all extensively elaborated in the whole
paragraph that you completely ignored.
No, it isn't. There is no reference to those words there. In common
language the words "Not at all", just like plain "No", refer to the
immediately previous sentence or sentences, usually said by someone
else. In this case the standard meaning is that you claim that
"It doesn't prove anything. Prolog merely executes the instructions
according to their standard semantics and implementation choices.
In particular," or at least "In particular," is false. But "In
particular," is not even a sentence and therefore cannot be false.
That Prolog meerely executes the instructions according to their
standard semantics and implementation choices should be quite obvious
but your "Not at all." means that you don't think it is far from
true. As it seems unplausible that you would disagree with a so
obvious truth it seems reasonable to think you meant sometnig else
but what?
--
Mikko
On 9/7/2025 3:27 AM, Mikko wrote:
On 2025-09-06 15:23:58 +0000, olcott said:
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value.
That is not a definition but could be a valid starting point for
a proof. One could also state that because it is not a truth-bearer
it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes
English declarative sentences and logical propositions.
"This sentence is not true"
Cannot possibly be resolved to a truth value.
If you try to
define a term that is alredy in use differently from its usual
meaning that is sufficient to reject it without further review.
The above definition is conventional. It is also a standard
convention that when there is no word for a meaning that
the word with the closest existing meaning is used and becomes
a term of the art by adapting this meaning.
It is not always the word with the closest meaning. Sometimes a
word with a meaning far from the needed meaning is chosen.
That makes communication very misleading rather than
effective. The best way to do this in natural language
is to choose an existing term with the closest meaning
and then specify the exact divergence from this conventional
meaning.
In
any case one must be sure that the word is not needed for any
other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings
that correspond to sense meanings of words or term-of-the-art
meanings of terms.
An important rule with the defined words is that they must not
be used before the definition. Unless the definition is already
well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the word.
If your first step is a premiss then reviewers must consdier
whether it is acceptable or should be proven or can be rejected
as false.
That the Liar Paradox is not a truth bearer is proven
completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to
do that only after the defintions, in particular the definition
of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not true"
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
It doesn't prove anything. Prolog merely executes the instructions
according to their standard semantics and implementation choices.
In particular,
Not at all.
What not at all? What is that intended to refer to?
That is all extensively elaborated in the whole
paragraph that you completely ignored.
Google[Minimal Type Theory] it knows my work.
It incorrectly attributes this to: Maietti and Sambin
I created a whole system named Minimal Type Theory
that translates logical expressions into the directed
graph of their resolution sequence. When MTT detects
a cycle in this graph that is exactly the same thing as:
?- unify_with_occurs_check(LP, not(true(LP))).
false.
On 9/6/2025 3:27 AM, Mikko wrote:
On 2025-09-05 14:47:56 +0000, olcott said:
On 9/5/2025 2:32 AM, Mikko wrote:
On 2025-09-04 23:39:24 +0000, olcott said:
On 9/4/2025 1:37 AM, Mikko wrote:
On 2025-09-03 14:32:11 +0000, olcott said:
On 9/3/2025 2:43 AM, Mikko wrote:
On 2025-09-02 12:13:23 +0000, olcott said:Likewise: "What time is it?" is equally unprovable
On 9/2/2025 3:07 AM, Mikko wrote:
On 2025-09-01 14:41:08 +0000, olcott said:
On 9/1/2025 2:46 AM, Mikko wrote:
On 2025-08-31 15:21:08 +0000, olcott said:
On 8/31/2025 3:24 AM, Mikko wrote:
On 2025-08-30 15:31:20 +0000, olcott said:
On 8/30/2025 2:51 AM, Mikko wrote:Prolog does not say anyathing about an infinite recursion. >>>>>>>>>>>>>> The result is the same for
On 2025-08-29 13:56:47 +0000, olcott said:
LP cannot be resolved to a truth value because >>>>>>>>>>>>>>>>> it specifies infinite recursion.
Prolog does not even try to resolve LP to a truth value. >>>>>>>>>>>>>>>>
Because it specifies infinite recursion.
Yes, but the cause is not reported. The result is the same as it would
be if the two arguments were bound to incompatible values. >>>>>>>>>>>>>>>>
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog rejects LP as specifying infinite recursion >>>>>>>>>>>>>>> thus rejecting the basis of the Tarski Undefinability Theorem >>>>>>>>>>>>>>
*Yes it does, you just deleted this*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the
unification used in Resolution. Most Prolog systems will allow you to
satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an uninstantiated
subterm of itself. In this example, foo(Y) is matched against Y, which
appears within it. As a result, Y will stand for foo(Y), which is
foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))),
and so on. So Y ends up standing for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)
Clocksin, W.F. and Mellish, C.S.
2003. Programming in Prolog Using the ISO Standard Fifth Edition, 254.
Berlin Heidelberg: Springer-Verlag.
https://www.researchgate.net/
publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Clocksin & Mellish merely say what I said above. They don't claim that
Prolog say anything about an infinite recursion.
foo(foo(foo(Y))), and so on. So Y ends up standing for
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
some kind of infinite structure.
Irrelevanto to your false claims about Prolog, which are
irrelevant to the topic specified on the subjec ||ine.
"This sentence is not true"
What is it not true about?
It is not true about being not true.
What is it is not true about being not true about?
It is not true about being not true about being not true.
Tarski thought that "This sentence is not true" must be unprovable. >>>>>>>
for the same reason.-a When making lunch house bricks
cannot be the main ingredient. When defining formal
systems of logic one must exclude expressions of
language having no truth value.
No, the reason is not the same. "What time is it?" does not claim
anything, so there is nothing to prove. "This sentence is not true" >>>>>> does claim but the sentence is not semantically well founded.
So both equally have no truth value.
Yes, but they are different enough that only one of them is useful
for Tarski's purposes.
I only used the other example so that you could
totally understand what "not a truth bearer" means.
Thanx but I knew already.
It means that the statement "Liar's paradox is not true" is true
because only a truth-bearer can be true.
Not all all see my other reply about cycles
in directed graphs of resolution sequences.
On 2025-09-07 17:26:36 +0000, olcott said:
That is all extensively elaborated in the whole
paragraph that you completely ignored.
Google[Minimal Type Theory] it knows my work.
It incorrectly attributes this to: Maietti and Sambin
I created a whole system named Minimal Type Theory
that translates logical expressions into the directed
graph of their resolution sequence. When MTT detects
a cycle in this graph that is exactly the same thing as:
?- unify_with_occurs_check(LP, not(true(LP))).
false.
No, it isn't. There is no reference to those words there.
In common
language the words "Not at all", just like plain "No", refer to the immediately previous sentence or sentences, usually said by someone
else. In this case the standard meaning is that you claim that
"It doesn't prove anything. Prolog merely executes the instructions
according to their standard semantics and implementation choices.
In particular," or at least "In particular," is false. But "In
particular," is not even a sentence and therefore cannot be false.
That Prolog meerely executes the instructions according to their
standard semantics and implementation choices should be quite obvious
but your "Not at all." means that you don't think it is far from
true. As it seems unplausible that you would disagree with a so
obvious truth it seems reasonable to think you meant sometnig else
but what?
On 2025-09-06 15:26:04 +0000, olcott said:
Not all all see my other reply about cycles
in directed graphs of resolution sequences.
Here your "not at all" says that you think that liar's paradox is true.
If it is true it must be a truth bearer. But you have also said that it
is not a truth bearer. Apparently you have no coherent opionion about
the liar's paradox.
On 9/9/2025 1:51 AM, Mikko wrote:
On 2025-09-07 17:26:36 +0000, olcott said:
That is all extensively elaborated in the whole
paragraph that you completely ignored.
Google[Minimal Type Theory] it knows my work.
It incorrectly attributes this to: Maietti and Sambin
I created a whole system named Minimal Type Theory
that translates logical expressions into the directed
graph of their resolution sequence. When MTT detects
a cycle in this graph that is exactly the same thing as:
?- unify_with_occurs_check(LP, not(true(LP))).
false.
No, it isn't. There is no reference to those words there.
This requires a deeper understanding of the meaning of
these words that you lack.
In common
language the words "Not at all", just like plain "No", refer to the
immediately previous sentence or sentences, usually said by someone
else. In this case the standard meaning is that you claim that
"It doesn't prove anything. Prolog merely executes the instructions
according to their standard semantics and implementation choices.
In particular," or at least "In particular," is false. But "In
particular," is not even a sentence and therefore cannot be false.
That Prolog meerely executes the instructions according to their
standard semantics and implementation choices should be quite obvious
but your "Not at all." means that you don't think it is far from
true. As it seems unplausible that you would disagree with a so
obvious truth it seems reasonable to think you meant sometnig else
but what?
On 9/9/2025 1:57 AM, Mikko wrote:
On 2025-09-06 15:26:04 +0000, olcott said:
Not all all see my other reply about cycles
in directed graphs of resolution sequences.
Here your "not at all" says that you think that liar's paradox is true.
*You got confused let me simplify*
Boolean True(Language L, Expression E);
X = "k*lsndesoiedfem,89234rm,dv0io9werf" // random gibberish
True(English, X)==FALSE
~True(English, X)==TRUE
True(English, "this sentence is not true" )==FALSE
~True(English, "this sentence is not true" )==TRUE
This sentence is not true: "This sentence is not true"
with the outer sentence referring to the inner sentence
is the same as this: ~True(English, "This sentence is not true")
--If it is true it must be a truth bearer. But you have also said that it
is not a truth bearer. Apparently you have no coherent opionion about
the liar's paradox.
On 2025-09-06 15:23:58 +0000, olcott said:
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value.
That is not a definition but could be a valid starting point for
a proof. One could also state that because it is not a truth-bearer
it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes
English declarative sentences and logical propositions.
"This sentence is not true"
Cannot possibly be resolved to a truth value.
If you try to
define a term that is alredy in use differently from its usual
meaning that is sufficient to reject it without further review.
The above definition is conventional. It is also a standard
convention that when there is no word for a meaning that
the word with the closest existing meaning is used and becomes
a term of the art by adapting this meaning.
It is not always the word with the closest meaning. Sometimes a
word with a meaning far from the needed meaning is chosen.
That makes communication very misleading rather than
effective. The best way to do this in natural language
is to choose an existing term with the closest meaning
and then specify the exact divergence from this conventional
meaning.
In
any case one must be sure that the word is not needed for any
other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings
that correspond to sense meanings of words or term-of-the-art
meanings of terms.
An important rule with the defined words is that they must not
be used before the definition. Unless the definition is already
well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the word.
If your first step is a premiss then reviewers must consdier
whether it is acceptable or should be proven or can be rejected
as false.
That the Liar Paradox is not a truth bearer is proven
completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to
do that only after the defintions, in particular the definition
of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not true"
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
It doesn't prove anything. Prolog merely executes the instructions
according to their standard semantics and implementation choices.
In particular,
Not at all.
What not at all? What is that intended to refer to?
On 2025-09-09 16:10:28 +0000, olcott said:
On 9/9/2025 1:57 AM, Mikko wrote:
On 2025-09-06 15:26:04 +0000, olcott said:
Not all all see my other reply about cycles
in directed graphs of resolution sequences.
Here your "not at all" says that you think that liar's paradox is true.
*You got confused let me simplify*
Boolean True(Language L, Expression E);
X = "k*lsndesoiedfem,89234rm,dv0io9werf" // random gibberish
-a True(English, X)==FALSE
~True(English, X)==TRUE
-a True(English, "this sentence is not true" )==FALSE
~True(English, "this sentence is not true" )==TRUE
This sentence is not true: "This sentence is not true"
with the outer sentence referring to the inner sentence
is the same as this: ~True(English, "This sentence is not true")
To me that is far less simple than "The liar paradox is not true"
if that is what you think or "The sentence 'This sentence is not true'
is not true" otherwise.
Anyway, this does not yet clarify whether you really mean that
Tarski's proof is invalid because you agree with Tarski about
someting.
If it is true it must be a truth bearer. But you have also said that it
is not a truth bearer. Apparently you have no coherent opionion about
the liar's paradox.
On 9/7/2025 3:27 AM, Mikko wrote:
On 2025-09-06 15:23:58 +0000, olcott said:
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value.
That is not a definition but could be a valid starting point for
a proof. One could also state that because it is not a truth-bearer
it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes
English declarative sentences and logical propositions.
"This sentence is not true"
Cannot possibly be resolved to a truth value.
If you try to
define a term that is alredy in use differently from its usual
meaning that is sufficient to reject it without further review.
The above definition is conventional. It is also a standard
convention that when there is no word for a meaning that
the word with the closest existing meaning is used and becomes
a term of the art by adapting this meaning.
It is not always the word with the closest meaning. Sometimes a
word with a meaning far from the needed meaning is chosen.
That makes communication very misleading rather than
effective. The best way to do this in natural language
is to choose an existing term with the closest meaning
and then specify the exact divergence from this conventional
meaning.
In
any case one must be sure that the word is not needed for any
other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings
that correspond to sense meanings of words or term-of-the-art
meanings of terms.
An important rule with the defined words is that they must not
be used before the definition. Unless the definition is already
well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the word.
If your first step is a premiss then reviewers must consdier
whether it is acceptable or should be proven or can be rejected
as false.
That the Liar Paradox is not a truth bearer is proven
completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to
do that only after the defintions, in particular the definition
of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not true"
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
It doesn't prove anything. Prolog merely executes the instructions
according to their standard semantics and implementation choices.
In particular,
Not at all.
What not at all? What is that intended to refer to?
Prolog does prove that the Liar Paradox has a
cycle in its resolution directed graph the same
way that I use Minimal Type Theory so show that
the G||del sentence has a cycle below.
On 9/10/2025 3:17 AM, Mikko wrote:
On 2025-09-09 16:10:28 +0000, olcott said:
On 9/9/2025 1:57 AM, Mikko wrote:
On 2025-09-06 15:26:04 +0000, olcott said:*You got confused let me simplify*
Not all all see my other reply about cycles
in directed graphs of resolution sequences.
Here your "not at all" says that you think that liar's paradox is true. >>>
Boolean True(Language L, Expression E);
X = "k*lsndesoiedfem,89234rm,dv0io9werf" // random gibberish
-a True(English, X)==FALSE
~True(English, X)==TRUE
-a True(English, "this sentence is not true" )==FALSE
~True(English, "this sentence is not true" )==TRUE
This sentence is not true: "This sentence is not true"
with the outer sentence referring to the inner sentence
is the same as this: ~True(English, "This sentence is not true")
To me that is far less simple than "The liar paradox is not true"
It is the way that we would correctly apply Tarski's
Boolean True(Language L, Expression E);
to the liar paradox.
Is this sentence true: "This sentence is not true" NO
Is this sentence false: "This sentence is not true" NO
In other words "This sentence is not true" is not a truth bearer.
if that is what you think or "The sentence 'This sentence is not true'
is not true" otherwise.
Anyway, this does not yet clarify whether you really mean that
Tarski's proof is invalid because you agree with Tarski about
someting.
I made it completely clear yet if you have no
idea what a directed graph is then you won't
understand it.
On 2025-09-10 15:14:53 +0000, olcott said:
On 9/7/2025 3:27 AM, Mikko wrote:
On 2025-09-06 15:23:58 +0000, olcott said:
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value.
That is not a definition but could be a valid starting point for
a proof. One could also state that because it is not a truth-bearer
it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes
English declarative sentences and logical propositions.
"This sentence is not true"
Cannot possibly be resolved to a truth value.
If you try to
define a term that is alredy in use differently from its usual
meaning that is sufficient to reject it without further review.
The above definition is conventional. It is also a standard
convention that when there is no word for a meaning that
the word with the closest existing meaning is used and becomes
a term of the art by adapting this meaning.
It is not always the word with the closest meaning. Sometimes a
word with a meaning far from the needed meaning is chosen.
That makes communication very misleading rather than
effective. The best way to do this in natural language
is to choose an existing term with the closest meaning
and then specify the exact divergence from this conventional
meaning.
In
any case one must be sure that the word is not needed for any
other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings
that correspond to sense meanings of words or term-of-the-art
meanings of terms.
An important rule with the defined words is that they must not
be used before the definition. Unless the definition is already
well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the word.
If your first step is a premiss then reviewers must consdier
whether it is acceptable or should be proven or can be rejected
as false.
That the Liar Paradox is not a truth bearer is proven
completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to
do that only after the defintions, in particular the definition
of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not true"
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
It doesn't prove anything. Prolog merely executes the instructions
according to their standard semantics and implementation choices.
In particular,
Not at all.
What not at all? What is that intended to refer to?
Prolog does prove that the Liar Paradox has a
cycle in its resolution directed graph the same
way that I use Minimal Type Theory so show that
the G||del sentence has a cycle below.
Prolog does not say "a cycle in resolution graph". It says "false".
On 2025-09-10 15:20:44 +0000, olcott said:
On 9/10/2025 3:17 AM, Mikko wrote:
On 2025-09-09 16:10:28 +0000, olcott said:
On 9/9/2025 1:57 AM, Mikko wrote:
On 2025-09-06 15:26:04 +0000, olcott said:
Not all all see my other reply about cycles
in directed graphs of resolution sequences.
Here your "not at all" says that you think that liar's paradox is
true.
*You got confused let me simplify*
Boolean True(Language L, Expression E);
X = "k*lsndesoiedfem,89234rm,dv0io9werf" // random gibberish
-a True(English, X)==FALSE
~True(English, X)==TRUE
-a True(English, "this sentence is not true" )==FALSE
~True(English, "this sentence is not true" )==TRUE
This sentence is not true: "This sentence is not true"
with the outer sentence referring to the inner sentence
is the same as this: ~True(English, "This sentence is not true")
To me that is far less simple than "The liar paradox is not true"
It is the way that we would correctly apply Tarski's
Boolean True(Language L, Expression E);
to the liar paradox.
The truth predicate Tarski was discussing has only one argument.
Is this sentence true:-a "This sentence is not true" NO
Is this sentence false: "This sentence is not true" NO
In other words "This sentence is not true" is not a truth bearer.
Tarski also required that every arithmetic sentence is either
true or false and that every sentence that can be validly
inferred from true sentences is true.
if that is what you think or "The sentence 'This sentence is not true'
is not true" otherwise.
Anyway, this does not yet clarify whether you really mean that
Tarski's proof is invalid because you agree with Tarski about
someting.
I made it completely clear yet if you have no
idea what a directed graph is then you won't
understand it.
You indeed made it complete clear that you think both that the
liar's paradox is true and that it has not truth value. Which
means that you have no coherent opinion on that.
On 9/11/2025 4:30 AM, Mikko wrote:
On 2025-09-10 15:14:53 +0000, olcott said:
On 9/7/2025 3:27 AM, Mikko wrote:
On 2025-09-06 15:23:58 +0000, olcott said:
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value.
That is not a definition but could be a valid starting point for
a proof. One could also state that because it is not a truth-bearer >>>>>> it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes
English declarative sentences and logical propositions.
"This sentence is not true"
Cannot possibly be resolved to a truth value.
If you try toThe above definition is conventional. It is also a standard
define a term that is alredy in use differently from its usual >>>>>>>> meaning that is sufficient to reject it without further review. >>>>>>>
convention that when there is no word for a meaning that
the word with the closest existing meaning is used and becomes
a term of the art by adapting this meaning.
It is not always the word with the closest meaning. Sometimes a
word with a meaning far from the needed meaning is chosen.
That makes communication very misleading rather than
effective. The best way to do this in natural language
is to choose an existing term with the closest meaning
and then specify the exact divergence from this conventional
meaning.
In
any case one must be sure that the word is not needed for any
other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings
that correspond to sense meanings of words or term-of-the-art
meanings of terms.
An important rule with the defined words is that they must not
be used before the definition. Unless the definition is already
well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the word.
If your first step is a premiss then reviewers must consdier
whether it is acceptable or should be proven or can be rejected >>>>>>>> as false.
That the Liar Paradox is not a truth bearer is proven
completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to
do that only after the defintions, in particular the definition
of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not true"
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
It doesn't prove anything. Prolog merely executes the instructions >>>>>> according to their standard semantics and implementation choices.
In particular,
Not at all.
What not at all? What is that intended to refer to?
Prolog does prove that the Liar Paradox has a
cycle in its resolution directed graph the same
way that I use Minimal Type Theory so show that
the G||del sentence has a cycle below.
Prolog does not say "a cycle in resolution graph". It says "false".
Yet the documentation that you dishonestly ignored does say
The SWI-Prolog implementation of unify_with_occurs_check/2
is cycle-safe and only guards against creating cycles, not
against cycles that may already be present in one of the
arguments.
https://www.swi-prolog.org/pldoc/man?predicate=unify_with_occurs_check/2
On 9/11/2025 4:43 AM, Mikko wrote:
On 2025-09-10 15:20:44 +0000, olcott said:
On 9/10/2025 3:17 AM, Mikko wrote:
On 2025-09-09 16:10:28 +0000, olcott said:
On 9/9/2025 1:57 AM, Mikko wrote:
On 2025-09-06 15:26:04 +0000, olcott said:*You got confused let me simplify*
Not all all see my other reply about cycles
in directed graphs of resolution sequences.
Here your "not at all" says that you think that liar's paradox is true. >>>>>
Boolean True(Language L, Expression E);
X = "k*lsndesoiedfem,89234rm,dv0io9werf" // random gibberish
-a True(English, X)==FALSE
~True(English, X)==TRUE
-a True(English, "this sentence is not true" )==FALSE
~True(English, "this sentence is not true" )==TRUE
This sentence is not true: "This sentence is not true"
with the outer sentence referring to the inner sentence
is the same as this: ~True(English, "This sentence is not true")
To me that is far less simple than "The liar paradox is not true"
It is the way that we would correctly apply Tarski's
Boolean True(Language L, Expression E);
to the liar paradox.
The truth predicate Tarski was discussing has only one argument.
This is within his false assumption that only
a single language exists.
Is this sentence true:-a "This sentence is not true" NO
Is this sentence false: "This sentence is not true" NO
In other words "This sentence is not true" is not a truth bearer.
Tarski also required that every arithmetic sentence is either
true or false and that every sentence that can be validly
inferred from true sentences is true.
Sure and by the same reasoning "What time is it?"
also proves that no True() predicate exists.
if that is what you think or "The sentence 'This sentence is not true' >>>> is not true" otherwise.
Anyway, this does not yet clarify whether you really mean that
Tarski's proof is invalid because you agree with Tarski about
someting.
I made it completely clear yet if you have no
idea what a directed graph is then you won't
understand it.
You indeed made it complete clear that you think both that the
liar's paradox is true and that it has not truth value. Which
means that you have no coherent opinion on that.
I never said anything like that.
"This sentence is not true"
has the same truth value as this sentence
"What time is it?"
On 2025-09-11 15:52:58 +0000, olcott said:
On 9/11/2025 4:30 AM, Mikko wrote:
On 2025-09-10 15:14:53 +0000, olcott said:
On 9/7/2025 3:27 AM, Mikko wrote:
On 2025-09-06 15:23:58 +0000, olcott said:
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value.
That is not a definition but could be a valid starting point for >>>>>>> a proof. One could also state that because it is not a truth-bearer >>>>>>> it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes
English declarative sentences and logical propositions.
"This sentence is not true"
Cannot possibly be resolved to a truth value.
If you try toThe above definition is conventional. It is also a standard
define a term that is alredy in use differently from its usual >>>>>>>>> meaning that is sufficient to reject it without further review. >>>>>>>>
convention that when there is no word for a meaning that
the word with the closest existing meaning is used and becomes >>>>>>>> a term of the art by adapting this meaning.
It is not always the word with the closest meaning. Sometimes a
word with a meaning far from the needed meaning is chosen.
That makes communication very misleading rather than
effective. The best way to do this in natural language
is to choose an existing term with the closest meaning
and then specify the exact divergence from this conventional
meaning.
In
any case one must be sure that the word is not needed for any
other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings
that correspond to sense meanings of words or term-of-the-art
meanings of terms.
An important rule with the defined words is that they must not
be used before the definition. Unless the definition is already
well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the word. >>>>>>>
If your first step is a premiss then reviewers must consdier >>>>>>>>> whether it is acceptable or should be proven or can be rejected >>>>>>>>> as false.
That the Liar Paradox is not a truth bearer is proven
completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to
do that only after the defintions, in particular the definition
of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not true"
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
It doesn't prove anything. Prolog merely executes the instructions >>>>>>> according to their standard semantics and implementation choices. >>>>>>> In particular,
Not at all.
What not at all? What is that intended to refer to?
Prolog does prove that the Liar Paradox has a
cycle in its resolution directed graph the same
way that I use Minimal Type Theory so show that
the G||del sentence has a cycle below.
Prolog does not say "a cycle in resolution graph". It says "false".
Yet the documentation that you dishonestly ignored does say
The SWI-Prolog implementation of unify_with_occurs_check/2
is cycle-safe and only guards against creating cycles, not
against cycles that may already be present in one of the
arguments.
https://www.swi-prolog.org/pldoc/man?predicate=unify_with_occurs_check/2
You are right. The point that it may accept already existing cyclic structures must not be forgotten.
On 2025-09-11 16:21:11 +0000, olcott said:
On 9/11/2025 4:43 AM, Mikko wrote:
On 2025-09-10 15:20:44 +0000, olcott said:
On 9/10/2025 3:17 AM, Mikko wrote:
On 2025-09-09 16:10:28 +0000, olcott said:
On 9/9/2025 1:57 AM, Mikko wrote:
On 2025-09-06 15:26:04 +0000, olcott said:
Not all all see my other reply about cycles
in directed graphs of resolution sequences.
Here your "not at all" says that you think that liar's paradox is >>>>>>> true.
*You got confused let me simplify*
Boolean True(Language L, Expression E);
X = "k*lsndesoiedfem,89234rm,dv0io9werf" // random gibberish
-a True(English, X)==FALSE
~True(English, X)==TRUE
-a True(English, "this sentence is not true" )==FALSE
~True(English, "this sentence is not true" )==TRUE
This sentence is not true: "This sentence is not true"
with the outer sentence referring to the inner sentence
is the same as this: ~True(English, "This sentence is not true")
To me that is far less simple than "The liar paradox is not true"
It is the way that we would correctly apply Tarski's
Boolean True(Language L, Expression E);
to the liar paradox.
The truth predicate Tarski was discussing has only one argument.
This is within his false assumption that only
a single language exists.
No, it does not. Tarski does not assume so. The discussion is for a
truth predicate for one language only, which is a language that can
express at least Peano arithmetic and possibly something else that
one would like to include in the scope of the truth predicate.
Is this sentence true:-a "This sentence is not true" NO
Is this sentence false: "This sentence is not true" NO
In other words "This sentence is not true" is not a truth bearer.
Tarski also required that every arithmetic sentence is either
true or false and that every sentence that can be validly
inferred from true sentences is true.
Sure and by the same reasoning "What time is it?"
also proves that no True() predicate exists.
Tarski didn't intend to prove that no truth predicate exists. One can construct a truth predicate for a sufficiently simple system, e.g.
Abelian groups. But he did prove that it is not possible to construct
a proof predicate that can determine the truth of a sentene in a
language that can express sentences of Peano arithmetic or any more
extended theory.
if that is what you think or "The sentence 'This sentence is not true' >>>>> is not true" otherwise.
Anyway, this does not yet clarify whether you really mean that
Tarski's proof is invalid because you agree with Tarski about
someting.
I made it completely clear yet if you have no
idea what a directed graph is then you won't
understand it.
You indeed made it complete clear that you think both that the
liar's paradox is true and that it has not truth value. Which
means that you have no coherent opinion on that.
I never said anything like that.
"This sentence is not true"
has the same truth value as this sentence
"What time is it?"
I said that the statement "Liar's paradox is not true" is true.
In message 109hjqc$33v70$1@dont-email.me you answered "Not all all".
Nothing said before that in the discussion supports any other
interpretation than that you believe that the liar's paradox
is true.
You may retract your statement if you think you were wrong
but so far you havn't.
On 9/12/2025 1:59 AM, Mikko wrote:
On 2025-09-11 15:52:58 +0000, olcott said:
On 9/11/2025 4:30 AM, Mikko wrote:
On 2025-09-10 15:14:53 +0000, olcott said:
On 9/7/2025 3:27 AM, Mikko wrote:
On 2025-09-06 15:23:58 +0000, olcott said:
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value.
That is not a definition but could be a valid starting point for >>>>>>>> a proof. One could also state that because it is not a truth-bearer >>>>>>>> it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes
English declarative sentences and logical propositions.
"This sentence is not true"
Cannot possibly be resolved to a truth value.
If you try toThe above definition is conventional. It is also a standard
define a term that is alredy in use differently from its usual >>>>>>>>>> meaning that is sufficient to reject it without further review. >>>>>>>>>
convention that when there is no word for a meaning that
the word with the closest existing meaning is used and becomes >>>>>>>>> a term of the art by adapting this meaning.
It is not always the word with the closest meaning. Sometimes a >>>>>>>> word with a meaning far from the needed meaning is chosen.
That makes communication very misleading rather than
effective. The best way to do this in natural language
is to choose an existing term with the closest meaning
and then specify the exact divergence from this conventional
meaning.
In
any case one must be sure that the word is not needed for any
other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings
that correspond to sense meanings of words or term-of-the-art
meanings of terms.
An important rule with the defined words is that they must not >>>>>>>> be used before the definition. Unless the definition is already >>>>>>>> well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the word. >>>>>>>>
If your first step is a premiss then reviewers must consdier >>>>>>>>>> whether it is acceptable or should be proven or can be rejected >>>>>>>>>> as false.
That the Liar Paradox is not a truth bearer is proven
completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to >>>>>>>> do that only after the defintions, in particular the definition >>>>>>>> of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not true" >>>>>>>
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
It doesn't prove anything. Prolog merely executes the instructions >>>>>>>> according to their standard semantics and implementation choices. >>>>>>>> In particular,
Not at all.
What not at all? What is that intended to refer to?
Prolog does prove that the Liar Paradox has a
cycle in its resolution directed graph the same
way that I use Minimal Type Theory so show that
the G||del sentence has a cycle below.
Prolog does not say "a cycle in resolution graph". It says "false".
Yet the documentation that you dishonestly ignored does say
The SWI-Prolog implementation of unify_with_occurs_check/2
is cycle-safe and only guards against creating cycles, not
against cycles that may already be present in one of the
arguments.
https://www.swi-prolog.org/pldoc/man?predicate=unify_with_occurs_check/2
You are right. The point that it may accept already existing cyclic
structures must not be forgotten.
In other words when you don't have it look at
errors it will not report them.
Formal logic make sure to make self-reference
inexpressible that I why I extended the syntax
of FOPL to include the "defined as" operator :=
On 9/12/2025 2:23 AM, Mikko wrote:
On 2025-09-11 16:21:11 +0000, olcott said:
On 9/11/2025 4:43 AM, Mikko wrote:
On 2025-09-10 15:20:44 +0000, olcott said:
On 9/10/2025 3:17 AM, Mikko wrote:
On 2025-09-09 16:10:28 +0000, olcott said:
On 9/9/2025 1:57 AM, Mikko wrote:
On 2025-09-06 15:26:04 +0000, olcott said:
Not all all see my other reply about cycles
in directed graphs of resolution sequences.
Here your "not at all" says that you think that liar's paradox is true.
*You got confused let me simplify*
Boolean True(Language L, Expression E);
X = "k*lsndesoiedfem,89234rm,dv0io9werf" // random gibberish
-a True(English, X)==FALSE
~True(English, X)==TRUE
-a True(English, "this sentence is not true" )==FALSE
~True(English, "this sentence is not true" )==TRUE
This sentence is not true: "This sentence is not true"
with the outer sentence referring to the inner sentence
is the same as this: ~True(English, "This sentence is not true")
To me that is far less simple than "The liar paradox is not true"
It is the way that we would correctly apply Tarski's
Boolean True(Language L, Expression E);
to the liar paradox.
The truth predicate Tarski was discussing has only one argument.
This is within his false assumption that only
a single language exists.
No, it does not. Tarski does not assume so. The discussion is for a
truth predicate for one language only, which is a language that can
express at least Peano arithmetic and possibly something else that
one would like to include in the scope of the truth predicate.
What the Hell good would that be for this:
True(English, "Election fraud change the outcome
of the 2020 US presidential election")==FALSE
Also it seems that you didn't bother to pay attention
to the two languages that his proof does use. The
language of his theory and the metalanguage of his
metatheory.
https://liarparadox.org/Tarski_247_248.pdf
Is this sentence true:-a "This sentence is not true" NO
Is this sentence false: "This sentence is not true" NO
In other words "This sentence is not true" is not a truth bearer.
Tarski also required that every arithmetic sentence is either
true or false and that every sentence that can be validly
inferred from true sentences is true.
Sure and by the same reasoning "What time is it?"
also proves that no True() predicate exists.
Tarski didn't intend to prove that no truth predicate exists. One can
construct a truth predicate for a sufficiently simple system, e.g.
Abelian groups. But he did prove that it is not possible to construct
a proof predicate that can determine the truth of a sentene in a
language that can express sentences of Peano arithmetic or any more
extended theory.
Only because he mandated rather than excluded an
expression of language having no truth value.
if that is what you think or "The sentence 'This sentence is not true' >>>>>> is not true" otherwise.
Anyway, this does not yet clarify whether you really mean that
Tarski's proof is invalid because you agree with Tarski about
someting.
I made it completely clear yet if you have no
idea what a directed graph is then you won't
understand it.
You indeed made it complete clear that you think both that the
liar's paradox is true and that it has not truth value. Which
means that you have no coherent opinion on that.
I never said anything like that.
"This sentence is not true"
has the same truth value as this sentence
"What time is it?"
I said that the statement "Liar's paradox is not true" is true.
*IT IS NOT TRUE*
On 2025-09-12 17:08:30 +0000, olcott said:
On 9/12/2025 1:59 AM, Mikko wrote:
On 2025-09-11 15:52:58 +0000, olcott said:
On 9/11/2025 4:30 AM, Mikko wrote:
On 2025-09-10 15:14:53 +0000, olcott said:
On 9/7/2025 3:27 AM, Mikko wrote:
On 2025-09-06 15:23:58 +0000, olcott said:
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value.
That is not a definition but could be a valid starting point for >>>>>>>>> a proof. One could also state that because it is not a truth- >>>>>>>>> bearer
it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes
English declarative sentences and logical propositions.
"This sentence is not true"
Cannot possibly be resolved to a truth value.
If you try toThe above definition is conventional. It is also a standard >>>>>>>>>> convention that when there is no word for a meaning that
define a term that is alredy in use differently from its usual >>>>>>>>>>> meaning that is sufficient to reject it without further review. >>>>>>>>>>
the word with the closest existing meaning is used and becomes >>>>>>>>>> a term of the art by adapting this meaning.
It is not always the word with the closest meaning. Sometimes a >>>>>>>>> word with a meaning far from the needed meaning is chosen.
That makes communication very misleading rather than
effective. The best way to do this in natural language
is to choose an existing term with the closest meaning
and then specify the exact divergence from this conventional
meaning.
In
any case one must be sure that the word is not needed for any >>>>>>>>> other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings
that correspond to sense meanings of words or term-of-the-art
meanings of terms.
An important rule with the defined words is that they must not >>>>>>>>> be used before the definition. Unless the definition is already >>>>>>>>> well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the word. >>>>>>>>>
If your first step is a premiss then reviewers must consdier >>>>>>>>>>> whether it is acceptable or should be proven or can be rejected >>>>>>>>>>> as false.
That the Liar Paradox is not a truth bearer is proven
completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to >>>>>>>>> do that only after the defintions, in particular the definition >>>>>>>>> of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not true" >>>>>>>>
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
It doesn't prove anything. Prolog merely executes the instructions >>>>>>>>> according to their standard semantics and implementation choices. >>>>>>>>> In particular,
Not at all.
What not at all? What is that intended to refer to?
Prolog does prove that the Liar Paradox has a
cycle in its resolution directed graph the same
way that I use Minimal Type Theory so show that
the G||del sentence has a cycle below.
Prolog does not say "a cycle in resolution graph". It says "false".
Yet the documentation that you dishonestly ignored does say
The SWI-Prolog implementation of unify_with_occurs_check/2
is cycle-safe and only guards against creating cycles, not
against cycles that may already be present in one of the
arguments.
https://www.swi-prolog.org/pldoc/man?
predicate=unify_with_occurs_check/2
You are right. The point that it may accept already existing cyclic
structures must not be forgotten.
In other words when you don't have it look at
errors it will not report them.
At least SWI-Prolog doesn't look for already existing cycles. As
SWI-Prolog permits creation of such cyles it is reasonable to
regard them as non-errors.
Formal logic make sure to make self-reference
inexpressible that I why I extended the syntax
of FOPL to include the "defined as" operator :=
One must either be very careful with the := operator or make clear
rules about self-references. The usual way, if := is permitted, is
to require that the symbol on the left side is different from all
symbols used on the right side or anywhere earlier.
However, the system Tarski used does not have the := operator,
so the above is irrelevant to the topic as specified on the subject
line.
On 2025-09-12 17:24:17 +0000, olcott said:
On 9/12/2025 2:23 AM, Mikko wrote:
On 2025-09-11 16:21:11 +0000, olcott said:
On 9/11/2025 4:43 AM, Mikko wrote:
On 2025-09-10 15:20:44 +0000, olcott said:
On 9/10/2025 3:17 AM, Mikko wrote:
On 2025-09-09 16:10:28 +0000, olcott said:It is the way that we would correctly apply Tarski's
On 9/9/2025 1:57 AM, Mikko wrote:To me that is far less simple than "The liar paradox is not true" >>>>>>
On 2025-09-06 15:26:04 +0000, olcott said:
Not all all see my other reply about cycles
in directed graphs of resolution sequences.
Here your "not at all" says that you think that liar's paradox >>>>>>>>> is true.
*You got confused let me simplify*
Boolean True(Language L, Expression E);
X = "k*lsndesoiedfem,89234rm,dv0io9werf" // random gibberish
-a True(English, X)==FALSE
~True(English, X)==TRUE
-a True(English, "this sentence is not true" )==FALSE
~True(English, "this sentence is not true" )==TRUE
This sentence is not true: "This sentence is not true"
with the outer sentence referring to the inner sentence
is the same as this: ~True(English, "This sentence is not true") >>>>>>>
Boolean True(Language L, Expression E);
to the liar paradox.
The truth predicate Tarski was discussing has only one argument.
This is within his false assumption that only
a single language exists.
No, it does not. Tarski does not assume so. The discussion is for a
truth predicate for one language only,
which is a language that can
express at least Peano arithmetic and possibly something else that
one would like to include in the scope of the truth predicate.
What the Hell good would that be for this:
True(English, "Election fraud change the outcome
of the 2020 US presidential election")==FALSE
Also it seems that you didn't bother to pay attention
to the two languages that his proof does use. The
language of his theory and the metalanguage of his
metatheory.
It is a sin to claim about another person anything that might
be false.
https://liarparadox.org/Tarski_247_248.pdf
Is this sentence true:-a "This sentence is not true" NO
Is this sentence false: "This sentence is not true" NO
In other words "This sentence is not true" is not a truth bearer.
Tarski also required that every arithmetic sentence is either
true or false and that every sentence that can be validly
inferred from true sentences is true.
Sure and by the same reasoning "What time is it?"
also proves that no True() predicate exists.
Tarski didn't intend to prove that no truth predicate exists. One can
construct a truth predicate for a sufficiently simple system, e.g.
Abelian groups. But he did prove that it is not possible to construct
a proof predicate that can determine the truth of a sentene in a
language that can express sentences of Peano arithmetic or any more
extended theory.
Only because he mandated rather than excluded an
expression of language having no truth value.
Taski did not require any lanugage features other that what is necessary
for the first order arithmetic of natural numbers. He permitted but did
not require other symbols. Then he proved that no matter what other
symbols are permitted the truth predicate cannot be constructed.
if that is what you think or "The sentence 'This sentence is not >>>>>>> true'
is not true" otherwise.
Anyway, this does not yet clarify whether you really mean that
Tarski's proof is invalid because you agree with Tarski about
someting.
I made it completely clear yet if you have no
idea what a directed graph is then you won't
understand it.
You indeed made it complete clear that you think both that the
liar's paradox is true and that it has not truth value. Which
means that you have no coherent opinion on that.
I never said anything like that.
"This sentence is not true"
has the same truth value as this sentence
"What time is it?"
I said that the statement "Liar's paradox is not true" is true.
*IT IS NOT TRUE*
And here you say it again.
On 9/13/2025 3:33 AM, Mikko wrote:
On 2025-09-12 17:08:30 +0000, olcott said:
On 9/12/2025 1:59 AM, Mikko wrote:
On 2025-09-11 15:52:58 +0000, olcott said:
On 9/11/2025 4:30 AM, Mikko wrote:You are right. The point that it may accept already existing cyclic
On 2025-09-10 15:14:53 +0000, olcott said:Yet the documentation that you dishonestly ignored does say
On 9/7/2025 3:27 AM, Mikko wrote:
On 2025-09-06 15:23:58 +0000, olcott said:
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value.
That is not a definition but could be a valid starting point for >>>>>>>>>> a proof. One could also state that because it is not a truth- bearer >>>>>>>>>> it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes
English declarative sentences and logical propositions.
"This sentence is not true"
Cannot possibly be resolved to a truth value.
If you try toThe above definition is conventional. It is also a standard >>>>>>>>>>> convention that when there is no word for a meaning that >>>>>>>>>>> the word with the closest existing meaning is used and becomes >>>>>>>>>>> a term of the art by adapting this meaning.
define a term that is alredy in use differently from its usual >>>>>>>>>>>> meaning that is sufficient to reject it without further review. >>>>>>>>>>>
It is not always the word with the closest meaning. Sometimes a >>>>>>>>>> word with a meaning far from the needed meaning is chosen.
That makes communication very misleading rather than
effective. The best way to do this in natural language
is to choose an existing term with the closest meaning
and then specify the exact divergence from this conventional >>>>>>>>> meaning.
In
any case one must be sure that the word is not needed for any >>>>>>>>>> other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings
that correspond to sense meanings of words or term-of-the-art >>>>>>>>> meanings of terms.
An important rule with the defined words is that they must not >>>>>>>>>> be used before the definition. Unless the definition is already >>>>>>>>>> well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the word. >>>>>>>>>>
If your first step is a premiss then reviewers must consdier >>>>>>>>>>>> whether it is acceptable or should be proven or can be rejected >>>>>>>>>>>> as false.
That the Liar Paradox is not a truth bearer is proven
completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to >>>>>>>>>> do that only after the defintions, in particular the definition >>>>>>>>>> of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not true" >>>>>>>>>
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
It doesn't prove anything. Prolog merely executes the instructions >>>>>>>>>> according to their standard semantics and implementation choices. >>>>>>>>>> In particular,
Not at all.
What not at all? What is that intended to refer to?
Prolog does prove that the Liar Paradox has a
cycle in its resolution directed graph the same
way that I use Minimal Type Theory so show that
the G||del sentence has a cycle below.
Prolog does not say "a cycle in resolution graph". It says "false". >>>>>
The SWI-Prolog implementation of unify_with_occurs_check/2
is cycle-safe and only guards against creating cycles, not
against cycles that may already be present in one of the
arguments.
https://www.swi-prolog.org/pldoc/man? predicate=unify_with_occurs_check/2 >>>>
structures must not be forgotten.
In other words when you don't have it look at
errors it will not report them.
At least SWI-Prolog doesn't look for already existing cycles. As
SWI-Prolog permits creation of such cyles it is reasonable to
regard them as non-errors.
They cause the system to get stuck in an infinite
loop and fail to answer.
Formal logic make sure to make self-reference
inexpressible that I why I extended the syntax
of FOPL to include the "defined as" operator :=
One must either be very careful with the := operator or make clear
rules about self-references. The usual way, if := is permitted, is
to require that the symbol on the left side is different from all
symbols used on the right side or anywhere earlier.
LP := ~True(LP)
means ~True(~True(~True(~True(~True(~True(~True(...))))))) forever
However, the system Tarski used does not have the := operator,
so the above is irrelevant to the topic as specified on the subject
line.
The Liar Paradox DOES have a cycle in its
evaluation sequence. Tarski was stupid to
not see this.
On 9/13/2025 3:46 AM, Mikko wrote:
On 2025-09-12 17:24:17 +0000, olcott said:
On 9/12/2025 2:23 AM, Mikko wrote:
On 2025-09-11 16:21:11 +0000, olcott said:
On 9/11/2025 4:43 AM, Mikko wrote:
On 2025-09-10 15:20:44 +0000, olcott said:
On 9/10/2025 3:17 AM, Mikko wrote:
On 2025-09-09 16:10:28 +0000, olcott said:It is the way that we would correctly apply Tarski's
On 9/9/2025 1:57 AM, Mikko wrote:To me that is far less simple than "The liar paradox is not true" >>>>>>>
On 2025-09-06 15:26:04 +0000, olcott said:
Not all all see my other reply about cycles
in directed graphs of resolution sequences.
Here your "not at all" says that you think that liar's paradox is true.
*You got confused let me simplify*
Boolean True(Language L, Expression E);
X = "k*lsndesoiedfem,89234rm,dv0io9werf" // random gibberish >>>>>>>>> -a True(English, X)==FALSE
~True(English, X)==TRUE
-a True(English, "this sentence is not true" )==FALSE
~True(English, "this sentence is not true" )==TRUE
This sentence is not true: "This sentence is not true"
with the outer sentence referring to the inner sentence
is the same as this: ~True(English, "This sentence is not true") >>>>>>>>
Boolean True(Language L, Expression E);
to the liar paradox.
The truth predicate Tarski was discussing has only one argument.
This is within his false assumption that only
a single language exists.
No, it does not. Tarski does not assume so. The discussion is for a
truth predicate for one language only,
counter factual
counter factual
counter factual
counter factual
counter factual
counter factual
He had the language of his theory and
the metalanguage of his metatheory
He had the language of his theory and
the metalanguage of his metatheory
He had the language of his theory and
the metalanguage of his metatheory
He had the language of his theory and
the metalanguage of his metatheory
I had to read and re-read his proof fifty times
to get a good understanding of it.
I said that the statement "Liar's paradox is not true" is true.
*IT IS NOT TRUE*
And here you say it again.
The outer sentence
The outer sentence
The outer sentence
The outer sentence
The outer sentence
is true
Because the inner sentence is not true
On 2025-09-13 14:34:02 +0000, olcott said:
On 9/13/2025 3:46 AM, Mikko wrote:
On 2025-09-12 17:24:17 +0000, olcott said:
On 9/12/2025 2:23 AM, Mikko wrote:
On 2025-09-11 16:21:11 +0000, olcott said:
On 9/11/2025 4:43 AM, Mikko wrote:
On 2025-09-10 15:20:44 +0000, olcott said:
On 9/10/2025 3:17 AM, Mikko wrote:
On 2025-09-09 16:10:28 +0000, olcott said:It is the way that we would correctly apply Tarski's
On 9/9/2025 1:57 AM, Mikko wrote:To me that is far less simple than "The liar paradox is not true" >>>>>>>>
On 2025-09-06 15:26:04 +0000, olcott said:
Not all all see my other reply about cycles
in directed graphs of resolution sequences.
Here your "not at all" says that you think that liar's
paradox is true.
*You got confused let me simplify*
Boolean True(Language L, Expression E);
X = "k*lsndesoiedfem,89234rm,dv0io9werf" // random gibberish >>>>>>>>>> -a True(English, X)==FALSE
~True(English, X)==TRUE
-a True(English, "this sentence is not true" )==FALSE
~True(English, "this sentence is not true" )==TRUE
This sentence is not true: "This sentence is not true"
with the outer sentence referring to the inner sentence
is the same as this: ~True(English, "This sentence is not true") >>>>>>>>>
Boolean True(Language L, Expression E);
to the liar paradox.
The truth predicate Tarski was discussing has only one argument.
This is within his false assumption that only
a single language exists.
No, it does not. Tarski does not assume so. The discussion is for a
truth predicate for one language only,
counter factual
counter factual
counter factual
counter factual
counter factual
counter factual
You should already know that "counter factual" does not work as
a magic spell. Nothing works if said six times instead of three
or nine.
He had the language of his theory and
the metalanguage of his metatheory
He had the language of his theory and
the metalanguage of his metatheory
He had the language of his theory and
the metalanguage of his metatheory
He had the language of his theory and
the metalanguage of his metatheory
I had to read and re-read his proof fifty times
to get a good understanding of it.
Apparently fifty times is not enough if you still don't know that
the proof is about one predicate that has one argument.
I said that the statement "Liar's paradox is not true" is true.
*IT IS NOT TRUE*
And here you say it again.
The outer sentence
The outer sentence
The outer sentence
The outer sentence
The outer sentence
is true
Yes, everyone can verify that I really said it. But your anser
"It is not true" quite clearly refers to the inner statement
that I said I had said.
Because the inner sentence is not true
The subordinate clause says that the "liar's paradox is not true"
is true. Becase the sentence "liar's paradox is not true" is true the subordinate clause is true. The sentence "Liar's paradox is not true"
is true because because liar's paradox is not true. The liar's paradox
is not true beause it is not a truth-bearer.
That you say "it is not true" does not make anything untrue.
On 2025-09-13 13:18:25 +0000, olcott said:
On 9/13/2025 3:33 AM, Mikko wrote:
On 2025-09-12 17:08:30 +0000, olcott said:
On 9/12/2025 1:59 AM, Mikko wrote:
On 2025-09-11 15:52:58 +0000, olcott said:
On 9/11/2025 4:30 AM, Mikko wrote:
On 2025-09-10 15:14:53 +0000, olcott said:Yet the documentation that you dishonestly ignored does say
On 9/7/2025 3:27 AM, Mikko wrote:
On 2025-09-06 15:23:58 +0000, olcott said:
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value.
That is not a definition but could be a valid starting point for >>>>>>>>>>> a proof. One could also state that because it is not a truth- >>>>>>>>>>> bearer
it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes
English declarative sentences and logical propositions.
"This sentence is not true"
Cannot possibly be resolved to a truth value.
That makes communication very misleading rather thanIf you try to
define a term that is alredy in use differently from its usual >>>>>>>>>>>>> meaning that is sufficient to reject it without further >>>>>>>>>>>>> review.
The above definition is conventional. It is also a standard >>>>>>>>>>>> convention that when there is no word for a meaning that >>>>>>>>>>>> the word with the closest existing meaning is used and becomes >>>>>>>>>>>> a term of the art by adapting this meaning.
It is not always the word with the closest meaning. Sometimes a >>>>>>>>>>> word with a meaning far from the needed meaning is chosen. >>>>>>>>>>
effective. The best way to do this in natural language
is to choose an existing term with the closest meaning
and then specify the exact divergence from this conventional >>>>>>>>>> meaning.
In
any case one must be sure that the word is not needed for any >>>>>>>>>>> other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings
that correspond to sense meanings of words or term-of-the-art >>>>>>>>>> meanings of terms.
An important rule with the defined words is that they must not >>>>>>>>>>> be used before the definition. Unless the definition is already >>>>>>>>>>> well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the >>>>>>>>>>> word.
If your first step is a premiss then reviewers must consdier >>>>>>>>>>>>> whether it is acceptable or should be proven or can be >>>>>>>>>>>>> rejected
as false.
That the Liar Paradox is not a truth bearer is proven
completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to >>>>>>>>>>> do that only after the defintions, in particular the definition >>>>>>>>>>> of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not true" >>>>>>>>>>
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
It doesn't prove anything. Prolog merely executes the
instructions
according to their standard semantics and implementation >>>>>>>>>>> choices.
In particular,
Not at all.
What not at all? What is that intended to refer to?
Prolog does prove that the Liar Paradox has a
cycle in its resolution directed graph the same
way that I use Minimal Type Theory so show that
the G||del sentence has a cycle below.
Prolog does not say "a cycle in resolution graph". It says "false". >>>>>>
The SWI-Prolog implementation of unify_with_occurs_check/2
is cycle-safe and only guards against creating cycles, not
against cycles that may already be present in one of the
arguments.
https://www.swi-prolog.org/pldoc/man?
predicate=unify_with_occurs_check/2
You are right. The point that it may accept already existing cyclic
structures must not be forgotten.
In other words when you don't have it look at
errors it will not report them.
At least SWI-Prolog doesn't look for already existing cycles. As
SWI-Prolog permits creation of such cyles it is reasonable to
regard them as non-errors.
They cause the system to get stuck in an infinite
loop and fail to answer.
Formal logic make sure to make self-reference
inexpressible that I why I extended the syntax
of FOPL to include the "defined as" operator :=
One must either be very careful with the := operator or make clear
rules about self-references. The usual way, if := is permitted, is
to require that the symbol on the left side is different from all
symbols used on the right side or anywhere earlier.
LP := ~True(LP)
which is only allowed in languages that don't prohibit the use fo the
same symbol on the left side and in the right side
means ~True(~True(~True(~True(~True(~True(~True(...))))))) forever
However, the system Tarski used does not have the := operator,
so the above is irrelevant to the topic as specified on the subject
line.
The Liar Paradox DOES have a cycle in its
evaluation sequence. Tarski was stupid to
not see this.
The Liar Paradox has but Tarski's language does not. Tarski was not
stupid: he knew how to transform the liar's paradox to an expression
that does need the := operator or any other non-arithmetic operator.
On 9/12/2025 2:23 AM, Mikko wrote:Therefore True(~X)=true (and ~True(~X)=false).
On 2025-09-11 16:21:11 +0000, olcott said:
On 9/11/2025 4:43 AM, Mikko wrote:
On 2025-09-10 15:20:44 +0000, olcott said:
On 9/10/2025 3:17 AM, Mikko wrote:
On 2025-09-09 16:10:28 +0000, olcott said:
On 9/9/2025 1:57 AM, Mikko wrote:
On 2025-09-06 15:26:04 +0000, olcott said:
Boolean True(Language L, Expression E);
X = "k*lsndesoiedfem,89234rm,dv0io9werf" // random gibberish
-a True(English, X)==FALSE
~True(English, X)==TRUE
Contradiction.-a True(English, "this sentence is not true" )==FALSE
~True(English, "this sentence is not true" )==TRUE
Isn't the outer sentence true?This sentence is not true: "This sentence is not true"
with the outer sentence referring to the inner sentence is the
same as this: ~True(English, "This sentence is not true")
I don't know why you want to do that! English is not a formal language.No, it does not. Tarski does not assume so. The discussion is for aWhat the Hell good would that be for this: True(English, "Election fraud change the outcome of the 2020 US presidential election")==FALSE
truth predicate for one language only, which is a language that can
express at least Peano arithmetic and possibly something else that one
would like to include in the scope of the truth predicate.
That is not a sentence.Is this sentence true:-a "This sentence is not true" NO Is this
sentence false: "This sentence is not true" NO In other words "This
sentence is not true" is not a truth bearer.
Tarski also required that every arithmetic sentence is either true or
false and that every sentence that can be validly inferred from true
sentences is true.
Sure and by the same reasoning "What time is it?"
also proves that no True() predicate exists.
Tarski didn't intend to prove that no truth predicate exists. One canOnly because he mandated rather than excluded an expression of language having no truth value.
construct a truth predicate for a sufficiently simple system, e.g.
Abelian groups. But he did prove that it is not possible to construct a
proof predicate that can determine the truth of a sentene in a language
that can express sentences of Peano arithmetic or any more extended
theory.
Yes. Or do you mean that "The liar sentence is not true" is wrong?*IT IS NOT TRUE*You indeed made it complete clear that you think both that the liar's
paradox is true and that it has not truth value. Which means that you
have no coherent opinion on that.
I never said anything like that.
"This sentence is not true"
has the same truth value as this sentence "What time is it?"
I said that the statement "Liar's paradox is not true" is true.
Do I have to repeat the term: cycle"No.
ten million times before you notice that I said it once?
--In message 109hjqc$33v70$1@dont-email.me you answered "Not all all".
Nothing said before that in the discussion supports any other
interpretation than that you believe that the liar's paradox is true.
You may retract your statement if you think you were wrong but so far
you havn't.
I had to cover this confusing case because this is the confusing caseConfusing case is confusing.
that confused Tarski.
The Liar Paradox written in the language of his theory is proved true byWDYM by a paradox being true?
the Liar Paradox written in the language of his metatheory.
"This sentence is not true" because it is not a truth bearer. When weIf it were not true, it would be saying the truth, making it wrong.
apply the same sentence to itself we get the Liar_Paradox_Squared this
new sentence becomes true because the inner sentence is not a truth
bearer.
On 9/14/2025 4:16 AM, Mikko wrote:
On 2025-09-13 13:18:25 +0000, olcott said:
On 9/13/2025 3:33 AM, Mikko wrote:
On 2025-09-12 17:08:30 +0000, olcott said:
On 9/12/2025 1:59 AM, Mikko wrote:
On 2025-09-11 15:52:58 +0000, olcott said:
On 9/11/2025 4:30 AM, Mikko wrote:
On 2025-09-10 15:14:53 +0000, olcott said:Yet the documentation that you dishonestly ignored does say
On 9/7/2025 3:27 AM, Mikko wrote:
On 2025-09-06 15:23:58 +0000, olcott said:
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>That is not a definition but could be a valid starting point for >>>>>>>>>>>> a proof. One could also state that because it is not a truth- bearer
The first step of a proof is usually a definition.
Here is is: "this sentence is not true" within the
philosophy of logic it would be called not a truth
bearer because it cannot possibly have a truth value. >>>>>>>>>>>>
it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes
English declarative sentences and logical propositions.
"This sentence is not true"
Cannot possibly be resolved to a truth value.
That makes communication very misleading rather thanIf you try toThe above definition is conventional. It is also a standard >>>>>>>>>>>>> convention that when there is no word for a meaning that >>>>>>>>>>>>> the word with the closest existing meaning is used and becomes >>>>>>>>>>>>> a term of the art by adapting this meaning.
define a term that is alredy in use differently from its usual >>>>>>>>>>>>>> meaning that is sufficient to reject it without further review. >>>>>>>>>>>>>
It is not always the word with the closest meaning. Sometimes a >>>>>>>>>>>> word with a meaning far from the needed meaning is chosen. >>>>>>>>>>>
effective. The best way to do this in natural language
is to choose an existing term with the closest meaning
and then specify the exact divergence from this conventional >>>>>>>>>>> meaning.
In
any case one must be sure that the word is not needed for any >>>>>>>>>>>> other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings
that correspond to sense meanings of words or term-of-the-art >>>>>>>>>>> meanings of terms.
An important rule with the defined words is that they must not >>>>>>>>>>>> be used before the definition. Unless the definition is already >>>>>>>>>>>> well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the word. >>>>>>>>>>>>
If your first step is a premiss then reviewers must consdier >>>>>>>>>>>>>> whether it is acceptable or should be proven or can be rejected >>>>>>>>>>>>>> as false.
That the Liar Paradox is not a truth bearer is proven >>>>>>>>>>>>> completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to >>>>>>>>>>>> do that only after the defintions, in particular the definition >>>>>>>>>>>> of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not true" >>>>>>>>>>>
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you
can comprehend.
It doesn't prove anything. Prolog merely executes the instructions >>>>>>>>>>>> according to their standard semantics and implementation choices. >>>>>>>>>>>> In particular,
Not at all.
What not at all? What is that intended to refer to?
Prolog does prove that the Liar Paradox has a
cycle in its resolution directed graph the same
way that I use Minimal Type Theory so show that
the G||del sentence has a cycle below.
Prolog does not say "a cycle in resolution graph". It says "false". >>>>>>>
The SWI-Prolog implementation of unify_with_occurs_check/2
is cycle-safe and only guards against creating cycles, not
against cycles that may already be present in one of the
arguments.
https://www.swi-prolog.org/pldoc/man? predicate=unify_with_occurs_check/2
You are right. The point that it may accept already existing cyclic >>>>>> structures must not be forgotten.
In other words when you don't have it look at
errors it will not report them.
At least SWI-Prolog doesn't look for already existing cycles. As
SWI-Prolog permits creation of such cyles it is reasonable to
regard them as non-errors.
They cause the system to get stuck in an infinite
loop and fail to answer.
Formal logic make sure to make self-reference
inexpressible that I why I extended the syntax
of FOPL to include the "defined as" operator :=
One must either be very careful with the := operator or make clear
rules about self-references. The usual way, if := is permitted, is
to require that the symbol on the left side is different from all
symbols used on the right side or anywhere earlier.
LP := ~True(LP)
which is only allowed in languages that don't prohibit the use fo the
same symbol on the left side and in the right side
means ~True(~True(~True(~True(~True(~True(~True(...))))))) forever
However, the system Tarski used does not have the := operator,
so the above is irrelevant to the topic as specified on the subject
line.
The Liar Paradox DOES have a cycle in its
evaluation sequence. Tarski was stupid to
not see this.
The Liar Paradox has but Tarski's language does not. Tarski was not
stupid: he knew how to transform the liar's paradox to an expression
that does need the := operator or any other non-arithmetic operator.
He was profoundly brilliant on most things. On the Liar Paradox
specifying a cycle in its evaluation graph it seems that most
of humanity is stupid.
On 9/14/2025 4:36 AM, Mikko wrote:
On 2025-09-13 14:34:02 +0000, olcott said:
On 9/13/2025 3:46 AM, Mikko wrote:
On 2025-09-12 17:24:17 +0000, olcott said:
On 9/12/2025 2:23 AM, Mikko wrote:
On 2025-09-11 16:21:11 +0000, olcott said:
On 9/11/2025 4:43 AM, Mikko wrote:
On 2025-09-10 15:20:44 +0000, olcott said:This is within his false assumption that only
On 9/10/2025 3:17 AM, Mikko wrote:
On 2025-09-09 16:10:28 +0000, olcott said:It is the way that we would correctly apply Tarski's
On 9/9/2025 1:57 AM, Mikko wrote:To me that is far less simple than "The liar paradox is not true" >>>>>>>>>
On 2025-09-06 15:26:04 +0000, olcott said:
Not all all see my other reply about cycles
in directed graphs of resolution sequences.
Here your "not at all" says that you think that liar's paradox is true.
*You got confused let me simplify*
Boolean True(Language L, Expression E);
X = "k*lsndesoiedfem,89234rm,dv0io9werf" // random gibberish >>>>>>>>>>> -a True(English, X)==FALSE
~True(English, X)==TRUE
-a True(English, "this sentence is not true" )==FALSE
~True(English, "this sentence is not true" )==TRUE
This sentence is not true: "This sentence is not true"
with the outer sentence referring to the inner sentence
is the same as this: ~True(English, "This sentence is not true") >>>>>>>>>>
Boolean True(Language L, Expression E);
to the liar paradox.
The truth predicate Tarski was discussing has only one argument. >>>>>>>
a single language exists.
No, it does not. Tarski does not assume so. The discussion is for a >>>>>> truth predicate for one language only,
counter factual
counter factual
counter factual
counter factual
counter factual
counter factual
You should already know that "counter factual" does not work as
a magic spell. Nothing works if said six times instead of three
or nine.
He had the language of his theory and
the metalanguage of his metatheory
He had the language of his theory and
the metalanguage of his metatheory
He had the language of his theory and
the metalanguage of his metatheory
He had the language of his theory and
the metalanguage of his metatheory
I had to read and re-read his proof fifty times
to get a good understanding of it.
Apparently fifty times is not enough if you still don't know that
the proof is about one predicate that has one argument.
I said that the statement "Liar's paradox is not true" is true.
*IT IS NOT TRUE*
And here you say it again.
The outer sentence
The outer sentence
The outer sentence
The outer sentence
The outer sentence
is true
Yes, everyone can verify that I really said it. But your anser
"It is not true" quite clearly refers to the inner statement
that I said I had said.
Because the inner sentence is not true
The subordinate clause says that the "liar's paradox is not true"
is true. Becase the sentence "liar's paradox is not true" is true the
subordinate clause is true. The sentence "Liar's paradox is not true"
is true because because liar's paradox is not true. The liar's paradox
is not true beause it is not a truth-bearer.
That you say "it is not true" does not make anything untrue.
This sentence is not true: "This sentence is not true" is true
is the whole essence of Tarski's proof that no sufficiently complex
system can define its own truth predicate.
When we simply toss out "This sentence is not true" as not a
bearer of truth his whole argument falls apart.
Also even within Tarski's reasoning a system that includes
multiple levels of logic within the same system such as
my Minimal Type Theory (MTT) can define its own truth
predicate by having one order of logic refer to the
next lower order of logic.
Am Fri, 12 Sep 2025 12:24:17 -0500 schrieb olcott:
On 9/12/2025 2:23 AM, Mikko wrote:
On 2025-09-11 16:21:11 +0000, olcott said:
On 9/11/2025 4:43 AM, Mikko wrote:
On 2025-09-10 15:20:44 +0000, olcott said:
On 9/10/2025 3:17 AM, Mikko wrote:
On 2025-09-09 16:10:28 +0000, olcott said:
On 9/9/2025 1:57 AM, Mikko wrote:
On 2025-09-06 15:26:04 +0000, olcott said:
Therefore True(~X)=true (and ~True(~X)=false).Boolean True(Language L, Expression E);
X = "k*lsndesoiedfem,89234rm,dv0io9werf" // random gibberish
-a True(English, X)==FALSE
~True(English, X)==TRUE
-a True(English, "this sentence is not true" )==FALSE
~True(English, "this sentence is not true" )==TRUE
Contradiction.
This sentence is not true: "This sentence is not true"
with the outer sentence referring to the inner sentence is the >>>>>>>> same as this: ~True(English, "This sentence is not true")
Isn't the outer sentence true?
I don't know why you want to do that! English is not a formal language.No, it does not. Tarski does not assume so. The discussion is for aWhat the Hell good would that be for this: True(English, "Election fraud
truth predicate for one language only, which is a language that can
express at least Peano arithmetic and possibly something else that one
would like to include in the scope of the truth predicate.
change the outcome of the 2020 US presidential election")==FALSE
That is not a sentence.Is this sentence true:-a "This sentence is not true" NO Is this
sentence false: "This sentence is not true" NO In other words "This >>>>>> sentence is not true" is not a truth bearer.
Tarski also required that every arithmetic sentence is either true or >>>>> false and that every sentence that can be validly inferred from true >>>>> sentences is true.
Sure and by the same reasoning "What time is it?"
also proves that no True() predicate exists.
Tarski didn't intend to prove that no truth predicate exists. One canOnly because he mandated rather than excluded an expression of language
construct a truth predicate for a sufficiently simple system, e.g.
Abelian groups. But he did prove that it is not possible to construct a
proof predicate that can determine the truth of a sentene in a language
that can express sentences of Peano arithmetic or any more extended
theory.
having no truth value.
There are probably many other sentences like it, and determining
if you've got one of them is probably impossible.
Yes. Or do you mean that "The liar sentence is not true" is wrong?*IT IS NOT TRUE*You indeed made it complete clear that you think both that the liar's >>>>> paradox is true and that it has not truth value. Which means that you >>>>> have no coherent opinion on that.
I never said anything like that.
"This sentence is not true"
has the same truth value as this sentence "What time is it?"
I said that the statement "Liar's paradox is not true" is true.
Do I have to repeat the term: cycle"No.
ten million times before you notice that I said it once?
--In message 109hjqc$33v70$1@dont-email.me you answered "Not all all".
Nothing said before that in the discussion supports any other
interpretation than that you believe that the liar's paradox is true.
You may retract your statement if you think you were wrong but so far
you havn't.
Am Thu, 11 Sep 2025 11:21:11 -0500 schrieb olcott:
I had to cover this confusing case because this is the confusing caseConfusing case is confusing.
that confused Tarski.
The Liar Paradox written in the language of his theory is proved true byWDYM by a paradox being true?
the Liar Paradox written in the language of his metatheory.
"This sentence is not true" because it is not a truth bearer. When weIf it were not true, it would be saying the truth, making it wrong.
apply the same sentence to itself we get the Liar_Paradox_Squared this
new sentence becomes true because the inner sentence is not a truth
bearer.
On 2025-09-14 14:12:47 +0000, olcott said:
On 9/14/2025 4:16 AM, Mikko wrote:
On 2025-09-13 13:18:25 +0000, olcott said:
On 9/13/2025 3:33 AM, Mikko wrote:
On 2025-09-12 17:08:30 +0000, olcott said:
On 9/12/2025 1:59 AM, Mikko wrote:
On 2025-09-11 15:52:58 +0000, olcott said:
On 9/11/2025 4:30 AM, Mikko wrote:
On 2025-09-10 15:14:53 +0000, olcott said:
On 9/7/2025 3:27 AM, Mikko wrote:
On 2025-09-06 15:23:58 +0000, olcott said:
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>That is not a definition but could be a valid starting >>>>>>>>>>>>> point for
The first step of a proof is usually a definition. >>>>>>>>>>>>>>Here is is: "this sentence is not true" within the >>>>>>>>>>>>>> philosophy of logic it would be called not a truth >>>>>>>>>>>>>> bearer because it cannot possibly have a truth value. >>>>>>>>>>>>>
a proof. One could also state that because it is not a >>>>>>>>>>>>> truth- bearer
it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes
English declarative sentences and logical propositions. >>>>>>>>>>>>
"This sentence is not true"
Cannot possibly be resolved to a truth value.
That makes communication very misleading rather thanIf you try to
define a term that is alredy in use differently from its >>>>>>>>>>>>>>> usual
meaning that is sufficient to reject it without further >>>>>>>>>>>>>>> review.
The above definition is conventional. It is also a standard >>>>>>>>>>>>>> convention that when there is no word for a meaning that >>>>>>>>>>>>>> the word with the closest existing meaning is used and >>>>>>>>>>>>>> becomes
a term of the art by adapting this meaning.
It is not always the word with the closest meaning. >>>>>>>>>>>>> Sometimes a
word with a meaning far from the needed meaning is chosen. >>>>>>>>>>>>
effective. The best way to do this in natural language >>>>>>>>>>>> is to choose an existing term with the closest meaning >>>>>>>>>>>> and then specify the exact divergence from this conventional >>>>>>>>>>>> meaning.
In
any case one must be sure that the word is not needed for any >>>>>>>>>>>>> other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings >>>>>>>>>>>> that correspond to sense meanings of words or term-of-the-art >>>>>>>>>>>> meanings of terms.
An important rule with the defined words is that they must not >>>>>>>>>>>>> be used before the definition. Unless the definition is >>>>>>>>>>>>> already
well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the >>>>>>>>>>>>> word.
If your first step is a premiss then reviewers must consdier >>>>>>>>>>>>>>> whether it is acceptable or should be proven or can be >>>>>>>>>>>>>>> rejected
as false.
That the Liar Paradox is not a truth bearer is proven >>>>>>>>>>>>>> completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is >>>>>>>>>>>>> better to
do that only after the defintions, in particular the >>>>>>>>>>>>> definition
of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not >>>>>>>>>>>> true"
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you >>>>>>>>>>>>>> can comprehend.
It doesn't prove anything. Prolog merely executes the >>>>>>>>>>>>> instructions
according to their standard semantics and implementation >>>>>>>>>>>>> choices.
In particular,
Not at all.
What not at all? What is that intended to refer to?
Prolog does prove that the Liar Paradox has a
cycle in its resolution directed graph the same
way that I use Minimal Type Theory so show that
the G||del sentence has a cycle below.
Prolog does not say "a cycle in resolution graph". It says
"false".
Yet the documentation that you dishonestly ignored does say
The SWI-Prolog implementation of unify_with_occurs_check/2
is cycle-safe and only guards against creating cycles, not
against cycles that may already be present in one of the
arguments.
https://www.swi-prolog.org/pldoc/man?
predicate=unify_with_occurs_check/2
You are right. The point that it may accept already existing cyclic >>>>>>> structures must not be forgotten.
In other words when you don't have it look at
errors it will not report them.
At least SWI-Prolog doesn't look for already existing cycles. As
SWI-Prolog permits creation of such cyles it is reasonable to
regard them as non-errors.
They cause the system to get stuck in an infinite
loop and fail to answer.
Formal logic make sure to make self-reference
inexpressible that I why I extended the syntax
of FOPL to include the "defined as" operator :=
One must either be very careful with the := operator or make clear
rules about self-references. The usual way, if := is permitted, is
to require that the symbol on the left side is different from all
symbols used on the right side or anywhere earlier.
LP := ~True(LP)
which is only allowed in languages that don't prohibit the use fo the
same symbol on the left side and in the right side
means ~True(~True(~True(~True(~True(~True(~True(...))))))) forever
However, the system Tarski used does not have the := operator,
so the above is irrelevant to the topic as specified on the subject
line.
The Liar Paradox DOES have a cycle in its
evaluation sequence. Tarski was stupid to
not see this.
The Liar Paradox has but Tarski's language does not. Tarski was not
stupid: he knew how to transform the liar's paradox to an expression
that does need the := operator or any other non-arithmetic operator.
He was profoundly brilliant on most things. On the Liar Paradox
specifying a cycle in its evaluation graph it seems that most
of humanity is stupid.
Perhaps most of humanity is stupid although only a small part is
stupic enough to shoe their naked stupidity to everyone. But that
does not matter. The topic of the discussion is Tarski, who was
not stupid.
Most people quickly see that it is not possibly to assign a truth
value to the liar's paradox. Some don't know what an "evaluation
graph" is but they can reach the same conclusion with different
thinking.
What is too hard for many but not everyone is that that
means that there cannot be a truth predicate over any domain that
includes the liar's paradox or any similar paradox, e.g., "This
sentence is false", "This sentence is not true", "This sentence
is not provable".
On 2025-09-14 14:10:32 +0000, olcott said:
On 9/14/2025 4:36 AM, Mikko wrote:
On 2025-09-13 14:34:02 +0000, olcott said:
On 9/13/2025 3:46 AM, Mikko wrote:
On 2025-09-12 17:24:17 +0000, olcott said:
On 9/12/2025 2:23 AM, Mikko wrote:
On 2025-09-11 16:21:11 +0000, olcott said:
On 9/11/2025 4:43 AM, Mikko wrote:
On 2025-09-10 15:20:44 +0000, olcott said:This is within his false assumption that only
On 9/10/2025 3:17 AM, Mikko wrote:
On 2025-09-09 16:10:28 +0000, olcott said:
On 9/9/2025 1:57 AM, Mikko wrote:
On 2025-09-06 15:26:04 +0000, olcott said:
Not all all see my other reply about cycles
in directed graphs of resolution sequences.
Here your "not at all" says that you think that liar's >>>>>>>>>>>>> paradox is true.
*You got confused let me simplify*
Boolean True(Language L, Expression E);
X = "k*lsndesoiedfem,89234rm,dv0io9werf" // random gibberish >>>>>>>>>>>> -a True(English, X)==FALSE
~True(English, X)==TRUE
-a True(English, "this sentence is not true" )==FALSE
~True(English, "this sentence is not true" )==TRUE
This sentence is not true: "This sentence is not true" >>>>>>>>>>>> with the outer sentence referring to the inner sentence >>>>>>>>>>>> is the same as this: ~True(English, "This sentence is not >>>>>>>>>>>> true")
To me that is far less simple than "The liar paradox is not >>>>>>>>>>> true"
It is the way that we would correctly apply Tarski's
Boolean True(Language L, Expression E);
to the liar paradox.
The truth predicate Tarski was discussing has only one argument. >>>>>>>>
a single language exists.
No, it does not. Tarski does not assume so. The discussion is for a >>>>>>> truth predicate for one language only,
counter factual
counter factual
counter factual
counter factual
counter factual
counter factual
You should already know that "counter factual" does not work as
a magic spell. Nothing works if said six times instead of three
or nine.
He had the language of his theory and
the metalanguage of his metatheory
He had the language of his theory and
the metalanguage of his metatheory
He had the language of his theory and
the metalanguage of his metatheory
He had the language of his theory and
the metalanguage of his metatheory
I had to read and re-read his proof fifty times
to get a good understanding of it.
Apparently fifty times is not enough if you still don't know that
the proof is about one predicate that has one argument.
I said that the statement "Liar's paradox is not true" is true.
*IT IS NOT TRUE*
And here you say it again.
The outer sentence
The outer sentence
The outer sentence
The outer sentence
The outer sentence
is true
Yes, everyone can verify that I really said it. But your anser
"It is not true" quite clearly refers to the inner statement
that I said I had said.
Because the inner sentence is not true
The subordinate clause says that the "liar's paradox is not true"
is true. Becase the sentence "liar's paradox is not true" is true the
subordinate clause is true. The sentence "Liar's paradox is not true"
is true because because liar's paradox is not true. The liar's paradox
is not true beause it is not a truth-bearer.
That you say "it is not true" does not make anything untrue.
This sentence is not true: "This sentence is not true" is true
is the whole essence of Tarski's proof that no sufficiently complex
system can define its own truth predicate.
When we simply toss out "This sentence is not true" as not a
bearer of truth his whole argument falls apart.
No, it does not. If "This sentence is not true" is not a truth
bearer it is neither true nor false. That means that there is
no predicate that can correctly say that it is true and there
is no truth predicate that can correctly say that it is false.
So there cannot be any truth predicate over any domain where
"This sentence is not true" can be expressed.
Also even within Tarski's reasoning a system that includes
multiple levels of logic within the same system such as
my Minimal Type Theory (MTT) can define its own truth
predicate by having one order of logic refer to the
next lower order of logic.
Taski's proof does not assume that the logic is first order. Consequently
the proof that any theory of any order that includes arithmetic cannot
have a truth predicate.
Every first order theory can be extended to a higher order so every
first order proof is also a higher order proof.
On 9/15/2025 2:39 AM, Mikko wrote:
On 2025-09-14 14:12:47 +0000, olcott said:
On 9/14/2025 4:16 AM, Mikko wrote:
On 2025-09-13 13:18:25 +0000, olcott said:
On 9/13/2025 3:33 AM, Mikko wrote:
On 2025-09-12 17:08:30 +0000, olcott said:
On 9/12/2025 1:59 AM, Mikko wrote:
On 2025-09-11 15:52:58 +0000, olcott said:
On 9/11/2025 4:30 AM, Mikko wrote:
On 2025-09-10 15:14:53 +0000, olcott said:Yet the documentation that you dishonestly ignored does say
On 9/7/2025 3:27 AM, Mikko wrote:
On 2025-09-06 15:23:58 +0000, olcott said:
On 9/6/2025 3:25 AM, Mikko wrote:
On 2025-09-05 14:46:13 +0000, olcott said:
On 9/5/2025 2:31 AM, Mikko wrote:>>>That is not a definition but could be a valid starting point for >>>>>>>>>>>>>> a proof. One could also state that because it is not a truth- bearer
The first step of a proof is usually a definition. >>>>>>>>>>>>>>>Here is is: "this sentence is not true" within the >>>>>>>>>>>>>>> philosophy of logic it would be called not a truth >>>>>>>>>>>>>>> bearer because it cannot possibly have a truth value. >>>>>>>>>>>>>>
it cannot be provable in a consistent system.
*I mixed two things together*
A truth bearer is any expression of language that
possibly be resolved to a truth value. This includes >>>>>>>>>>>>> English declarative sentences and logical propositions. >>>>>>>>>>>>>
"This sentence is not true"
Cannot possibly be resolved to a truth value.
That makes communication very misleading rather than >>>>>>>>>>>>> effective. The best way to do this in natural language >>>>>>>>>>>>> is to choose an existing term with the closest meaning >>>>>>>>>>>>> and then specify the exact divergence from this conventional >>>>>>>>>>>>> meaning.If you try to
define a term that is alredy in use differently from its usual >>>>>>>>>>>>>>>> meaning that is sufficient to reject it without further review.
The above definition is conventional. It is also a standard >>>>>>>>>>>>>>> convention that when there is no word for a meaning that >>>>>>>>>>>>>>> the word with the closest existing meaning is used and becomes >>>>>>>>>>>>>>> a term of the art by adapting this meaning.
It is not always the word with the closest meaning. Sometimes a >>>>>>>>>>>>>> word with a meaning far from the needed meaning is chosen. >>>>>>>>>>>>>
In
any case one must be sure that the word is not needed for any >>>>>>>>>>>>>> other meaning in the same context.
The CYC project uses 128-bit GUIDs for unique meanings >>>>>>>>>>>>> that correspond to sense meanings of words or term-of-the-art >>>>>>>>>>>>> meanings of terms.
An important rule with the defined words is that they must not >>>>>>>>>>>>>> be used before the definition. Unless the definition is already >>>>>>>>>>>>>> well known
Such as truth bearer.
this includes the title and the abstract. In the
introduction one can say "will be defined" and then use the word.
If your first step is a premiss then reviewers must consdier >>>>>>>>>>>>>>>> whether it is acceptable or should be proven or can be rejected
as false.
That the Liar Paradox is not a truth bearer is proven >>>>>>>>>>>>>>> completely true by the meaning is these words.
Therefore it can be introduced as a premiss but it is better to >>>>>>>>>>>>>> do that only after the defintions, in particular the definition >>>>>>>>>>>>>> of "the Liar Paradox".
I always define the Liar Paradox as: "This sentence is not true" >>>>>>>>>>>>>
?- LP = not(true_(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Also proves that this is true, yet beyond what you >>>>>>>>>>>>>>> can comprehend.
It doesn't prove anything. Prolog merely executes the instructions
according to their standard semantics and implementation choices.
In particular,
Not at all.
What not at all? What is that intended to refer to?
Prolog does prove that the Liar Paradox has a
cycle in its resolution directed graph the same
way that I use Minimal Type Theory so show that
the G||del sentence has a cycle below.
Prolog does not say "a cycle in resolution graph". It says "false". >>>>>>>>>
The SWI-Prolog implementation of unify_with_occurs_check/2
is cycle-safe and only guards against creating cycles, not
against cycles that may already be present in one of the
arguments.
https://www.swi-prolog.org/pldoc/man? predicate=unify_with_occurs_check/2
You are right. The point that it may accept already existing cyclic >>>>>>>> structures must not be forgotten.
In other words when you don't have it look at
errors it will not report them.
At least SWI-Prolog doesn't look for already existing cycles. As
SWI-Prolog permits creation of such cyles it is reasonable to
regard them as non-errors.
They cause the system to get stuck in an infinite
loop and fail to answer.
Formal logic make sure to make self-reference
inexpressible that I why I extended the syntax
of FOPL to include the "defined as" operator :=
One must either be very careful with the := operator or make clear >>>>>> rules about self-references. The usual way, if := is permitted, is >>>>>> to require that the symbol on the left side is different from all
symbols used on the right side or anywhere earlier.
LP := ~True(LP)
which is only allowed in languages that don't prohibit the use fo the
same symbol on the left side and in the right side
means ~True(~True(~True(~True(~True(~True(~True(...))))))) forever
However, the system Tarski used does not have the := operator,
so the above is irrelevant to the topic as specified on the subject >>>>>> line.
The Liar Paradox DOES have a cycle in its
evaluation sequence. Tarski was stupid to
not see this.
The Liar Paradox has but Tarski's language does not. Tarski was not
stupid: he knew how to transform the liar's paradox to an expression
that does need the := operator or any other non-arithmetic operator.
He was profoundly brilliant on most things. On the Liar Paradox
specifying a cycle in its evaluation graph it seems that most
of humanity is stupid.
Perhaps most of humanity is stupid although only a small part is
stupic enough to shoe their naked stupidity to everyone. But that
does not matter. The topic of the discussion is Tarski, who was
not stupid.
Most people quickly see that it is not possibly to assign a truth
value to the liar's paradox. Some don't know what an "evaluation
graph" is but they can reach the same conclusion with different
thinking.
By detecting cycles in the evaluation graphs of
formalized expressions of language automated
systems can automatically reject such expressions
when they implement their truth predicate that
Tarski incorrectly proved cannot be implemented.
What is too hard for many but not everyone is that that
means that there cannot be a truth predicate over any domain that
includes the liar's paradox or any similar paradox, e.g., "This
sentence is false", "This sentence is not true", "This sentence
is not provable".
Likewise there cannot be any truth predicate over any
domain that has questions when people are stupid enough
to think that questions have a truth value.
On 9/15/2025 2:53 AM, Mikko wrote:
On 2025-09-14 14:10:32 +0000, olcott said:
On 9/14/2025 4:36 AM, Mikko wrote:
On 2025-09-13 14:34:02 +0000, olcott said:
On 9/13/2025 3:46 AM, Mikko wrote:
On 2025-09-12 17:24:17 +0000, olcott said:
On 9/12/2025 2:23 AM, Mikko wrote:
On 2025-09-11 16:21:11 +0000, olcott said:
On 9/11/2025 4:43 AM, Mikko wrote:
On 2025-09-10 15:20:44 +0000, olcott said:This is within his false assumption that only
On 9/10/2025 3:17 AM, Mikko wrote:
On 2025-09-09 16:10:28 +0000, olcott said:It is the way that we would correctly apply Tarski's
On 9/9/2025 1:57 AM, Mikko wrote:To me that is far less simple than "The liar paradox is not true" >>>>>>>>>>>
On 2025-09-06 15:26:04 +0000, olcott said:
Not all all see my other reply about cycles
in directed graphs of resolution sequences.
Here your "not at all" says that you think that liar's paradox is true.
*You got confused let me simplify*
Boolean True(Language L, Expression E);
X = "k*lsndesoiedfem,89234rm,dv0io9werf" // random gibberish >>>>>>>>>>>>> -a True(English, X)==FALSE
~True(English, X)==TRUE
-a True(English, "this sentence is not true" )==FALSE >>>>>>>>>>>>> ~True(English, "this sentence is not true" )==TRUE
This sentence is not true: "This sentence is not true" >>>>>>>>>>>>> with the outer sentence referring to the inner sentence >>>>>>>>>>>>> is the same as this: ~True(English, "This sentence is not true") >>>>>>>>>>>>
Boolean True(Language L, Expression E);
to the liar paradox.
The truth predicate Tarski was discussing has only one argument. >>>>>>>>>
a single language exists.
No, it does not. Tarski does not assume so. The discussion is for a >>>>>>>> truth predicate for one language only,
counter factual
counter factual
counter factual
counter factual
counter factual
counter factual
You should already know that "counter factual" does not work as
a magic spell. Nothing works if said six times instead of three
or nine.
He had the language of his theory and
the metalanguage of his metatheory
He had the language of his theory and
the metalanguage of his metatheory
He had the language of his theory and
the metalanguage of his metatheory
He had the language of his theory and
the metalanguage of his metatheory
I had to read and re-read his proof fifty times
to get a good understanding of it.
Apparently fifty times is not enough if you still don't know that
the proof is about one predicate that has one argument.
I said that the statement "Liar's paradox is not true" is true. >>>>>>>*IT IS NOT TRUE*
And here you say it again.
The outer sentence
The outer sentence
The outer sentence
The outer sentence
The outer sentence
is true
Yes, everyone can verify that I really said it. But your anser
"It is not true" quite clearly refers to the inner statement
that I said I had said.
Because the inner sentence is not true
The subordinate clause says that the "liar's paradox is not true"
is true. Becase the sentence "liar's paradox is not true" is true the >>>> subordinate clause is true. The sentence "Liar's paradox is not true"
is true because because liar's paradox is not true. The liar's paradox >>>> is not true beause it is not a truth-bearer.
That you say "it is not true" does not make anything untrue.
This sentence is not true: "This sentence is not true" is true
is the whole essence of Tarski's proof that no sufficiently complex
system can define its own truth predicate.
When we simply toss out "This sentence is not true" as not a
bearer of truth his whole argument falls apart.
No, it does not. If "This sentence is not true" is not a truth
bearer it is neither true nor false. That means that there is
no predicate that can correctly say that it is true and there
is no truth predicate that can correctly say that it is false.
So there cannot be any truth predicate over any domain where
"This sentence is not true" can be expressed.
Also even within Tarski's reasoning a system that includes
multiple levels of logic within the same system such as
my Minimal Type Theory (MTT) can define its own truth
predicate by having one order of logic refer to the
next lower order of logic.
Taski's proof does not assume that the logic is first order. Consequently
the proof that any theory of any order that includes arithmetic cannot
have a truth predicate.
Every first order theory can be extended to a higher order so every
first order proof is also a higher order proof.
He assumes that it is a single fixed order otherwise
the dumb bunny would understand that he could make
a truth predicate that formalizes:
This sentence is not true: "This sentence is not true"
at his two levels and do this in the same single formal system.
On 9/14/2025 11:58 AM, joes wrote:Neither is it false. Not being well-formed, it can't be negated.
Am Thu, 11 Sep 2025 11:21:11 -0500 schrieb olcott:
This gibberish: "klJK897BJHUYTDKJAoi8ew" is not true because it is"This sentence is not true" because it is not a truth bearer. When weIf it were not true, it would be saying the truth, making it wrong.
apply the same sentence to itself we get the Liar_Paradox_Squared this
new sentence becomes true because the inner sentence is not a truth
bearer.
gibberish.
True("klJK897BJHUYTDKJAoi8ew")==FALSE
~True("klJK897BJHUYTDKJAoi8ew")==TRUE
Am Mon, 15 Sep 2025 11:00:40 -0500 schrieb olcott:
On 9/14/2025 11:58 AM, joes wrote:
Am Thu, 11 Sep 2025 11:21:11 -0500 schrieb olcott:
Neither is it false. Not being well-formed, it can't be negated.This gibberish: "klJK897BJHUYTDKJAoi8ew" is not true because it is"This sentence is not true" because it is not a truth bearer. When weIf it were not true, it would be saying the truth, making it wrong.
apply the same sentence to itself we get the Liar_Paradox_Squared this >>>> new sentence becomes true because the inner sentence is not a truth
bearer.
gibberish.
True("klJK897BJHUYTDKJAoi8ew")==FALSE
~True("klJK897BJHUYTDKJAoi8ew")==TRUE
But I was talking about the liar sentence.
On 2025-09-15 16:16:29 +0000, olcott said:
On 9/15/2025 2:39 AM, Mikko wrote:
Most people quickly see that it is not possibly to assign a truth
value to the liar's paradox. Some don't know what an "evaluation
graph" is but they can reach the same conclusion with different
thinking.
By detecting cycles in the evaluation graphs of
formalized expressions of language automated
systems can automatically reject such expressions
when they implement their truth predicate that
Tarski incorrectly proved cannot be implemented.
Wrong. Most graphs that need be checked don't have truth values.
Checking for cycles is Turing computable, truth is not. The
reason the check is not always done is that it is a complex
computation that may cost more than the value of the result.
What is too hard for many but not everyone is that that
means that there cannot be a truth predicate over any domain that
includes the liar's paradox or any similar paradox, e.g., "This
sentence is false", "This sentence is not true", "This sentence
is not provable".
Likewise there cannot be any truth predicate over any
domain that has questions when people are stupid enough
to think that questions have a truth value.
Predicates only answer what a theory predicts. No theory about
stupidity of people is exact.
On 2025-09-15 16:19:57 +0000, olcott said:
On 9/15/2025 2:53 AM, Mikko wrote:
Taski's proof does not assume that the logic is first order.
Consequently
the proof that any theory of any order that includes arithmetic cannot
have a truth predicate.
Every first order theory can be extended to a higher order so every
first order proof is also a higher order proof.
He assumes that it is a single fixed order otherwise
the dumb bunny would understand that he could make
a truth predicate that formalizes:
This sentence is not true: "This sentence is not true"
at his two levels and do this in the same single formal system.
Every theory of any order contains all lower orders.
On 9/16/2025 3:54 AM, Mikko wrote:
On 2025-09-15 16:16:29 +0000, olcott said:
On 9/15/2025 2:39 AM, Mikko wrote:
Most people quickly see that it is not possibly to assign a truth
value to the liar's paradox. Some don't know what an "evaluation
graph" is but they can reach the same conclusion with different
thinking.
By detecting cycles in the evaluation graphs of
formalized expressions of language automated
systems can automatically reject such expressions
when they implement their truth predicate that
Tarski incorrectly proved cannot be implemented.
Wrong. Most graphs that need be checked don't have truth values.
I am not talking about most graphs.
I have restricted this to directed graphs of the
evaluation sequence of logic expressions.
Checking for cycles is Turing computable, truth is not. The
Every expression of language that is proven true on the
basis of other expressions of language (AKA analytic truth)
is Turing computable.
These same expressions form the body of analytic knowledge
that nitwit Willard Van Orman Quine convinced most everyone
does not exist.
On 9/16/2025 3:56 AM, Mikko wrote:
On 2025-09-15 16:19:57 +0000, olcott said:https://liarparadox.org/Tarski_275_276.pdf
On 9/15/2025 2:53 AM, Mikko wrote:
Taski's proof does not assume that the logic is first order. Consequently >>>> the proof that any theory of any order that includes arithmetic cannot >>>> have a truth predicate.
Every first order theory can be extended to a higher order so every
first order proof is also a higher order proof.
He assumes that it is a single fixed order otherwise
the dumb bunny would understand that he could make
a truth predicate that formalizes:
This sentence is not true: "This sentence is not true"
at his two levels and do this in the same single formal system.
Every theory of any order contains all lower orders.
That may be true, yet then why would Tarski say this:
the sentence x which is undecidable in the original
theory becomes a decidable sentence in the enriched theory.
These theories only vary by orders of logic.
On 9/16/2025 11:33 AM, joes wrote:
Am Mon, 15 Sep 2025 11:00:40 -0500 schrieb olcott:
On 9/14/2025 11:58 AM, joes wrote:Neither is it false. Not being well-formed, it can't be negated.
Am Thu, 11 Sep 2025 11:21:11 -0500 schrieb olcott:
This gibberish: "klJK897BJHUYTDKJAoi8ew" is not true because it is"This sentence is not true" because it is not a truth bearer. When we >>>>> apply the same sentence to itself we get the Liar_Paradox_Squared this >>>>> new sentence becomes true because the inner sentence is not a truthIf it were not true, it would be saying the truth, making it wrong.
bearer.
gibberish.
True("klJK897BJHUYTDKJAoi8ew")==FALSE
~True("klJK897BJHUYTDKJAoi8ew")==TRUE
But I was talking about the liar sentence.
It is not true that gibberish is true.
It is not true that gibberish is false.
This same thing goes for the Liar Paradox and Tarski didn't get it.
On 2025-09-16 20:22:28 +0000, olcott said:
On 9/16/2025 3:54 AM, Mikko wrote:
On 2025-09-15 16:16:29 +0000, olcott said:
On 9/15/2025 2:39 AM, Mikko wrote:
Most people quickly see that it is not possibly to assign a truth
value to the liar's paradox. Some don't know what an "evaluation
graph" is but they can reach the same conclusion with different
thinking.
By detecting cycles in the evaluation graphs of
formalized expressions of language automated
systems can automatically reject such expressions
when they implement their truth predicate that
Tarski incorrectly proved cannot be implemented.
Wrong. Most graphs that need be checked don't have truth values.
I am not talking about most graphs.
I have restricted this to directed graphs of the
evaluation sequence of logic expressions.
Checking for cycles is Turing computable, truth is not. The
Every expression of language that is proven true on the
basis of other expressions of language (AKA analytic truth)
is Turing computable.
If you already know that it is proven there is nothing to compute.
There is no Turing decider that can determine whether a sentence
is a theorem except for some simple theories. There is one for
the Abelian group theory but none for the group theory.
These same expressions form the body of analytic knowledge
that nitwit Willard Van Orman Quine convinced most everyone
does not exist.
Does the body of analytic knowledge include what is not yet known
but will be found in the future?
On 2025-09-16 20:27:05 +0000, olcott said:
On 9/16/2025 3:56 AM, Mikko wrote:
On 2025-09-15 16:19:57 +0000, olcott said:https://liarparadox.org/Tarski_275_276.pdf
On 9/15/2025 2:53 AM, Mikko wrote:
Taski's proof does not assume that the logic is first order.
Consequently
the proof that any theory of any order that includes arithmetic cannot >>>>> have a truth predicate.
Every first order theory can be extended to a higher order so every
first order proof is also a higher order proof.
He assumes that it is a single fixed order otherwise
the dumb bunny would understand that he could make
a truth predicate that formalizes:
This sentence is not true: "This sentence is not true"
at his two levels and do this in the same single formal system.
Every theory of any order contains all lower orders.
That may be true, yet then why would Tarski say this:
-a-a the sentence x which is undecidable in the original
-a-a theory becomes a decidable sentence in the enriched theory.
These theories only vary by orders of logic.
No, there are other extensions, too. And if the object theory already
is a higher order theory the enriched theory needs not be higher.
Tarski can say what he says because at that point he has already
proven both claims.
On 2025-09-16 20:12:45 +0000, olcott said:
On 9/16/2025 11:33 AM, joes wrote:
Am Mon, 15 Sep 2025 11:00:40 -0500 schrieb olcott:
On 9/14/2025 11:58 AM, joes wrote:Neither is it false. Not being well-formed, it can't be negated.
Am Thu, 11 Sep 2025 11:21:11 -0500 schrieb olcott:
This gibberish: "klJK897BJHUYTDKJAoi8ew" is not true because it is"This sentence is not true" because it is not a truth bearer. When we >>>>>> apply the same sentence to itself we get the Liar_Paradox_Squared >>>>>> thisIf it were not true, it would be saying the truth, making it wrong.
new sentence becomes true because the inner sentence is not a truth >>>>>> bearer.
gibberish.
True("klJK897BJHUYTDKJAoi8ew")==FALSE
~True("klJK897BJHUYTDKJAoi8ew")==TRUE
But I was talking about the liar sentence.
It is not true that gibberish is true.
It is not true that gibberish is false.
This same thing goes for the Liar Paradox and Tarski didn't get it.
That Tarski agrees with you is not quite sufficient to infer that Tarski didn't get it.
On 9/17/2025 2:43 AM, Mikko wrote:
On 2025-09-16 20:22:28 +0000, olcott said:
On 9/16/2025 3:54 AM, Mikko wrote:
On 2025-09-15 16:16:29 +0000, olcott said:
On 9/15/2025 2:39 AM, Mikko wrote:
Most people quickly see that it is not possibly to assign a truth
value to the liar's paradox. Some don't know what an "evaluation
graph" is but they can reach the same conclusion with different
thinking.
By detecting cycles in the evaluation graphs of
formalized expressions of language automated
systems can automatically reject such expressions
when they implement their truth predicate that
Tarski incorrectly proved cannot be implemented.
Wrong. Most graphs that need be checked don't have truth values.
I am not talking about most graphs.
I have restricted this to directed graphs of the
evaluation sequence of logic expressions.
Checking for cycles is Turing computable, truth is not. The
Every expression of language that is proven true on the
basis of other expressions of language (AKA analytic truth)
is Turing computable.
If you already know that it is proven there is nothing to compute.
Every expression of language that is proven true on the
basis of other expressions of language (AKA analytic truth)
Includes every expression of math or logic.
G||del's famous G simply becomes untrue in PA.
Tarski's:
"We shall show that the sentence x is
actually undecidable and at the same time true." https://liarparadox.org/Tarski_275_276.pdf
Cannot possibly occur.
On 9/17/2025 2:52 AM, Mikko wrote:
On 2025-09-16 20:27:05 +0000, olcott said:
On 9/16/2025 3:56 AM, Mikko wrote:
On 2025-09-15 16:19:57 +0000, olcott said:https://liarparadox.org/Tarski_275_276.pdf
On 9/15/2025 2:53 AM, Mikko wrote:
Taski's proof does not assume that the logic is first order. Consequently
the proof that any theory of any order that includes arithmetic cannot >>>>>> have a truth predicate.
Every first order theory can be extended to a higher order so every >>>>>> first order proof is also a higher order proof.
He assumes that it is a single fixed order otherwise
the dumb bunny would understand that he could make
a truth predicate that formalizes:
This sentence is not true: "This sentence is not true"
at his two levels and do this in the same single formal system.
Every theory of any order contains all lower orders.
That may be true, yet then why would Tarski say this:
-a-a the sentence x which is undecidable in the original
-a-a theory becomes a decidable sentence in the enriched theory.
These theories only vary by orders of logic.
No, there are other extensions, too. And if the object theory already
is a higher order theory the enriched theory needs not be higher.
Tarski can say what he says because at that point he has already
proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic. https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
On 9/17/2025 2:55 AM, Mikko wrote:
On 2025-09-16 20:12:45 +0000, olcott said:
On 9/16/2025 11:33 AM, joes wrote:
Am Mon, 15 Sep 2025 11:00:40 -0500 schrieb olcott:
On 9/14/2025 11:58 AM, joes wrote:Neither is it false. Not being well-formed, it can't be negated.
Am Thu, 11 Sep 2025 11:21:11 -0500 schrieb olcott:
gibberish."This sentence is not true" because it is not a truth bearer. When we >>>>>>> apply the same sentence to itself we get the Liar_Paradox_Squared this >>>>>>> new sentence becomes true because the inner sentence is not a truth >>>>>>> bearer.If it were not true, it would be saying the truth, making it wrong. >>>>> This gibberish: "klJK897BJHUYTDKJAoi8ew" is not true because it is
True("klJK897BJHUYTDKJAoi8ew")==FALSE
~True("klJK897BJHUYTDKJAoi8ew")==TRUE
But I was talking about the liar sentence.
It is not true that gibberish is true.
It is not true that gibberish is false.
This same thing goes for the Liar Paradox and Tarski didn't get it.
That Tarski agrees with you is not quite sufficient to infer that Tarski
didn't get it.
Tarski an otherwise profoundly brilliant man stupidly
anchored his whole Undefinability proof in the semantic
gibberish of the Liar Paradox.
On 2025-09-17 14:48:42 +0000, olcott said:
On 9/17/2025 2:43 AM, Mikko wrote:
On 2025-09-16 20:22:28 +0000, olcott said:
On 9/16/2025 3:54 AM, Mikko wrote:
On 2025-09-15 16:16:29 +0000, olcott said:
On 9/15/2025 2:39 AM, Mikko wrote:
Most people quickly see that it is not possibly to assign a truth >>>>>>> value to the liar's paradox. Some don't know what an "evaluation >>>>>>> graph" is but they can reach the same conclusion with different
thinking.
By detecting cycles in the evaluation graphs of
formalized expressions of language automated
systems can automatically reject such expressions
when they implement their truth predicate that
Tarski incorrectly proved cannot be implemented.
Wrong. Most graphs that need be checked don't have truth values.
I am not talking about most graphs.
I have restricted this to directed graphs of the
evaluation sequence of logic expressions.
Checking for cycles is Turing computable, truth is not. The
Every expression of language that is proven true on the
basis of other expressions of language (AKA analytic truth)
is Turing computable.
If you already know that it is proven there is nothing to compute.
Every expression of language that is proven true on the
basis of other expressions of language (AKA analytic truth)
Includes every expression of math or logic.
If every expression of your math or logic is proven true then
your math and logic are inconsistent.
G||del's famous G simply becomes untrue in PA.
Yet is says someting about natural numbers that is either true
or false.
Tarski's:
-a-a "We shall show that the sentence x is
-a-a-a actually undecidable and at the same time true."
https://liarparadox.org/Tarski_275_276.pdf
Cannot possibly occur.
The formal expression that the above refers to is proven true from
axioms and definitions with truth preserving transformations so it
is a part of analytic truth.
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:
No, there are other extensions, too. And if the object theory already
is a higher order theory the enriched theory needs not be higher.
Tarski can say what he says because at that point he has already
proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic.
https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF
Nice to see that you don't disagree.
On 2025-09-17 14:53:58 +0000, olcott said:
Tarski an otherwise profoundly brilliant man stupidly
anchored his whole Undefinability proof in the semantic
gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic gibberish.
On 9/18/2025 4:24 AM, Mikko wrote:
On 2025-09-17 14:48:42 +0000, olcott said:
On 9/17/2025 2:43 AM, Mikko wrote:
On 2025-09-16 20:22:28 +0000, olcott said:
On 9/16/2025 3:54 AM, Mikko wrote:
On 2025-09-15 16:16:29 +0000, olcott said:
On 9/15/2025 2:39 AM, Mikko wrote:
Most people quickly see that it is not possibly to assign a truth >>>>>>>> value to the liar's paradox. Some don't know what an "evaluation >>>>>>>> graph" is but they can reach the same conclusion with different >>>>>>>> thinking.
By detecting cycles in the evaluation graphs of
formalized expressions of language automated
systems can automatically reject such expressions
when they implement their truth predicate that
Tarski incorrectly proved cannot be implemented.
Wrong. Most graphs that need be checked don't have truth values.
I am not talking about most graphs.
I have restricted this to directed graphs of the
evaluation sequence of logic expressions.
Checking for cycles is Turing computable, truth is not. The
Every expression of language that is proven true on the
basis of other expressions of language (AKA analytic truth)
is Turing computable.
If you already know that it is proven there is nothing to compute.
Every expression of language that is proven true on the
basis of other expressions of language (AKA analytic truth)
Includes every expression of math or logic.
If every expression of your math or logic is proven true then
your math and logic are inconsistent.
Not at all. Unlike the screwballs of the past I don't
fully integrate expressions having pathological self-reference
into my formal system.
G||del's famous G simply becomes untrue in PA.
Yet is says someting about natural numbers that is either true
or false.
Bullshit G||del's own words say otherwise.
(c) G||del's 1931 Incompleteness theorem
rCLWe are therefore confronted with a proposition
which asserts its own unprovability.rCY (G||del 1931:40-41)
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:
No, there are other extensions, too. And if the object theory already
is a higher order theory the enriched theory needs not be higher.
Tarski can say what he says because at that point he has already
proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic.
https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF
Nice to see that you don't disagree.
I agree with you and thus we both disagree with Tarski.
Tarski has his Theory and his Meta-Theory that are separate.
This seems to be the same as FOPL and SOPL.
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said:
Tarski an otherwise profoundly brilliant man stupidly
anchored his whole Undefinability proof in the semantic
gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic gibberish.
This sentence is not true.
What it is not true about?
On 2025-09-18 14:38:27 +0000, olcott said:
On 9/18/2025 4:24 AM, Mikko wrote:
On 2025-09-17 14:48:42 +0000, olcott said:
On 9/17/2025 2:43 AM, Mikko wrote:
On 2025-09-16 20:22:28 +0000, olcott said:
On 9/16/2025 3:54 AM, Mikko wrote:
On 2025-09-15 16:16:29 +0000, olcott said:
On 9/15/2025 2:39 AM, Mikko wrote:
Most people quickly see that it is not possibly to assign a truth >>>>>>>>> value to the liar's paradox. Some don't know what an "evaluation >>>>>>>>> graph" is but they can reach the same conclusion with different >>>>>>>>> thinking.
By detecting cycles in the evaluation graphs of
formalized expressions of language automated
systems can automatically reject such expressions
when they implement their truth predicate that
Tarski incorrectly proved cannot be implemented.
Wrong. Most graphs that need be checked don't have truth values.
I am not talking about most graphs.
I have restricted this to directed graphs of the
evaluation sequence of logic expressions.
Checking for cycles is Turing computable, truth is not. The
Every expression of language that is proven true on the
basis of other expressions of language (AKA analytic truth)
is Turing computable.
If you already know that it is proven there is nothing to compute.
Every expression of language that is proven true on the
basis of other expressions of language (AKA analytic truth)
Includes every expression of math or logic.
If every expression of your math or logic is proven true then
your math and logic are inconsistent.
Not at all. Unlike the screwballs of the past I don't
fully integrate expressions having pathological self-reference
into my formal system.
The phrase "every expression of math or logic" includes "1 + 1 = 1".
You said that it is included is "every expression of language that
is proven true on the basis of other expressions of language".
Therefore "1 + 1 = 1" is proven true according to your logic.
But it is proven false in ordinary arithmetic. So you "1 + 1 = 1"
is both true and false, which is an inconsistency.
The term "consistent" is often defined as: a theroy is consisten
if some sentence in the language of the theory is not provable
in the theory.
G||del's famous G simply becomes untrue in PA.
Yet is says someting about natural numbers that is either true
or false.
Bullshit G||del's own words say otherwise.
(c) G||del's 1931 Incompleteness theorem
rCLWe are therefore confronted with a proposition
which asserts its own unprovability.rCY (G||del 1931:40-41)
Where "unprovability" means that it cannot be proven within the
first order theory of Peano arithmetic unless the first order
theory of Peano arithmetic is inconsistent.
But in the metatheory
G||del proved that that proposition has in a model of the first
order Peano arithmetic that proposition is true if it is not
provable in Peano arthmetic. The conclusion of the proof can be
expressed as G||del did above.
On 9/19/2025 4:19 AM, Mikko wrote:
On 2025-09-18 14:38:27 +0000, olcott said:
On 9/18/2025 4:24 AM, Mikko wrote:
On 2025-09-17 14:48:42 +0000, olcott said:
On 9/17/2025 2:43 AM, Mikko wrote:
On 2025-09-16 20:22:28 +0000, olcott said:
On 9/16/2025 3:54 AM, Mikko wrote:
On 2025-09-15 16:16:29 +0000, olcott said:I am not talking about most graphs.
On 9/15/2025 2:39 AM, Mikko wrote:
Most people quickly see that it is not possibly to assign a truth >>>>>>>>>> value to the liar's paradox. Some don't know what an "evaluation >>>>>>>>>> graph" is but they can reach the same conclusion with different >>>>>>>>>> thinking.
By detecting cycles in the evaluation graphs of
formalized expressions of language automated
systems can automatically reject such expressions
when they implement their truth predicate that
Tarski incorrectly proved cannot be implemented.
Wrong. Most graphs that need be checked don't have truth values. >>>>>>>
I have restricted this to directed graphs of the
evaluation sequence of logic expressions.
Checking for cycles is Turing computable, truth is not. The
Every expression of language that is proven true on the
basis of other expressions of language (AKA analytic truth)
is Turing computable.
If you already know that it is proven there is nothing to compute.
Every expression of language that is proven true on the
basis of other expressions of language (AKA analytic truth)
Includes every expression of math or logic.
If every expression of your math or logic is proven true then
your math and logic are inconsistent.
Not at all. Unlike the screwballs of the past I don't
fully integrate expressions having pathological self-reference
into my formal system.
The phrase "every expression of math or logic" includes "1 + 1 = 1".
You said that it is included is "every expression of language that
is proven true on the basis of other expressions of language".
Therefore "1 + 1 = 1" is proven true according to your logic.
But it is proven false in ordinary arithmetic. So you "1 + 1 = 1"
is both true and false, which is an inconsistency.
The term "consistent" is often defined as: a theroy is consisten
if some sentence in the language of the theory is not provable
in the theory.
G||del's famous G simply becomes untrue in PA.
Yet is says someting about natural numbers that is either true
or false.
Bullshit G||del's own words say otherwise.
(c) G||del's 1931 Incompleteness theorem
rCLWe are therefore confronted with a proposition
which asserts its own unprovability.rCY (G||del 1931:40-41)
Where "unprovability" means that it cannot be proven within the
first order theory of Peano arithmetic unless the first order
theory of Peano arithmetic is inconsistent.
Self-referential expressions are stupidly incorrect.
rCLWe are therefore confronted with a proposition
which asserts its own unprovability.rCY (G||del 1931:40-41)
On 2025-09-19 15:10:06 +0000, olcott said:
On 9/19/2025 4:19 AM, Mikko wrote:
On 2025-09-18 14:38:27 +0000, olcott said:
On 9/18/2025 4:24 AM, Mikko wrote:
On 2025-09-17 14:48:42 +0000, olcott said:
On 9/17/2025 2:43 AM, Mikko wrote:
On 2025-09-16 20:22:28 +0000, olcott said:Every expression of language that is proven true on the
On 9/16/2025 3:54 AM, Mikko wrote:
On 2025-09-15 16:16:29 +0000, olcott said:I am not talking about most graphs.
On 9/15/2025 2:39 AM, Mikko wrote:
Most people quickly see that it is not possibly to assign a >>>>>>>>>>> truth
value to the liar's paradox. Some don't know what an "evaluation >>>>>>>>>>> graph" is but they can reach the same conclusion with different >>>>>>>>>>> thinking.
By detecting cycles in the evaluation graphs of
formalized expressions of language automated
systems can automatically reject such expressions
when they implement their truth predicate that
Tarski incorrectly proved cannot be implemented.
Wrong. Most graphs that need be checked don't have truth values. >>>>>>>>
I have restricted this to directed graphs of the
evaluation sequence of logic expressions.
Checking for cycles is Turing computable, truth is not. The
Every expression of language that is proven true on the
basis of other expressions of language (AKA analytic truth)
is Turing computable.
If you already know that it is proven there is nothing to compute. >>>>>>
basis of other expressions of language (AKA analytic truth)
Includes every expression of math or logic.
If every expression of your math or logic is proven true then
your math and logic are inconsistent.
Not at all. Unlike the screwballs of the past I don't
fully integrate expressions having pathological self-reference
into my formal system.
The phrase "every expression of math or logic" includes "1 + 1 = 1".
You said that it is included is "every expression of language that
is proven true on the basis of other expressions of language".
Therefore "1 + 1 = 1" is proven true according to your logic.
But it is proven false in ordinary arithmetic. So you "1 + 1 = 1"
is both true and false, which is an inconsistency.
The term "consistent" is often defined as: a theroy is consisten
if some sentence in the language of the theory is not provable
in the theory.
G||del's famous G simply becomes untrue in PA.
Yet is says someting about natural numbers that is either true
or false.
Bullshit G||del's own words say otherwise.
(c) G||del's 1931 Incompleteness theorem
rCLWe are therefore confronted with a proposition
which asserts its own unprovability.rCY (G||del 1931:40-41)
Where "unprovability" means that it cannot be proven within the
first order theory of Peano arithmetic unless the first order
theory of Peano arithmetic is inconsistent.
Self-referential expressions are stupidly incorrect.
rCLWe are therefore confronted with a proposition
-a which asserts its own unprovability.rCY (G||del 1931:40-41)
G||del's sentence is not really self-referential. It is a valid
sentence in the first order language of Peano arithmetic. That
the value of an arithmetic expression in that sentence evaluates
to the G||del number of the sentence has no arithmetic significance.
On 2025-09-18 14:47:10 +0000, olcott said:
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said:
Tarski an otherwise profoundly brilliant man stupidly
anchored his whole Undefinability proof in the semantic
gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic gibberish.
This sentence is not true.
What it is not true about?
The sentence claims that it is not true about itself.
On 2025-09-18 14:42:11 +0000, olcott said:
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:
No, there are other extensions, too. And if the object theory already >>>>> is a higher order theory the enriched theory needs not be higher.
Tarski can say what he says because at that point he has already
proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic.
https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF
Nice to see that you don't disagree.
I agree with you and thus we both disagree with Tarski.
Tarski has his Theory and his Meta-Theory that are separate.
This seems to be the same as FOPL and SOPL.
When You and Tarski and I say that "The Liar's paradox is not true"
then we all agree.
On 9/20/2025 4:31 AM, Mikko wrote:
On 2025-09-19 15:10:06 +0000, olcott said:
On 9/19/2025 4:19 AM, Mikko wrote:
On 2025-09-18 14:38:27 +0000, olcott said:
On 9/18/2025 4:24 AM, Mikko wrote:
On 2025-09-17 14:48:42 +0000, olcott said:
On 9/17/2025 2:43 AM, Mikko wrote:
On 2025-09-16 20:22:28 +0000, olcott said:Every expression of language that is proven true on the
On 9/16/2025 3:54 AM, Mikko wrote:
On 2025-09-15 16:16:29 +0000, olcott said:I am not talking about most graphs.
On 9/15/2025 2:39 AM, Mikko wrote:
Most people quickly see that it is not possibly to assign a truth >>>>>>>>>>>> value to the liar's paradox. Some don't know what an "evaluation >>>>>>>>>>>> graph" is but they can reach the same conclusion with different >>>>>>>>>>>> thinking.
By detecting cycles in the evaluation graphs of
formalized expressions of language automated
systems can automatically reject such expressions
when they implement their truth predicate that
Tarski incorrectly proved cannot be implemented.
Wrong. Most graphs that need be checked don't have truth values. >>>>>>>>>
I have restricted this to directed graphs of the
evaluation sequence of logic expressions.
Checking for cycles is Turing computable, truth is not. The >>>>>>>>>Every expression of language that is proven true on the
basis of other expressions of language (AKA analytic truth)
is Turing computable.
If you already know that it is proven there is nothing to compute. >>>>>>>
basis of other expressions of language (AKA analytic truth)
Includes every expression of math or logic.
If every expression of your math or logic is proven true then
your math and logic are inconsistent.
Not at all. Unlike the screwballs of the past I don't
fully integrate expressions having pathological self-reference
into my formal system.
The phrase "every expression of math or logic" includes "1 + 1 = 1".
You said that it is included is "every expression of language that
is proven true on the basis of other expressions of language".
Therefore "1 + 1 = 1" is proven true according to your logic.
But it is proven false in ordinary arithmetic. So you "1 + 1 = 1"
is both true and false, which is an inconsistency.
The term "consistent" is often defined as: a theroy is consisten
if some sentence in the language of the theory is not provable
in the theory.
G||del's famous G simply becomes untrue in PA.
Yet is says someting about natural numbers that is either true
or false.
Bullshit G||del's own words say otherwise.
(c) G||del's 1931 Incompleteness theorem
rCLWe are therefore confronted with a proposition
which asserts its own unprovability.rCY (G||del 1931:40-41)
Where "unprovability" means that it cannot be proven within the
first order theory of Peano arithmetic unless the first order
theory of Peano arithmetic is inconsistent.
Self-referential expressions are stupidly incorrect.
rCLWe are therefore confronted with a proposition
-a which asserts its own unprovability.rCY (G||del 1931:40-41)
G||del's sentence is not really self-referential. It is a valid
sentence in the first order language of Peano arithmetic. That
the value of an arithmetic expression in that sentence evaluates
to the G||del number of the sentence has no arithmetic significance.
Yes that is the moronic received view yet these stupid
people stupidly ignore G||del's own words.
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ... ...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...
...We are therefore confronted with a proposition which asserts its own unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
On 9/19/2025 4:20 AM, Mikko wrote:
On 2025-09-18 14:42:11 +0000, olcott said:
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:
No, there are other extensions, too. And if the object theory already >>>>>> is a higher order theory the enriched theory needs not be higher.
Tarski can say what he says because at that point he has already
proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic.
https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF
Nice to see that you don't disagree.
I agree with you and thus we both disagree with Tarski.
Tarski has his Theory and his Meta-Theory that are separate.
This seems to be the same as FOPL and SOPL.
When You and Tarski and I say that "The Liar's paradox is not true"
then we all agree.
Its not false either.
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said:
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said:
Tarski an otherwise profoundly brilliant man stupidly
anchored his whole Undefinability proof in the semantic
gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic gibberish.
This sentence is not true.
What it is not true about?
The sentence claims that it is not true about itself.
In an infinitely recursive chain that you dishonestly
erased.
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
G||del's sentence is not really self-referential. It is a valid
sentence in the first order language of Peano arithmetic. That
the value of an arithmetic expression in that sentence evaluates
to the G||del number of the sentence has no arithmetic significance.
Yes that is the moronic received view yet these stupid
people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...
...We are therefore confronted with a proposition which asserts its
own unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
The most important aspect is the theorem itself: every theory that
has the symbols and axioms of the first order Peano arithmetic is
either incomplete or inconsistent.
The incompleteness theorem is called a teorem because it is inferred from
the axioms of Peano arithmetic with truth preserving transformations.
On 2025-09-20 15:03:01 +0000, olcott said:
On 9/19/2025 4:20 AM, Mikko wrote:
On 2025-09-18 14:42:11 +0000, olcott said:
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:
No, there are other extensions, too. And if the object theory
already
is a higher order theory the enriched theory needs not be higher. >>>>>>> Tarski can say what he says because at that point he has already >>>>>>> proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic.
https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF
Nice to see that you don't disagree.
I agree with you and thus we both disagree with Tarski.
Tarski has his Theory and his Meta-Theory that are separate.
This seems to be the same as FOPL and SOPL.
When You and Tarski and I say that "The Liar's paradox is not true"
then we all agree.
Its not false either.
That fact is not needed for the proof. What matters is that because
it is not true it cannot be provable.
On 2025-09-20 14:58:33 +0000, olcott said:
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said:
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said:This sentence is not true.
Tarski an otherwise profoundly brilliant man stupidly
anchored his whole Undefinability proof in the semantic
gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic gibberish. >>>>
What it is not true about?
The sentence claims that it is not true about itself.
In an infinitely recursive chain that you dishonestly
erased.
No, that meaning can be found without considering any recursion.
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
G||del's sentence is not really self-referential. It is a valid
sentence in the first order language of Peano arithmetic. That
the value of an arithmetic expression in that sentence evaluates
to the G||del number of the sentence has no arithmetic significance.
Yes that is the moronic received view yet these stupid
people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ... >>> ...14 Every epistemological antinomy can likewise be used for a similar >>> undecidability proof...
...We are therefore confronted with a proposition which asserts its own >>> unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
The most important aspect is the theorem itself: every theory that
has the symbols and axioms of the first order Peano arithmetic is
either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
An expression of language claims through an enormously
convoluted mess that itself is not provable.
G||del himself summed it up that way (see quotes).
He merely took the classic incorrect question:
Is this sentence true or false:
"This sentence is not true" adapted it slightly
and converted into convoluted math.
The incompleteness theorem is called a teorem because it is inferred from
the axioms of Peano arithmetic with truth preserving transformations.
Yes that is just his bullshit misdirection.
He already laid out his whole game in simple
English above.
On 9/21/2025 4:25 AM, Mikko wrote:
On 2025-09-20 15:03:01 +0000, olcott said:
On 9/19/2025 4:20 AM, Mikko wrote:
On 2025-09-18 14:42:11 +0000, olcott said:
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:
No, there are other extensions, too. And if the object theory already >>>>>>>> is a higher order theory the enriched theory needs not be higher. >>>>>>>> Tarski can say what he says because at that point he has already >>>>>>>> proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic.
https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF
Nice to see that you don't disagree.
I agree with you and thus we both disagree with Tarski.
Tarski has his Theory and his Meta-Theory that are separate.
This seems to be the same as FOPL and SOPL.
When You and Tarski and I say that "The Liar's paradox is not true"
then we all agree.
Its not false either.
That fact is not needed for the proof. What matters is that because
it is not true it cannot be provable.
Yes and the square root of a dead chicken
is uncomputable for the same reason.
On 9/21/2025 4:26 AM, Mikko wrote:
On 2025-09-20 14:58:33 +0000, olcott said:
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said:
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said:This sentence is not true.
Tarski an otherwise profoundly brilliant man stupidly
anchored his whole Undefinability proof in the semantic
gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic gibberish. >>>>>
What it is not true about?
The sentence claims that it is not true about itself.
In an infinitely recursive chain that you dishonestly
erased.
No, that meaning can be found without considering any recursion.
The meaning is that it is not a truth bearer
thus has no truth value.
On 2025-09-23 00:57:36 +0000, olcott said:
On 9/21/2025 4:25 AM, Mikko wrote:
On 2025-09-20 15:03:01 +0000, olcott said:
On 9/19/2025 4:20 AM, Mikko wrote:
On 2025-09-18 14:42:11 +0000, olcott said:
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:
No, there are other extensions, too. And if the object theory >>>>>>>>> already
is a higher order theory the enriched theory needs not be higher. >>>>>>>>> Tarski can say what he says because at that point he has already >>>>>>>>> proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic.
https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF
Nice to see that you don't disagree.
I agree with you and thus we both disagree with Tarski.
Tarski has his Theory and his Meta-Theory that are separate.
This seems to be the same as FOPL and SOPL.
When You and Tarski and I say that "The Liar's paradox is not true"
then we all agree.
Its not false either.
That fact is not needed for the proof. What matters is that because
it is not true it cannot be provable.
Yes and the square root of a dead chicken
is uncomputable for the same reason.
Nice to see that you don't disagree.
On 2025-09-23 00:59:54 +0000, olcott said:
On 9/21/2025 4:26 AM, Mikko wrote:
On 2025-09-20 14:58:33 +0000, olcott said:
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said:
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said:
Tarski an otherwise profoundly brilliant man stupidly
anchored his whole Undefinability proof in the semantic
gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic
gibberish.
This sentence is not true.
What it is not true about?
The sentence claims that it is not true about itself.
In an infinitely recursive chain that you dishonestly
erased.
No, that meaning can be found without considering any recursion.
The meaning is that it is not a truth bearer
thus has no truth value.
If the sentence "This sentence is not true" has no truth value then
it is not true.
On 2025-09-23 00:56:19 +0000, olcott said:
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
G||del's sentence is not really self-referential. It is a valid
sentence in the first order language of Peano arithmetic. That
the value of an arithmetic expression in that sentence evaluates
to the G||del number of the sentence has no arithmetic significance.
Yes that is the moronic received view yet these stupid
people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ... >>>> ...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...
...We are therefore confronted with a proposition which asserts its
own unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
The most important aspect is the theorem itself: every theory that
has the symbols and axioms of the first order Peano arithmetic is
either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important.
Many poeple also
find it useful to know that any attempt to construct a cmplete theory
of arithemtic would be a waste of time.
An expression of language claims through an enormously
convoluted mess that itself is not provable.
G||del himself summed it up that way (see quotes).
That is, if the sentence is true it is unprovable. If it is false
and arithmetic is consistent it is unprovable. If it is provable
then it is false and arithmetic is inconsistent.
He merely took the classic incorrect question:
Is this sentence true or false:
"This sentence is not true" adapted it slightly
and converted into convoluted math.
The metamathematical proof proves that the sentence is true only if
it is unprovable. As it is unprovable there is a model of first order arithmetic where the sentence is false but that model is not the one
that we consider the space of natural numbers.
The incompleteness theorem is called a teorem because it is inferred
from
the axioms of Peano arithmetic with truth preserving transformations.
Yes that is just his bullshit misdirection.
He already laid out his whole game in simple
English above.
Analytic truth is what can be proven, including G||del's incompleteness theorem and Tarski's undefinability theorem. That you don't understand
the proofs is irrelevant.
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said:
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
Yes that is the moronic received view yet these stupid
G||del's sentence is not really self-referential. It is a valid
sentence in the first order language of Peano arithmetic. That
the value of an arithmetic expression in that sentence evaluates
to the G||del number of the sentence has no arithmetic significance. >>>>>
people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ... >>>>> ...14 Every epistemological antinomy can likewise be used for a similar >>>>> undecidability proof...
...We are therefore confronted with a proposition which asserts its own >>>>> unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
The most important aspect is the theorem itself: every theory that
has the symbols and axioms of the first order Peano arithmetic is
either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important.
Prior to Pythagoras there was a universal consensus
that the Earth is flat.
Many poeple also
find it useful to know that any attempt to construct a cmplete theory
of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is screwed up.
If you want to build a formal system that is not anchored in a
screwed up idea than this is straight forward.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply
the truth preserving operation of semantic logical entailment
to these basic facts.
Anything not derived on this basis is either untrue or unknown.
Screwy stuff such as an expression of language asserting its own unprovability is rejected as not a truth bearer.
On 9/23/2025 4:23 AM, Mikko wrote:
On 2025-09-23 00:57:36 +0000, olcott said:
On 9/21/2025 4:25 AM, Mikko wrote:
On 2025-09-20 15:03:01 +0000, olcott said:
On 9/19/2025 4:20 AM, Mikko wrote:
On 2025-09-18 14:42:11 +0000, olcott said:
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:
No, there are other extensions, too. And if the object theory already
is a higher order theory the enriched theory needs not be higher. >>>>>>>>>> Tarski can say what he says because at that point he has already >>>>>>>>>> proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic.
https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF
Nice to see that you don't disagree.
I agree with you and thus we both disagree with Tarski.
Tarski has his Theory and his Meta-Theory that are separate.
This seems to be the same as FOPL and SOPL.
When You and Tarski and I say that "The Liar's paradox is not true" >>>>>> then we all agree.
Its not false either.
That fact is not needed for the proof. What matters is that because
it is not true it cannot be provable.
Yes and the square root of a dead chicken
is uncomputable for the same reason.
Nice to see that you don't disagree.
Computation is not limited when it is required
to answer any question that has no correct answer.
On 9/23/2025 4:29 AM, Mikko wrote:
On 2025-09-23 00:59:54 +0000, olcott said:
On 9/21/2025 4:26 AM, Mikko wrote:
On 2025-09-20 14:58:33 +0000, olcott said:
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said:
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said:This sentence is not true.
Tarski an otherwise profoundly brilliant man stupidly
anchored his whole Undefinability proof in the semantic
gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic gibberish. >>>>>>>
What it is not true about?
The sentence claims that it is not true about itself.
In an infinitely recursive chain that you dishonestly
erased.
No, that meaning can be found without considering any recursion.
The meaning is that it is not a truth bearer
thus has no truth value.
If the sentence "This sentence is not true" has no truth value then
it is not true.
And it is not false, thus must be rejected
as not a member of any formal logic system
thus cannot form a basis for any Undefinability proof.
On 2025-09-23 16:04:38 +0000, olcott said:
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said:
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
Yes that is the moronic received view yet these stupid
G||del's sentence is not really self-referential. It is a valid
sentence in the first order language of Peano arithmetic. That
the value of an arithmetic expression in that sentence evaluates >>>>>>> to the G||del number of the sentence has no arithmetic significance. >>>>>>
people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...
...We are therefore confronted with a proposition which asserts
its own unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And >>>>>> Related Systems
The most important aspect is the theorem itself: every theory that
has the symbols and axioms of the first order Peano arithmetic is
either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important.
Prior to Pythagoras there was a universal consensus
that the Earth is flat.
To think the Earth as flat is simpler and good enough for many
purposes. For a long time there was no need to think about the
shape of the Earth.
Many poeple also
find it useful to know that any attempt to construct a cmplete theory
of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is screwed up.
If you want to build a formal system that is not anchored in a
screwed up idea than this is straight forward.
That 2 + 3 = 5 has practical value even if the theory around it
cannot be made complete.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply
the truth preserving operation of semantic logical entailment
to these basic facts.
It is generally accepted that the set of axioms can be infinite
as long as it is Turing computable whether a sentence is an
axiom. It is also required that the correctness of an inference
is Turing computable. With these requirements one can ensure
that the correctness of every proof is Turing computable.
Anything not derived on this basis is either untrue or unknown.
Screwy stuff such as an expression of language asserting its own
unprovability is rejected as not a truth bearer.
Numbers are not required to be truth-bearers. That a sentence of
arithmetic can be encoded as a number is not part of arithmetics
and does not affect the validity of that number.
On 2025-09-23 15:37:27 +0000, olcott said:
On 9/23/2025 4:23 AM, Mikko wrote:
On 2025-09-23 00:57:36 +0000, olcott said:
On 9/21/2025 4:25 AM, Mikko wrote:
On 2025-09-20 15:03:01 +0000, olcott said:
On 9/19/2025 4:20 AM, Mikko wrote:
On 2025-09-18 14:42:11 +0000, olcott said:
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:
No, there are other extensions, too. And if the object theory >>>>>>>>>>> already
is a higher order theory the enriched theory needs not be >>>>>>>>>>> higher.
Tarski can say what he says because at that point he has already >>>>>>>>>>> proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic.
https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF
Nice to see that you don't disagree.
I agree with you and thus we both disagree with Tarski.
Tarski has his Theory and his Meta-Theory that are separate.
This seems to be the same as FOPL and SOPL.
When You and Tarski and I say that "The Liar's paradox is not true" >>>>>>> then we all agree.
Its not false either.
That fact is not needed for the proof. What matters is that because
it is not true it cannot be provable.
Yes and the square root of a dead chicken
is uncomputable for the same reason.
Nice to see that you don't disagree.
Computation is not limited when it is required
to answer any question that has no correct answer.
Irrelevant to Tarski's undefinability theorem. Atirhmetic truth is a
valid an important concept even when not formally definable.
On 2025-09-23 15:39:53 +0000, olcott said:
On 9/23/2025 4:29 AM, Mikko wrote:
On 2025-09-23 00:59:54 +0000, olcott said:
On 9/21/2025 4:26 AM, Mikko wrote:
On 2025-09-20 14:58:33 +0000, olcott said:
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said:
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said:
Tarski an otherwise profoundly brilliant man stupidly
anchored his whole Undefinability proof in the semantic
gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic
gibberish.
This sentence is not true.
What it is not true about?
The sentence claims that it is not true about itself.
In an infinitely recursive chain that you dishonestly
erased.
No, that meaning can be found without considering any recursion.
The meaning is that it is not a truth bearer
thus has no truth value.
If the sentence "This sentence is not true" has no truth value then
it is not true.
And it is not false, thus must be rejected
as not a member of any formal logic system
thus cannot form a basis for any Undefinability proof.
The sentence "The sentence 'This sentence is not true' is not true"
is true and can be used as an element of a proof.
On 9/24/2025 2:12 AM, Mikko wrote:
On 2025-09-23 16:04:38 +0000, olcott said:
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said:
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
Yes that is the moronic received view yet these stupid
G||del's sentence is not really self-referential. It is a valid >>>>>>>> sentence in the first order language of Peano arithmetic. That >>>>>>>> the value of an arithmetic expression in that sentence evaluates >>>>>>>> to the G||del number of the sentence has no arithmetic significance. >>>>>>>
people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 Incompleteness theorem >>>>>>> are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...
...We are therefore confronted with a proposition which asserts its own
unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And >>>>>>> Related Systems
The most important aspect is the theorem itself: every theory that >>>>>> has the symbols and axioms of the first order Peano arithmetic is
either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important.
Prior to Pythagoras there was a universal consensus
that the Earth is flat.
To think the Earth as flat is simpler and good enough for many
purposes. For a long time there was no need to think about the
shape of the Earth.
The point is that not even a universal consensus equates to truth.
Many poeple also
find it useful to know that any attempt to construct a cmplete theory
of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is screwed up.
If you want to build a formal system that is not anchored in a
screwed up idea than this is straight forward.
That 2 + 3 = 5 has practical value even if the theory around it
cannot be made complete.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply
the truth preserving operation of semantic logical entailment
to these basic facts.
It is generally accepted that the set of axioms can be infinite
Not when we are representing the finite set of human general knowledge.
as long as it is Turing computable whether a sentence is an
axiom. It is also required that the correctness of an inference
is Turing computable. With these requirements one can ensure
that the correctness of every proof is Turing computable.
You are totally missing the point. I redefined the notion
of a formal system such that incompleteness is impossible.
On 9/24/2025 2:15 AM, Mikko wrote:
On 2025-09-23 15:37:27 +0000, olcott said:
On 9/23/2025 4:23 AM, Mikko wrote:
On 2025-09-23 00:57:36 +0000, olcott said:
On 9/21/2025 4:25 AM, Mikko wrote:
On 2025-09-20 15:03:01 +0000, olcott said:
On 9/19/2025 4:20 AM, Mikko wrote:
On 2025-09-18 14:42:11 +0000, olcott said:
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:
No, there are other extensions, too. And if the object theory already
is a higher order theory the enriched theory needs not be higher. >>>>>>>>>>>> Tarski can say what he says because at that point he has already >>>>>>>>>>>> proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic.
https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF
Nice to see that you don't disagree.
I agree with you and thus we both disagree with Tarski.
Tarski has his Theory and his Meta-Theory that are separate. >>>>>>>>> This seems to be the same as FOPL and SOPL.
When You and Tarski and I say that "The Liar's paradox is not true" >>>>>>>> then we all agree.
Its not false either.
That fact is not needed for the proof. What matters is that because >>>>>> it is not true it cannot be provable.
Yes and the square root of a dead chicken
is uncomputable for the same reason.
Nice to see that you don't disagree.
Computation is not limited when it is required
to answer any question that has no correct answer.
Irrelevant to Tarski's undefinability theorem. Atirhmetic truth is a
valid an important concept even when not formally definable.
Tarski merely did the same thing as G||del yet did this
much more succinctly and clearly.
He mathematized an ordinary English expression of
language that is not a truth bearer and anchored his
formal proof in an expression that cannot be a member
of any formal logic system.
On 9/24/2025 2:19 AM, Mikko wrote:
On 2025-09-23 15:39:53 +0000, olcott said:
On 9/23/2025 4:29 AM, Mikko wrote:
On 2025-09-23 00:59:54 +0000, olcott said:
On 9/21/2025 4:26 AM, Mikko wrote:
On 2025-09-20 14:58:33 +0000, olcott said:
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said:
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said:
Tarski an otherwise profoundly brilliant man stupidly
anchored his whole Undefinability proof in the semantic
gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic gibberish.
This sentence is not true.
What it is not true about?
The sentence claims that it is not true about itself.
In an infinitely recursive chain that you dishonestly
erased.
No, that meaning can be found without considering any recursion.
The meaning is that it is not a truth bearer
thus has no truth value.
If the sentence "This sentence is not true" has no truth value then
it is not true.
And it is not false, thus must be rejected
as not a member of any formal logic system
thus cannot form a basis for any Undefinability proof.
The sentence "The sentence 'This sentence is not true' is not true"
is true and can be used as an element of a proof.
Yes and likewise with this:
"The sentence 'What time is it?' is not true".
Thus in neither case does this prevent a Truth
predicate from being defined at the same logic level.
On 2025-09-24 14:27:00 +0000, olcott said:
On 9/24/2025 2:12 AM, Mikko wrote:
On 2025-09-23 16:04:38 +0000, olcott said:
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said:
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
G||del's sentence is not really self-referential. It is a valid >>>>>>>>> sentence in the first order language of Peano arithmetic. That >>>>>>>>> the value of an arithmetic expression in that sentence evaluates >>>>>>>>> to the G||del number of the sentence has no arithmetic
significance.
Yes that is the moronic received view yet these stupid
people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 Incompleteness theorem >>>>>>>> are these plain English direct quotes of G||del from his paper: >>>>>>>>
...there is also a close relationship with the rCLliarrCY
antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a >>>>>>>> similar undecidability proof...
...We are therefore confronted with a proposition which asserts >>>>>>>> its own unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica >>>>>>>> And Related Systems
The most important aspect is the theorem itself: every theory that >>>>>>> has the symbols and axioms of the first order Peano arithmetic is >>>>>>> either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important.
Prior to Pythagoras there was a universal consensus
that the Earth is flat.
To think the Earth as flat is simpler and good enough for many
purposes. For a long time there was no need to think about the
shape of the Earth.
The point is that not even a universal consensus equates to truth.
No, but it is a significant aspect of culture. A question of importance
is not a matter of truth but a matter of opinion.
Many poeple also
find it useful to know that any attempt to construct a cmplete theory >>>>> of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is screwed up.
If you want to build a formal system that is not anchored in a
screwed up idea than this is straight forward.
That 2 + 3 = 5 has practical value even if the theory around it
cannot be made complete.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply
the truth preserving operation of semantic logical entailment
to these basic facts.
It is generally accepted that the set of axioms can be infinite
Not when we are representing the finite set of human general knowledge.
Once again you try to deceive with a change of topic. There is no
need to prove the incompletenes of human general knowledge as that
already is obvious. But G||del's and Tarski's theorems are about
natural number arithmetic and its extensions so they need to cover
the possibility that there are infinitely many axioms.
as long as it is Turing computable whether a sentence is an
axiom. It is also required that the correctness of an inference
is Turing computable. With these requirements one can ensure
that the correctness of every proof is Turing computable.
You are totally missing the point. I redefined the notion
of a formal system such that incompleteness is impossible.
Consequently your results are irrelevant to systems that G||del's and Tarski's results apply to.
On 2025-09-24 14:31:55 +0000, olcott said:
On 9/24/2025 2:15 AM, Mikko wrote:
On 2025-09-23 15:37:27 +0000, olcott said:
On 9/23/2025 4:23 AM, Mikko wrote:
On 2025-09-23 00:57:36 +0000, olcott said:
On 9/21/2025 4:25 AM, Mikko wrote:
On 2025-09-20 15:03:01 +0000, olcott said:
On 9/19/2025 4:20 AM, Mikko wrote:
On 2025-09-18 14:42:11 +0000, olcott said:
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:
No, there are other extensions, too. And if the object >>>>>>>>>>>>> theory already
is a higher order theory the enriched theory needs not be >>>>>>>>>>>>> higher.
Tarski can say what he says because at that point he has >>>>>>>>>>>>> already
proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic.
https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF
Nice to see that you don't disagree.
I agree with you and thus we both disagree with Tarski.
Tarski has his Theory and his Meta-Theory that are separate. >>>>>>>>>> This seems to be the same as FOPL and SOPL.
When You and Tarski and I say that "The Liar's paradox is not >>>>>>>>> true"
then we all agree.
Its not false either.
That fact is not needed for the proof. What matters is that because >>>>>>> it is not true it cannot be provable.
Yes and the square root of a dead chicken
is uncomputable for the same reason.
Nice to see that you don't disagree.
Computation is not limited when it is required
to answer any question that has no correct answer.
Irrelevant to Tarski's undefinability theorem. Atirhmetic truth is a
valid an important concept even when not formally definable.
Tarski merely did the same thing as G||del yet did this
much more succinctly and clearly.
Not really, he applied the methods G||del had already developed to
a different problem.
He mathematized an ordinary English expression of
language that is not a truth bearer and anchored his
formal proof in an expression that cannot be a member
of any formal logic system.
No, he did not do that. The expressions he considered were not of
ordinary English (or Polish or German) but of a formal theory of
natural numbers and possibly some additional things.
On 2025-09-24 14:36:46 +0000, olcott said:
On 9/24/2025 2:19 AM, Mikko wrote:
On 2025-09-23 15:39:53 +0000, olcott said:
On 9/23/2025 4:29 AM, Mikko wrote:
On 2025-09-23 00:59:54 +0000, olcott said:
On 9/21/2025 4:26 AM, Mikko wrote:
On 2025-09-20 14:58:33 +0000, olcott said:
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said:
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said:
Tarski an otherwise profoundly brilliant man stupidly
anchored his whole Undefinability proof in the semantic >>>>>>>>>>>> gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic >>>>>>>>>>> gibberish.
This sentence is not true.
What it is not true about?
The sentence claims that it is not true about itself.
In an infinitely recursive chain that you dishonestly
erased.
No, that meaning can be found without considering any recursion.
The meaning is that it is not a truth bearer
thus has no truth value.
If the sentence "This sentence is not true" has no truth value then
it is not true.
And it is not false, thus must be rejected
as not a member of any formal logic system
thus cannot form a basis for any Undefinability proof.
The sentence "The sentence 'This sentence is not true' is not true"
is true and can be used as an element of a proof.
Yes and likewise with this:
"The sentence 'What time is it?' is not true".
Thus in neither case does this prevent a Truth
predicate from being defined at the same logic level.
Not in any obvious way but turns out that if there is a definable truth predicate then there is a proof of a false sentence that asserts its
own unprovability, i.e., the arithmetic with a definable truth predicate
is provably inconsistent.
On 9/25/2025 2:24 AM, Mikko wrote:
On 2025-09-24 14:31:55 +0000, olcott said:
On 9/24/2025 2:15 AM, Mikko wrote:
On 2025-09-23 15:37:27 +0000, olcott said:
On 9/23/2025 4:23 AM, Mikko wrote:
On 2025-09-23 00:57:36 +0000, olcott said:
On 9/21/2025 4:25 AM, Mikko wrote:
On 2025-09-20 15:03:01 +0000, olcott said:
On 9/19/2025 4:20 AM, Mikko wrote:
On 2025-09-18 14:42:11 +0000, olcott said:
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:
No, there are other extensions, too. And if the object theory already
is a higher order theory the enriched theory needs not be higher.
Tarski can say what he says because at that point he has already >>>>>>>>>>>>>> proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic.
https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF
Nice to see that you don't disagree.
I agree with you and thus we both disagree with Tarski.
Tarski has his Theory and his Meta-Theory that are separate. >>>>>>>>>>> This seems to be the same as FOPL and SOPL.
When You and Tarski and I say that "The Liar's paradox is not true" >>>>>>>>>> then we all agree.
Its not false either.
That fact is not needed for the proof. What matters is that because >>>>>>>> it is not true it cannot be provable.
Yes and the square root of a dead chicken
is uncomputable for the same reason.
Nice to see that you don't disagree.
Computation is not limited when it is required
to answer any question that has no correct answer.
Irrelevant to Tarski's undefinability theorem. Atirhmetic truth is a
valid an important concept even when not formally definable.
Tarski merely did the same thing as G||del yet did this
much more succinctly and clearly.
Not really, he applied the methods G||del had already developed to
a different problem.
Tarski admits that he anchored his whole proof on the
liar paradox and G||del admitted essentially the same thing:
On 9/25/2025 2:34 AM, Mikko wrote:
On 2025-09-24 14:36:46 +0000, olcott said:
On 9/24/2025 2:19 AM, Mikko wrote:
On 2025-09-23 15:39:53 +0000, olcott said:
On 9/23/2025 4:29 AM, Mikko wrote:
On 2025-09-23 00:59:54 +0000, olcott said:
On 9/21/2025 4:26 AM, Mikko wrote:
On 2025-09-20 14:58:33 +0000, olcott said:The meaning is that it is not a truth bearer
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said:
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said:
Tarski an otherwise profoundly brilliant man stupidly >>>>>>>>>>>>> anchored his whole Undefinability proof in the semantic >>>>>>>>>>>>> gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic gibberish.
This sentence is not true.
What it is not true about?
The sentence claims that it is not true about itself.
In an infinitely recursive chain that you dishonestly
erased.
No, that meaning can be found without considering any recursion. >>>>>>>
thus has no truth value.
If the sentence "This sentence is not true" has no truth value then >>>>>> it is not true.
And it is not false, thus must be rejected
as not a member of any formal logic system
thus cannot form a basis for any Undefinability proof.
The sentence "The sentence 'This sentence is not true' is not true"
is true and can be used as an element of a proof.
Yes and likewise with this:
"The sentence 'What time is it?' is not true".
Thus in neither case does this prevent a Truth
predicate from being defined at the same logic level.
Not in any obvious way but turns out that if there is a definable truth
predicate then there is a proof of a false sentence that asserts its
own unprovability, i.e., the arithmetic with a definable truth predicate
is provably inconsistent.
There is no true and unprovable.
On 2025-09-26 01:11:01 +0000, olcott said:
On 9/25/2025 2:24 AM, Mikko wrote:
On 2025-09-24 14:31:55 +0000, olcott said:
On 9/24/2025 2:15 AM, Mikko wrote:
On 2025-09-23 15:37:27 +0000, olcott said:
On 9/23/2025 4:23 AM, Mikko wrote:
On 2025-09-23 00:57:36 +0000, olcott said:
On 9/21/2025 4:25 AM, Mikko wrote:
On 2025-09-20 15:03:01 +0000, olcott said:
On 9/19/2025 4:20 AM, Mikko wrote:
On 2025-09-18 14:42:11 +0000, olcott said:
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:
No, there are other extensions, too. And if the object >>>>>>>>>>>>>>> theory already
is a higher order theory the enriched theory needs not be >>>>>>>>>>>>>>> higher.
Tarski can say what he says because at that point he has >>>>>>>>>>>>>>> already
proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic.
https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF
Nice to see that you don't disagree.
I agree with you and thus we both disagree with Tarski. >>>>>>>>>>>> Tarski has his Theory and his Meta-Theory that are separate. >>>>>>>>>>>> This seems to be the same as FOPL and SOPL.
When You and Tarski and I say that "The Liar's paradox is not >>>>>>>>>>> true"
then we all agree.
Its not false either.
That fact is not needed for the proof. What matters is that >>>>>>>>> because
it is not true it cannot be provable.
Yes and the square root of a dead chicken
is uncomputable for the same reason.
Nice to see that you don't disagree.
Computation is not limited when it is required
to answer any question that has no correct answer.
Irrelevant to Tarski's undefinability theorem. Atirhmetic truth is a >>>>> valid an important concept even when not formally definable.
Tarski merely did the same thing as G||del yet did this
much more succinctly and clearly.
Not really, he applied the methods G||del had already developed to
a different problem.
Tarski admits that he anchored his whole proof on the
liar paradox and G||del admitted essentially the same thing:
Yes, and you addmitted above that "The sentence 'This sentence is
not true' is not true" is true, so can be used in a sound proof.
Tarski also said he got the method from G||del.
On 2025-09-26 01:19:50 +0000, olcott said:
On 9/25/2025 2:34 AM, Mikko wrote:
On 2025-09-24 14:36:46 +0000, olcott said:
On 9/24/2025 2:19 AM, Mikko wrote:
On 2025-09-23 15:39:53 +0000, olcott said:
On 9/23/2025 4:29 AM, Mikko wrote:
On 2025-09-23 00:59:54 +0000, olcott said:
On 9/21/2025 4:26 AM, Mikko wrote:
On 2025-09-20 14:58:33 +0000, olcott said:The meaning is that it is not a truth bearer
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said:
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said:
Tarski an otherwise profoundly brilliant man stupidly >>>>>>>>>>>>>> anchored his whole Undefinability proof in the semantic >>>>>>>>>>>>>> gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic >>>>>>>>>>>>> gibberish.
This sentence is not true.
What it is not true about?
The sentence claims that it is not true about itself.
In an infinitely recursive chain that you dishonestly
erased.
No, that meaning can be found without considering any recursion. >>>>>>>>
thus has no truth value.
If the sentence "This sentence is not true" has no truth value then >>>>>>> it is not true.
And it is not false, thus must be rejected
as not a member of any formal logic system
thus cannot form a basis for any Undefinability proof.
The sentence "The sentence 'This sentence is not true' is not true"
is true and can be used as an element of a proof.
Yes and likewise with this:
"The sentence 'What time is it?' is not true".
Thus in neither case does this prevent a Truth
predicate from being defined at the same logic level.
Not in any obvious way but turns out that if there is a definable truth
predicate then there is a proof of a false sentence that asserts its
own unprovability, i.e., the arithmetic with a definable truth predicate >>> is provably inconsistent.
There is no true and unprovable.
G||del proved that if a first order theory is incomplete it has models
where some unprovable sentence is true and other models where the same sentence is false.
On 9/25/2025 2:15 AM, Mikko wrote:
On 2025-09-24 14:27:00 +0000, olcott said:
On 9/24/2025 2:12 AM, Mikko wrote:
On 2025-09-23 16:04:38 +0000, olcott said:
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said:
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
Yes that is the moronic received view yet these stupid
G||del's sentence is not really self-referential. It is a valid >>>>>>>>>> sentence in the first order language of Peano arithmetic. That >>>>>>>>>> the value of an arithmetic expression in that sentence evaluates >>>>>>>>>> to the G||del number of the sentence has no arithmetic significance. >>>>>>>>>
people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 Incompleteness theorem >>>>>>>>> are these plain English direct quotes of G||del from his paper: >>>>>>>>>
...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...
...We are therefore confronted with a proposition which asserts its own
unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And >>>>>>>>> Related Systems
The most important aspect is the theorem itself: every theory that >>>>>>>> has the symbols and axioms of the first order Peano arithmetic is >>>>>>>> either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important.
Prior to Pythagoras there was a universal consensus
that the Earth is flat.
To think the Earth as flat is simpler and good enough for many
purposes. For a long time there was no need to think about the
shape of the Earth.
The point is that not even a universal consensus equates to truth.
No, but it is a significant aspect of culture. A question of importance
is not a matter of truth but a matter of opinion.
Many poeple also
find it useful to know that any attempt to construct a cmplete theory >>>>>> of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is screwed up.
If you want to build a formal system that is not anchored in a
screwed up idea than this is straight forward.
That 2 + 3 = 5 has practical value even if the theory around it
cannot be made complete.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply
the truth preserving operation of semantic logical entailment
to these basic facts.
It is generally accepted that the set of axioms can be infinite
Not when we are representing the finite set of human general knowledge.
Once again you try to deceive with a change of topic. There is no
need to prove the incompletenes of human general knowledge as that
already is obvious. But G||del's and Tarski's theorems are about
natural number arithmetic and its extensions so they need to cover
the possibility that there are infinitely many axioms.
Tarski admits that he anchor his whole proof on the
liar paradox and
On 9/26/2025 2:43 AM, Mikko wrote:
On 2025-09-26 01:11:01 +0000, olcott said:
On 9/25/2025 2:24 AM, Mikko wrote:
On 2025-09-24 14:31:55 +0000, olcott said:
On 9/24/2025 2:15 AM, Mikko wrote:
On 2025-09-23 15:37:27 +0000, olcott said:
On 9/23/2025 4:23 AM, Mikko wrote:
On 2025-09-23 00:57:36 +0000, olcott said:
On 9/21/2025 4:25 AM, Mikko wrote:
On 2025-09-20 15:03:01 +0000, olcott said:
On 9/19/2025 4:20 AM, Mikko wrote:
On 2025-09-18 14:42:11 +0000, olcott said:
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:Nice to see that you don't disagree.
No, there are other extensions, too. And if the object theory already
is a higher order theory the enriched theory needs not be higher.
Tarski can say what he says because at that point he has already
proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic.
https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF >>>>>>>>>>>>>>
I agree with you and thus we both disagree with Tarski. >>>>>>>>>>>>> Tarski has his Theory and his Meta-Theory that are separate. >>>>>>>>>>>>> This seems to be the same as FOPL and SOPL.
When You and Tarski and I say that "The Liar's paradox is not true"
then we all agree.
Its not false either.
That fact is not needed for the proof. What matters is that because >>>>>>>>>> it is not true it cannot be provable.
Yes and the square root of a dead chicken
is uncomputable for the same reason.
Nice to see that you don't disagree.
Computation is not limited when it is required
to answer any question that has no correct answer.
Irrelevant to Tarski's undefinability theorem. Atirhmetic truth is a >>>>>> valid an important concept even when not formally definable.
Tarski merely did the same thing as G||del yet did this
much more succinctly and clearly.
Not really, he applied the methods G||del had already developed to
a different problem.
Tarski admits that he anchored his whole proof on the
liar paradox and G||del admitted essentially the same thing:
Yes, and you addmitted above that "The sentence 'This sentence is
not true' is not true" is true, so can be used in a sound proof.
Tarski also said he got the method from G||del.
We can do the exact same thing for this sentence:
"What time is it (yes or no)?" is not true.
On 9/26/2025 2:48 AM, Mikko wrote:
On 2025-09-26 01:19:50 +0000, olcott said:
On 9/25/2025 2:34 AM, Mikko wrote:
On 2025-09-24 14:36:46 +0000, olcott said:
On 9/24/2025 2:19 AM, Mikko wrote:
On 2025-09-23 15:39:53 +0000, olcott said:
On 9/23/2025 4:29 AM, Mikko wrote:
On 2025-09-23 00:59:54 +0000, olcott said:
On 9/21/2025 4:26 AM, Mikko wrote:
On 2025-09-20 14:58:33 +0000, olcott said:The meaning is that it is not a truth bearer
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said:
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said:
Tarski an otherwise profoundly brilliant man stupidly >>>>>>>>>>>>>>> anchored his whole Undefinability proof in the semantic >>>>>>>>>>>>>>> gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic gibberish.
This sentence is not true.
What it is not true about?
The sentence claims that it is not true about itself.
In an infinitely recursive chain that you dishonestly
erased.
No, that meaning can be found without considering any recursion. >>>>>>>>>
thus has no truth value.
If the sentence "This sentence is not true" has no truth value then >>>>>>>> it is not true.
And it is not false, thus must be rejected
as not a member of any formal logic system
thus cannot form a basis for any Undefinability proof.
The sentence "The sentence 'This sentence is not true' is not true" >>>>>> is true and can be used as an element of a proof.
Yes and likewise with this:
"The sentence 'What time is it?' is not true".
Thus in neither case does this prevent a Truth
predicate from being defined at the same logic level.
Not in any obvious way but turns out that if there is a definable truth >>>> predicate then there is a proof of a false sentence that asserts its
own unprovability, i.e., the arithmetic with a definable truth predicate >>>> is provably inconsistent.
There is no true and unprovable.
G||del proved that if a first order theory is incomplete it has models
where some unprovable sentence is true and other models where the same
sentence is false.
That is only because he did not screen out sentences
that are not truth bearers like: "What time is it (yes or no)?"
"This sentence is not true", "This sentence cannot be proven".
On 2025-09-26 01:08:45 +0000, olcott said:
On 9/25/2025 2:15 AM, Mikko wrote:
On 2025-09-24 14:27:00 +0000, olcott said:
On 9/24/2025 2:12 AM, Mikko wrote:
On 2025-09-23 16:04:38 +0000, olcott said:
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said:
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
G||del's sentence is not really self-referential. It is a valid >>>>>>>>>>> sentence in the first order language of Peano arithmetic. That >>>>>>>>>>> the value of an arithmetic expression in that sentence evaluates >>>>>>>>>>> to the G||del number of the sentence has no arithmetic
significance.
Yes that is the moronic received view yet these stupid
people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 Incompleteness theorem >>>>>>>>>> are these plain English direct quotes of G||del from his paper: >>>>>>>>>>
...there is also a close relationship with the rCLliarrCY >>>>>>>>>> antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for >>>>>>>>>> a similar undecidability proof...
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica >>>>>>>>>> And Related Systems
The most important aspect is the theorem itself: every theory that >>>>>>>>> has the symbols and axioms of the first order Peano arithmetic is >>>>>>>>> either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important.
Prior to Pythagoras there was a universal consensus
that the Earth is flat.
To think the Earth as flat is simpler and good enough for many
purposes. For a long time there was no need to think about the
shape of the Earth.
The point is that not even a universal consensus equates to truth.
No, but it is a significant aspect of culture. A question of importance
is not a matter of truth but a matter of opinion.
Once again you try to deceive with a change of topic. There is no
Many poeple also
find it useful to know that any attempt to construct a cmplete
theory
of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is screwed up. >>>>>> If you want to build a formal system that is not anchored in a
screwed up idea than this is straight forward.
That 2 + 3 = 5 has practical value even if the theory around it
cannot be made complete.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply
the truth preserving operation of semantic logical entailment
to these basic facts.
It is generally accepted that the set of axioms can be infinite
Not when we are representing the finite set of human general knowledge. >>>
need to prove the incompletenes of human general knowledge as that
already is obvious. But G||del's and Tarski's theorems are about
natural number arithmetic and its extensions so they need to cover
the possibility that there are infinitely many axioms.
Tarski admits that he anchor his whole proof on the
liar paradox and
He doesn't "anchor" it to the liar paradix. The liar paradox has some
formal similarity to the sentence Tarski constructs but is not a part
of the proof. Consequently anything said about the liar's paracos is irrelevant to the correctness of the proof.
On 2025-09-26 15:24:27 +0000, olcott said:
On 9/26/2025 2:43 AM, Mikko wrote:
On 2025-09-26 01:11:01 +0000, olcott said:
On 9/25/2025 2:24 AM, Mikko wrote:
On 2025-09-24 14:31:55 +0000, olcott said:
On 9/24/2025 2:15 AM, Mikko wrote:
On 2025-09-23 15:37:27 +0000, olcott said:
On 9/23/2025 4:23 AM, Mikko wrote:
On 2025-09-23 00:57:36 +0000, olcott said:
On 9/21/2025 4:25 AM, Mikko wrote:
On 2025-09-20 15:03:01 +0000, olcott said:
On 9/19/2025 4:20 AM, Mikko wrote:
On 2025-09-18 14:42:11 +0000, olcott said:
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:Nice to see that you don't disagree.
No, there are other extensions, too. And if the object >>>>>>>>>>>>>>>>> theory already
is a higher order theory the enriched theory needs not >>>>>>>>>>>>>>>>> be higher.
Tarski can say what he says because at that point he >>>>>>>>>>>>>>>>> has already
proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic.
https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF >>>>>>>>>>>>>>>
I agree with you and thus we both disagree with Tarski. >>>>>>>>>>>>>> Tarski has his Theory and his Meta-Theory that are separate. >>>>>>>>>>>>>> This seems to be the same as FOPL and SOPL.
When You and Tarski and I say that "The Liar's paradox is >>>>>>>>>>>>> not true"
then we all agree.
Its not false either.
That fact is not needed for the proof. What matters is that >>>>>>>>>>> because
it is not true it cannot be provable.
Yes and the square root of a dead chicken
is uncomputable for the same reason.
Nice to see that you don't disagree.
Computation is not limited when it is required
to answer any question that has no correct answer.
Irrelevant to Tarski's undefinability theorem. Atirhmetic truth is a >>>>>>> valid an important concept even when not formally definable.
Tarski merely did the same thing as G||del yet did this
much more succinctly and clearly.
Not really, he applied the methods G||del had already developed to
a different problem.
Tarski admits that he anchored his whole proof on the
liar paradox and G||del admitted essentially the same thing:
Yes, and you addmitted above that "The sentence 'This sentence is
not true' is not true" is true, so can be used in a sound proof.
Tarski also said he got the method from G||del.
We can do the exact same thing for this sentence:
"What time is it (yes or no)?" is not true.
Yes, "'What time is it (yes or no)?' is not true" is true and can be
used in a sound proof. However, it is hardly useful for any interesting proof.
On 2025-09-26 15:28:52 +0000, olcott said:
On 9/26/2025 2:48 AM, Mikko wrote:
On 2025-09-26 01:19:50 +0000, olcott said:
On 9/25/2025 2:34 AM, Mikko wrote:
On 2025-09-24 14:36:46 +0000, olcott said:
On 9/24/2025 2:19 AM, Mikko wrote:
On 2025-09-23 15:39:53 +0000, olcott said:
On 9/23/2025 4:29 AM, Mikko wrote:
On 2025-09-23 00:59:54 +0000, olcott said:
On 9/21/2025 4:26 AM, Mikko wrote:
On 2025-09-20 14:58:33 +0000, olcott said:The meaning is that it is not a truth bearer
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said:In an infinitely recursive chain that you dishonestly
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said:
Tarski an otherwise profoundly brilliant man stupidly >>>>>>>>>>>>>>>> anchored his whole Undefinability proof in the semantic >>>>>>>>>>>>>>>> gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not >>>>>>>>>>>>>>> semantic gibberish.
This sentence is not true.
What it is not true about?
The sentence claims that it is not true about itself. >>>>>>>>>>>>
erased.
No, that meaning can be found without considering any recursion. >>>>>>>>>>
thus has no truth value.
If the sentence "This sentence is not true" has no truth value >>>>>>>>> then
it is not true.
And it is not false, thus must be rejected
as not a member of any formal logic system
thus cannot form a basis for any Undefinability proof.
The sentence "The sentence 'This sentence is not true' is not true" >>>>>>> is true and can be used as an element of a proof.
Yes and likewise with this:
"The sentence 'What time is it?' is not true".
Thus in neither case does this prevent a Truth
predicate from being defined at the same logic level.
Not in any obvious way but turns out that if there is a definable
truth
predicate then there is a proof of a false sentence that asserts its >>>>> own unprovability, i.e., the arithmetic with a definable truth
predicate
is provably inconsistent.
There is no true and unprovable.
G||del proved that if a first order theory is incomplete it has models
where some unprovable sentence is true and other models where the same
sentence is false.
That is only because he did not screen out sentences
that are not truth bearers like: "What time is it (yes or no)?"
"This sentence is not true", "This sentence cannot be proven".
He didn't need to screen out anything. His proof covers all first order theories. In many theories your examples are unexpressible anyway, so
there is no need to screen them out.
On 9/27/2025 5:05 AM, Mikko wrote:
On 2025-09-26 01:08:45 +0000, olcott said:
On 9/25/2025 2:15 AM, Mikko wrote:
On 2025-09-24 14:27:00 +0000, olcott said:
On 9/24/2025 2:12 AM, Mikko wrote:
On 2025-09-23 16:04:38 +0000, olcott said:
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said:
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
G||del's sentence is not really self-referential. It is a valid >>>>>>>>>>>> sentence in the first order language of Peano arithmetic. That >>>>>>>>>>>> the value of an arithmetic expression in that sentence evaluates >>>>>>>>>>>> to the G||del number of the sentence has no arithmetic significance.
Yes that is the moronic received view yet these stupid
people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 Incompleteness theorem >>>>>>>>>>> are these plain English direct quotes of G||del from his paper: >>>>>>>>>>>
...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...
...We are therefore confronted with a proposition which asserts its own
unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And >>>>>>>>>>> Related Systems
The most important aspect is the theorem itself: every theory that >>>>>>>>>> has the symbols and axioms of the first order Peano arithmetic is >>>>>>>>>> either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important.
Prior to Pythagoras there was a universal consensus
that the Earth is flat.
To think the Earth as flat is simpler and good enough for many
purposes. For a long time there was no need to think about the
shape of the Earth.
The point is that not even a universal consensus equates to truth.
No, but it is a significant aspect of culture. A question of importance >>>> is not a matter of truth but a matter of opinion.
Once again you try to deceive with a change of topic. There is no
Many poeple also
find it useful to know that any attempt to construct a cmplete theory >>>>>>>> of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is screwed up. >>>>>>> If you want to build a formal system that is not anchored in a
screwed up idea than this is straight forward.
That 2 + 3 = 5 has practical value even if the theory around it
cannot be made complete.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply
the truth preserving operation of semantic logical entailment
to these basic facts.
It is generally accepted that the set of axioms can be infinite
Not when we are representing the finite set of human general knowledge. >>>>
need to prove the incompletenes of human general knowledge as that
already is obvious. But G||del's and Tarski's theorems are about
natural number arithmetic and its extensions so they need to cover
the possibility that there are infinitely many axioms.
Tarski admits that he anchor his whole proof on the
liar paradox and
He doesn't "anchor" it to the liar paradix. The liar paradox has some
formal similarity to the sentence Tarski constructs but is not a part
of the proof. Consequently anything said about the liar's paracos is
irrelevant to the correctness of the proof.
Factually incorrect.
Tarski's Liar Paradox from page 248--
It would then be possible to reconstruct the antinomy of the liar
in the metalanguage, by forming in the language itself a sentence
x such that the sentence of the metalanguage which is correlated
with x asserts that x is not a true sentence.
https://liarparadox.org/Tarski_247_248.pdf
On 9/27/2025 5:07 AM, Mikko wrote:
On 2025-09-26 15:24:27 +0000, olcott said:
On 9/26/2025 2:43 AM, Mikko wrote:
On 2025-09-26 01:11:01 +0000, olcott said:
On 9/25/2025 2:24 AM, Mikko wrote:
On 2025-09-24 14:31:55 +0000, olcott said:
On 9/24/2025 2:15 AM, Mikko wrote:
On 2025-09-23 15:37:27 +0000, olcott said:
On 9/23/2025 4:23 AM, Mikko wrote:
On 2025-09-23 00:57:36 +0000, olcott said:
On 9/21/2025 4:25 AM, Mikko wrote:
On 2025-09-20 15:03:01 +0000, olcott said:
On 9/19/2025 4:20 AM, Mikko wrote:
On 2025-09-18 14:42:11 +0000, olcott said:
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:Nice to see that you don't disagree.
No, there are other extensions, too. And if the object theory already
is a higher order theory the enriched theory needs not be higher.
Tarski can say what he says because at that point he has already
proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic. >>>>>>>>>>>>>>>>> https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF >>>>>>>>>>>>>>>>
I agree with you and thus we both disagree with Tarski. >>>>>>>>>>>>>>> Tarski has his Theory and his Meta-Theory that are separate. >>>>>>>>>>>>>>> This seems to be the same as FOPL and SOPL.
When You and Tarski and I say that "The Liar's paradox is not true"
then we all agree.
Its not false either.
That fact is not needed for the proof. What matters is that because
it is not true it cannot be provable.
Yes and the square root of a dead chicken
is uncomputable for the same reason.
Nice to see that you don't disagree.
Computation is not limited when it is required
to answer any question that has no correct answer.
Irrelevant to Tarski's undefinability theorem. Atirhmetic truth is a >>>>>>>> valid an important concept even when not formally definable.
Tarski merely did the same thing as G||del yet did this
much more succinctly and clearly.
Not really, he applied the methods G||del had already developed to >>>>>> a different problem.
Tarski admits that he anchored his whole proof on the
liar paradox and G||del admitted essentially the same thing:
Yes, and you addmitted above that "The sentence 'This sentence is
not true' is not true" is true, so can be used in a sound proof.
Tarski also said he got the method from G||del.
We can do the exact same thing for this sentence:
"What time is it (yes or no)?" is not true.
Yes, "'What time is it (yes or no)?' is not true" is true and can be
used in a sound proof. However, it is hardly useful for any interesting
proof.
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
On 2025-09-29 12:21:25 +0000, olcott said:
On 9/27/2025 5:05 AM, Mikko wrote:
On 2025-09-26 01:08:45 +0000, olcott said:
On 9/25/2025 2:15 AM, Mikko wrote:
On 2025-09-24 14:27:00 +0000, olcott said:
On 9/24/2025 2:12 AM, Mikko wrote:
On 2025-09-23 16:04:38 +0000, olcott said:
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said:
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
G||del's sentence is not really self-referential. It is a valid >>>>>>>>>>>>> sentence in the first order language of Peano arithmetic. That >>>>>>>>>>>>> the value of an arithmetic expression in that sentence >>>>>>>>>>>>> evaluates
to the G||del number of the sentence has no arithmetic >>>>>>>>>>>>> significance.
Yes that is the moronic received view yet these stupid >>>>>>>>>>>> people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 Incompleteness >>>>>>>>>>>> theorem
are these plain English direct quotes of G||del from his paper: >>>>>>>>>>>>
...there is also a close relationship with the rCLliarrCY >>>>>>>>>>>> antinomy,14 ...
...14 Every epistemological antinomy can likewise be used >>>>>>>>>>>> for a similar undecidability proof...
...We are therefore confronted with a proposition which >>>>>>>>>>>> asserts its own unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia
Mathematica And Related Systems
The most important aspect is the theorem itself: every theory >>>>>>>>>>> that
has the symbols and axioms of the first order Peano
arithmetic is
either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important.
Prior to Pythagoras there was a universal consensus
that the Earth is flat.
To think the Earth as flat is simpler and good enough for many
purposes. For a long time there was no need to think about the
shape of the Earth.
The point is that not even a universal consensus equates to truth.
No, but it is a significant aspect of culture. A question of
importance
is not a matter of truth but a matter of opinion.
Many poeple also
find it useful to know that any attempt to construct a cmplete >>>>>>>>> theory
of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is screwed up. >>>>>>>> If you want to build a formal system that is not anchored in a >>>>>>>> screwed up idea than this is straight forward.
That 2 + 3 = 5 has practical value even if the theory around it
cannot be made complete.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply
the truth preserving operation of semantic logical entailment
to these basic facts.
It is generally accepted that the set of axioms can be infinite
Not when we are representing the finite set of human general
knowledge.
Once again you try to deceive with a change of topic. There is no
need to prove the incompletenes of human general knowledge as that
already is obvious. But G||del's and Tarski's theorems are about
natural number arithmetic and its extensions so they need to cover
the possibility that there are infinitely many axioms.
Tarski admits that he anchor his whole proof on the
liar paradox and
He doesn't "anchor" it to the liar paradix. The liar paradox has some
formal similarity to the sentence Tarski constructs but is not a part
of the proof. Consequently anything said about the liar's paracos is
irrelevant to the correctness of the proof.
Factually incorrect.
False. Tarski confirms what I said:
Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy of the liar
-a-a-a in the metalanguage, by forming in the language itself a sentence
-a-a-a x such that the sentence of the metalanguage which is correlated
-a-a-a with x asserts that x is not a true sentence.
-a-a-a https://liarparadox.org/Tarski_247_248.pdf
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
On 2025-09-26 15:24:27 +0000, olcott said:
On 9/26/2025 2:43 AM, Mikko wrote:
On 2025-09-26 01:11:01 +0000, olcott said:
On 9/25/2025 2:24 AM, Mikko wrote:
On 2025-09-24 14:31:55 +0000, olcott said:
On 9/24/2025 2:15 AM, Mikko wrote:
On 2025-09-23 15:37:27 +0000, olcott said:
On 9/23/2025 4:23 AM, Mikko wrote:
On 2025-09-23 00:57:36 +0000, olcott said:
On 9/21/2025 4:25 AM, Mikko wrote:
On 2025-09-20 15:03:01 +0000, olcott said:
On 9/19/2025 4:20 AM, Mikko wrote:
On 2025-09-18 14:42:11 +0000, olcott said:
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said:
On 9/17/2025 2:52 AM, Mikko wrote:Nice to see that you don't disagree.
No, there are other extensions, too. And if the >>>>>>>>>>>>>>>>>>> object theory already
is a higher order theory the enriched theory needs >>>>>>>>>>>>>>>>>>> not be higher.
Tarski can say what he says because at that point he >>>>>>>>>>>>>>>>>>> has already
proven both claims.
Minimal Type Theory (MTT) that I created
start with the syntax of FOPL and this
can be extended to any higher order of logic. >>>>>>>>>>>>>>>>>> https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF >>>>>>>>>>>>>>>>>
I agree with you and thus we both disagree with Tarski. >>>>>>>>>>>>>>>> Tarski has his Theory and his Meta-Theory that are >>>>>>>>>>>>>>>> separate.
This seems to be the same as FOPL and SOPL.
When You and Tarski and I say that "The Liar's paradox is >>>>>>>>>>>>>>> not true"
then we all agree.
Its not false either.
That fact is not needed for the proof. What matters is that >>>>>>>>>>>>> because
it is not true it cannot be provable.
Yes and the square root of a dead chicken
is uncomputable for the same reason.
Nice to see that you don't disagree.
Computation is not limited when it is required
to answer any question that has no correct answer.
Irrelevant to Tarski's undefinability theorem. Atirhmetic truth >>>>>>>>> is a
valid an important concept even when not formally definable.
Tarski merely did the same thing as G||del yet did this
much more succinctly and clearly.
Not really, he applied the methods G||del had already developed to >>>>>>> a different problem.
Tarski admits that he anchored his whole proof on the
liar paradox and G||del admitted essentially the same thing:
Yes, and you addmitted above that "The sentence 'This sentence is
not true' is not true" is true, so can be used in a sound proof.
Tarski also said he got the method from G||del.
We can do the exact same thing for this sentence:
"What time is it (yes or no)?" is not true.
Yes, "'What time is it (yes or no)?' is not true" is true and can be
used in a sound proof. However, it is hardly useful for any interesting
proof.
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or dontradiction is
true in some contexts and false in others.
Theories need additionan
postulates that identify which sentences are intended to be true
and which false in the intended domain of the theory.
Anyway, the sentence "'What time is it (yes or no)?' is not true" is
true and therefore is a truth-bearer and is a valid and sound element
of proof, though perhaps not very useful.
On 9/30/2025 7:48 AM, Mikko wrote:
On 2025-09-29 12:21:25 +0000, olcott said:
On 9/27/2025 5:05 AM, Mikko wrote:
On 2025-09-26 01:08:45 +0000, olcott said:
On 9/25/2025 2:15 AM, Mikko wrote:
On 2025-09-24 14:27:00 +0000, olcott said:
On 9/24/2025 2:12 AM, Mikko wrote:No, but it is a significant aspect of culture. A question of importance >>>>>> is not a matter of truth but a matter of opinion.
On 2025-09-23 16:04:38 +0000, olcott said:
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said:
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
G||del's sentence is not really self-referential. It is a valid >>>>>>>>>>>>>> sentence in the first order language of Peano arithmetic. That >>>>>>>>>>>>>> the value of an arithmetic expression in that sentence evaluates >>>>>>>>>>>>>> to the G||del number of the sentence has no arithmetic significance.
Yes that is the moronic received view yet these stupid >>>>>>>>>>>>> people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 Incompleteness theorem >>>>>>>>>>>>> are these plain English direct quotes of G||del from his paper: >>>>>>>>>>>>>
...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...
...We are therefore confronted with a proposition which asserts its own
unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
The most important aspect is the theorem itself: every theory that >>>>>>>>>>>> has the symbols and axioms of the first order Peano arithmetic is >>>>>>>>>>>> either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important.
Prior to Pythagoras there was a universal consensus
that the Earth is flat.
To think the Earth as flat is simpler and good enough for many >>>>>>>> purposes. For a long time there was no need to think about the >>>>>>>> shape of the Earth.
The point is that not even a universal consensus equates to truth. >>>>>>
Once again you try to deceive with a change of topic. There is no
Not when we are representing the finite set of human general knowledge. >>>>>>Many poeple also
find it useful to know that any attempt to construct a cmplete theory
of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is screwed up. >>>>>>>>> If you want to build a formal system that is not anchored in a >>>>>>>>> screwed up idea than this is straight forward.
That 2 + 3 = 5 has practical value even if the theory around it >>>>>>>> cannot be made complete.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply
the truth preserving operation of semantic logical entailment >>>>>>>>> to these basic facts.
It is generally accepted that the set of axioms can be infinite >>>>>>>
need to prove the incompletenes of human general knowledge as that >>>>>> already is obvious. But G||del's and Tarski's theorems are about
natural number arithmetic and its extensions so they need to cover >>>>>> the possibility that there are infinitely many axioms.
Tarski admits that he anchor his whole proof on the
liar paradox and
He doesn't "anchor" it to the liar paradix. The liar paradox has some
formal similarity to the sentence Tarski constructs but is not a part
of the proof. Consequently anything said about the liar's paracos is
irrelevant to the correctness of the proof.
Factually incorrect.
False. Tarski confirms what I said:
And I prove my point in the paragraph that you skipped.
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
On 2025-09-26 15:24:27 +0000, olcott said:
On 9/26/2025 2:43 AM, Mikko wrote:
On 2025-09-26 01:11:01 +0000, olcott said:
On 9/25/2025 2:24 AM, Mikko wrote:
On 2025-09-24 14:31:55 +0000, olcott said:
On 9/24/2025 2:15 AM, Mikko wrote:
On 2025-09-23 15:37:27 +0000, olcott said:Tarski merely did the same thing as G||del yet did this
On 9/23/2025 4:23 AM, Mikko wrote:
On 2025-09-23 00:57:36 +0000, olcott said:
On 9/21/2025 4:25 AM, Mikko wrote:
On 2025-09-20 15:03:01 +0000, olcott said:
On 9/19/2025 4:20 AM, Mikko wrote:
On 2025-09-18 14:42:11 +0000, olcott said:
On 9/18/2025 4:25 AM, Mikko wrote:
On 2025-09-17 14:51:01 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 9/17/2025 2:52 AM, Mikko wrote:Nice to see that you don't disagree.
No, there are other extensions, too. And if the object theory already
is a higher order theory the enriched theory needs not be higher.
Tarski can say what he says because at that point he has already
proven both claims.
Minimal Type Theory (MTT) that I created >>>>>>>>>>>>>>>>>>> start with the syntax of FOPL and this
can be extended to any higher order of logic. >>>>>>>>>>>>>>>>>>> https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF >>>>>>>>>>>>>>>>>>
I agree with you and thus we both disagree with Tarski. >>>>>>>>>>>>>>>>> Tarski has his Theory and his Meta-Theory that are separate. >>>>>>>>>>>>>>>>> This seems to be the same as FOPL and SOPL.
When You and Tarski and I say that "The Liar's paradox is not true"
then we all agree.
Its not false either.
That fact is not needed for the proof. What matters is that because
it is not true it cannot be provable.
Yes and the square root of a dead chicken
is uncomputable for the same reason.
Nice to see that you don't disagree.
Computation is not limited when it is required
to answer any question that has no correct answer.
Irrelevant to Tarski's undefinability theorem. Atirhmetic truth is a >>>>>>>>>> valid an important concept even when not formally definable. >>>>>>>>>
much more succinctly and clearly.
Not really, he applied the methods G||del had already developed to >>>>>>>> a different problem.
Tarski admits that he anchored his whole proof on the
liar paradox and G||del admitted essentially the same thing:
Yes, and you addmitted above that "The sentence 'This sentence is
not true' is not true" is true, so can be used in a sound proof.
Tarski also said he got the method from G||del.
We can do the exact same thing for this sentence:
"What time is it (yes or no)?" is not true.
Yes, "'What time is it (yes or no)?' is not true" is true and can be
used in a sound proof. However, it is hardly useful for any interesting >>>> proof.
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or dontradiction is
true in some contexts and false in others.
A mere false assumption
On 2025-10-01 01:46:15 +0000, olcott said:
On 9/30/2025 7:48 AM, Mikko wrote:
On 2025-09-29 12:21:25 +0000, olcott said:
On 9/27/2025 5:05 AM, Mikko wrote:
On 2025-09-26 01:08:45 +0000, olcott said:
On 9/25/2025 2:15 AM, Mikko wrote:
On 2025-09-24 14:27:00 +0000, olcott said:
On 9/24/2025 2:12 AM, Mikko wrote:No, but it is a significant aspect of culture. A question of
On 2025-09-23 16:04:38 +0000, olcott said:
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said:
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
G||del's sentence is not really self-referential. It is a >>>>>>>>>>>>>>> valid
sentence in the first order language of Peano arithmetic. >>>>>>>>>>>>>>> That
the value of an arithmetic expression in that sentence >>>>>>>>>>>>>>> evaluates
to the G||del number of the sentence has no arithmetic >>>>>>>>>>>>>>> significance.
Yes that is the moronic received view yet these stupid >>>>>>>>>>>>>> people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 Incompleteness >>>>>>>>>>>>>> theorem
are these plain English direct quotes of G||del from his >>>>>>>>>>>>>> paper:
...there is also a close relationship with the rCLliarrCY >>>>>>>>>>>>>> antinomy,14 ...
...14 Every epistemological antinomy can likewise be used >>>>>>>>>>>>>> for a similar undecidability proof...
...We are therefore confronted with a proposition which >>>>>>>>>>>>>> asserts its own unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia >>>>>>>>>>>>>> Mathematica And Related Systems
The most important aspect is the theorem itself: every >>>>>>>>>>>>> theory that
has the symbols and axioms of the first order Peano >>>>>>>>>>>>> arithmetic is
either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important.
Prior to Pythagoras there was a universal consensus
that the Earth is flat.
To think the Earth as flat is simpler and good enough for many >>>>>>>>> purposes. For a long time there was no need to think about the >>>>>>>>> shape of the Earth.
The point is that not even a universal consensus equates to truth. >>>>>>>
importance
is not a matter of truth but a matter of opinion.
Not when we are representing the finite set of human generalMany poeple also
find it useful to know that any attempt to construct a
cmplete theory
of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is screwed >>>>>>>>>> up.
If you want to build a formal system that is not anchored in a >>>>>>>>>> screwed up idea than this is straight forward.
That 2 + 3 = 5 has practical value even if the theory around it >>>>>>>>> cannot be made complete.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply >>>>>>>>>> the truth preserving operation of semantic logical entailment >>>>>>>>>> to these basic facts.
It is generally accepted that the set of axioms can be infinite >>>>>>>>
knowledge.
Once again you try to deceive with a change of topic. There is no >>>>>>> need to prove the incompletenes of human general knowledge as that >>>>>>> already is obvious. But G||del's and Tarski's theorems are about >>>>>>> natural number arithmetic and its extensions so they need to cover >>>>>>> the possibility that there are infinitely many axioms.
Tarski admits that he anchor his whole proof on the
liar paradox and
He doesn't "anchor" it to the liar paradix. The liar paradox has some >>>>> formal similarity to the sentence Tarski constructs but is not a part >>>>> of the proof. Consequently anything said about the liar's paracos is >>>>> irrelevant to the correctness of the proof.
Factually incorrect.
False. Tarski confirms what I said:
And I prove my point in the paragraph that you skipped.
Not relevant to Tarski's rerutation of your "Factually incorrect".
On 2025-10-01 01:48:56 +0000, olcott said:
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or dontradiction is
true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words.
On 10/1/2025 5:12 AM, Mikko wrote:
On 2025-10-01 01:46:15 +0000, olcott said:
On 9/30/2025 7:48 AM, Mikko wrote:
On 2025-09-29 12:21:25 +0000, olcott said:
On 9/27/2025 5:05 AM, Mikko wrote:
On 2025-09-26 01:08:45 +0000, olcott said:
On 9/25/2025 2:15 AM, Mikko wrote:
On 2025-09-24 14:27:00 +0000, olcott said:
On 9/24/2025 2:12 AM, Mikko wrote:No, but it is a significant aspect of culture. A question of importance
On 2025-09-23 16:04:38 +0000, olcott said:
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said:
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
G||del's sentence is not really self-referential. It is a valid
sentence in the first order language of Peano arithmetic. That >>>>>>>>>>>>>>>> the value of an arithmetic expression in that sentence evaluates
to the G||del number of the sentence has no arithmetic significance.
Yes that is the moronic received view yet these stupid >>>>>>>>>>>>>>> people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper: >>>>>>>>>>>>>>>
...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...
...We are therefore confronted with a proposition which asserts its own
unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
The most important aspect is the theorem itself: every theory that
has the symbols and axioms of the first order Peano arithmetic is
either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important.
Prior to Pythagoras there was a universal consensus
that the Earth is flat.
To think the Earth as flat is simpler and good enough for many >>>>>>>>>> purposes. For a long time there was no need to think about the >>>>>>>>>> shape of the Earth.
The point is that not even a universal consensus equates to truth. >>>>>>>>
is not a matter of truth but a matter of opinion.
Not when we are representing the finite set of human general knowledge.Many poeple also
find it useful to know that any attempt to construct a cmplete theory
of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is screwed up. >>>>>>>>>>> If you want to build a formal system that is not anchored in a >>>>>>>>>>> screwed up idea than this is straight forward.
That 2 + 3 = 5 has practical value even if the theory around it >>>>>>>>>> cannot be made complete.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply >>>>>>>>>>> the truth preserving operation of semantic logical entailment >>>>>>>>>>> to these basic facts.
It is generally accepted that the set of axioms can be infinite >>>>>>>>>
Once again you try to deceive with a change of topic. There is no >>>>>>>> need to prove the incompletenes of human general knowledge as that >>>>>>>> already is obvious. But G||del's and Tarski's theorems are about >>>>>>>> natural number arithmetic and its extensions so they need to cover >>>>>>>> the possibility that there are infinitely many axioms.
Tarski admits that he anchor his whole proof on the
liar paradox and
He doesn't "anchor" it to the liar paradix. The liar paradox has some >>>>>> formal similarity to the sentence Tarski constructs but is not a part >>>>>> of the proof. Consequently anything said about the liar's paracos is >>>>>> irrelevant to the correctness of the proof.
Factually incorrect.
False. Tarski confirms what I said:
And I prove my point in the paragraph that you skipped.
Not relevant to Tarski's rerutation of your "Factually incorrect".
He anchored his whole proof in that he
needed an extra level of logic to do this:
X is any expression of language that is not
a truth bearer. It is true that X is not true.
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or dontradiction is
true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words.
The syntax of formal logical languages allows
some expressions to be created having pathological
self-reference(Olcott 2004).
It was enormously more complicated for G||del
to say this Olcott Minimal Type Theory Expression.
G := ((F re4 G) re? (F re4 -4G)) // this one may be imperfect
Semantically these expressions are not truth bearers.
...We are therefore confronted with a proposition
which asserts its own unprovability. (G||del 1931:40-41)
This is the exactly correct conventional expression:
Incomplete(T) rao rea-a ((T re4 -a) reo (T re4 -4-a)).
On 2025-10-01 15:40:06 +0000, olcott said:
On 10/1/2025 5:12 AM, Mikko wrote:
On 2025-10-01 01:46:15 +0000, olcott said:
On 9/30/2025 7:48 AM, Mikko wrote:
On 2025-09-29 12:21:25 +0000, olcott said:
On 9/27/2025 5:05 AM, Mikko wrote:
On 2025-09-26 01:08:45 +0000, olcott said:
On 9/25/2025 2:15 AM, Mikko wrote:
On 2025-09-24 14:27:00 +0000, olcott said:
On 9/24/2025 2:12 AM, Mikko wrote:
On 2025-09-23 16:04:38 +0000, olcott said:
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said:Prior to Pythagoras there was a universal consensus
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
G||del's sentence is not really self-referential. It is >>>>>>>>>>>>>>>>> a valid
sentence in the first order language of Peano >>>>>>>>>>>>>>>>> arithmetic. That
the value of an arithmetic expression in that sentence >>>>>>>>>>>>>>>>> evaluates
to the G||del number of the sentence has no arithmetic >>>>>>>>>>>>>>>>> significance.
Yes that is the moronic received view yet these stupid >>>>>>>>>>>>>>>> people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 Incompleteness >>>>>>>>>>>>>>>> theorem
are these plain English direct quotes of G||del from his >>>>>>>>>>>>>>>> paper:
...there is also a close relationship with the rCLliarrCY >>>>>>>>>>>>>>>> antinomy,14 ...
...14 Every epistemological antinomy can likewise be >>>>>>>>>>>>>>>> used for a similar undecidability proof...
...We are therefore confronted with a proposition which >>>>>>>>>>>>>>>> asserts its own unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia >>>>>>>>>>>>>>>> Mathematica And Related Systems
The most important aspect is the theorem itself: every >>>>>>>>>>>>>>> theory that
has the symbols and axioms of the first order Peano >>>>>>>>>>>>>>> arithmetic is
either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important. >>>>>>>>>>>>
that the Earth is flat.
To think the Earth as flat is simpler and good enough for many >>>>>>>>>>> purposes. For a long time there was no need to think about the >>>>>>>>>>> shape of the Earth.
The point is that not even a universal consensus equates to >>>>>>>>>> truth.
No, but it is a significant aspect of culture. A question of >>>>>>>>> importance
is not a matter of truth but a matter of opinion.
Not when we are representing the finite set of human general >>>>>>>>>> knowledge.Many poeple also
find it useful to know that any attempt to construct a >>>>>>>>>>>>> cmplete theory
of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is >>>>>>>>>>>> screwed up.
If you want to build a formal system that is not anchored in a >>>>>>>>>>>> screwed up idea than this is straight forward.
That 2 + 3 = 5 has practical value even if the theory around it >>>>>>>>>>> cannot be made complete.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply >>>>>>>>>>>> the truth preserving operation of semantic logical entailment >>>>>>>>>>>> to these basic facts.
It is generally accepted that the set of axioms can be infinite >>>>>>>>>>
Once again you try to deceive with a change of topic. There is no >>>>>>>>> need to prove the incompletenes of human general knowledge as that >>>>>>>>> already is obvious. But G||del's and Tarski's theorems are about >>>>>>>>> natural number arithmetic and its extensions so they need to cover >>>>>>>>> the possibility that there are infinitely many axioms.
Tarski admits that he anchor his whole proof on the
liar paradox and
He doesn't "anchor" it to the liar paradix. The liar paradox has >>>>>>> some
formal similarity to the sentence Tarski constructs but is not a >>>>>>> part
of the proof. Consequently anything said about the liar's paracos is >>>>>>> irrelevant to the correctness of the proof.
Factually incorrect.
False. Tarski confirms what I said:
And I prove my point in the paragraph that you skipped.
Not relevant to Tarski's rerutation of your "Factually incorrect".
He anchored his whole proof in that he
needed an extra level of logic to do this:
You need metalogic if you want to say anything about logic.
X is any expression of language that is not
a truth bearer. It is true that X is not true.
You cannot say that in the plain language of logic. You need a
metatheory that can express and infer about expressions and
relate them to truth.
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or dontradiction is
true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words.
The syntax of formal logical languages allows
some expressions to be created having pathological
self-reference(Olcott 2004).
No syntax is enough for self-reference.
The semantics determines whether
any syntactic construct is a self-reference. For example. the arithmetic semantics of a formal language of arithmetics do not permit a self- reference.
It was enormously more complicated for G||del
to say this Olcott Minimal Type Theory Expression.
G := ((F re4 G) re? (F re4 -4G))-a // this one may be imperfect
Semantically these expressions are not truth bearers.
Neither the usual first order logic nor the arithmetic semantics
assingns any meaning to the symbols := and re4. Because G||del's
proof was about the Peano arithmetic he could only use the symbols
of the language of Peano arithmetic.
...We are therefore confronted with a proposition
which asserts its own unprovability. (G||del 1931:40-41)
That is, G||del proved that a particular sentence of Peano arithmetic
is provable only if it is arithmetically false.
This is the exactly correct conventional expression:
Incomplete(T) rao rea-a ((T re4 -a) reo (T re4 -4-a)).
Here one could use := instead of rao. But I think the conventional way
is simply to use words.
All of which is irrelevant to the tautology "Every sentence of logic
that is not tautology or dontradiction is true in some contexts and
false in others" and to your false response to it.
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or dontradiction is
true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words.
The syntax of formal logical languages allows
some expressions to be created having pathological
self-reference(Olcott 2004).
No syntax is enough for self-reference.
Syntax is enough for self-reference.
Tarski's Liar Paradox from page 248
It would then be possible to reconstruct the antinomy of the liar
in the metalanguage, by forming in the language itself a sentence
x such that the sentence of the metalanguage which is correlated
with x asserts that x is not a true sentence.
https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. the arithmetic
semantics of a formal language of arithmetics do not permit a self-
reference.
G||del uses tricks for that.
https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
LP := ~True(LP)
It was enormously more complicated for G||del
to say this Olcott Minimal Type Theory Expression.
G := ((F re4 G) re? (F re4 -4G))-a // this one may be imperfect
Semantically these expressions are not truth bearers.
Neither the usual first order logic nor the arithmetic semantics
assingns any meaning to the symbols := and re4. Because G||del's
proof was about the Peano arithmetic he could only use the symbols
of the language of Peano arithmetic.
Yes he had to go though quite a mess so say the same thing.
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ... ...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...
...We are therefore confronted with a proposition which asserts its own unprovability. 15 ...
(G||del 1931:40-41)
...We are therefore confronted with a proposition
which asserts its own unprovability. (G||del 1931:40-41)
That is, G||del proved that a particular sentence of Peano arithmetic
is provable only if it is arithmetically false.
This is the exactly correct conventional expression:
Incomplete(T) rao rea-a ((T re4 -a) reo (T re4 -4-a)).
Here one could use := instead of rao. But I think the conventional way
is simply to use words.
All of which is irrelevant to the tautology "Every sentence of logic
that is not tautology or dontradiction is true in some contexts and
false in others" and to your false response to it.
LP := ~True(LP) is a counter-example.
On 10/2/2025 4:38 AM, Mikko wrote:
On 2025-10-01 15:40:06 +0000, olcott said:
On 10/1/2025 5:12 AM, Mikko wrote:
On 2025-10-01 01:46:15 +0000, olcott said:
On 9/30/2025 7:48 AM, Mikko wrote:
On 2025-09-29 12:21:25 +0000, olcott said:
On 9/27/2025 5:05 AM, Mikko wrote:
On 2025-09-26 01:08:45 +0000, olcott said:
On 9/25/2025 2:15 AM, Mikko wrote:
On 2025-09-24 14:27:00 +0000, olcott said:
On 9/24/2025 2:12 AM, Mikko wrote:No, but it is a significant aspect of culture. A question of importance
On 2025-09-23 16:04:38 +0000, olcott said:
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said:Prior to Pythagoras there was a universal consensus
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
G||del's sentence is not really self-referential. It is a valid
sentence in the first order language of Peano arithmetic. That
the value of an arithmetic expression in that sentence evaluates
to the G||del number of the sentence has no arithmetic significance.
Yes that is the moronic received view yet these stupid >>>>>>>>>>>>>>>>> people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...
...We are therefore confronted with a proposition which asserts its own
unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
The most important aspect is the theorem itself: every theory that
has the symbols and axioms of the first order Peano arithmetic is
either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important. >>>>>>>>>>>>>
that the Earth is flat.
To think the Earth as flat is simpler and good enough for many >>>>>>>>>>>> purposes. For a long time there was no need to think about the >>>>>>>>>>>> shape of the Earth.
The point is that not even a universal consensus equates to truth. >>>>>>>>>>
is not a matter of truth but a matter of opinion.
Not when we are representing the finite set of human general knowledge.Many poeple also
find it useful to know that any attempt to construct a cmplete theory
of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is screwed up.
If you want to build a formal system that is not anchored in a >>>>>>>>>>>>> screwed up idea than this is straight forward.
That 2 + 3 = 5 has practical value even if the theory around it >>>>>>>>>>>> cannot be made complete.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply >>>>>>>>>>>>> the truth preserving operation of semantic logical entailment >>>>>>>>>>>>> to these basic facts.
It is generally accepted that the set of axioms can be infinite >>>>>>>>>>>
Once again you try to deceive with a change of topic. There is no >>>>>>>>>> need to prove the incompletenes of human general knowledge as that >>>>>>>>>> already is obvious. But G||del's and Tarski's theorems are about >>>>>>>>>> natural number arithmetic and its extensions so they need to cover >>>>>>>>>> the possibility that there are infinitely many axioms.
Tarski admits that he anchor his whole proof on the
liar paradox and
He doesn't "anchor" it to the liar paradix. The liar paradox has some >>>>>>>> formal similarity to the sentence Tarski constructs but is not a part >>>>>>>> of the proof. Consequently anything said about the liar's paracos is >>>>>>>> irrelevant to the correctness of the proof.
Factually incorrect.
False. Tarski confirms what I said:
And I prove my point in the paragraph that you skipped.
Not relevant to Tarski's rerutation of your "Factually incorrect".
He anchored his whole proof in that he
needed an extra level of logic to do this:
You need metalogic if you want to say anything about logic.
X is any expression of language that is not
a truth bearer. It is true that X is not true.
You cannot say that in the plain language of logic. You need a
metatheory that can express and infer about expressions and
relate them to truth.
I proved otherwise https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or dontradiction is >>>>>>> true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words.
The syntax of formal logical languages allows
some expressions to be created having pathological
self-reference(Olcott 2004).
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string without meaning
does not refer.
Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy of the liar
-a-a-a in the metalanguage, by forming in the language itself a sentence
-a-a-a x such that the sentence of the metalanguage which is correlated
-a-a-a with x asserts that x is not a true sentence.
-a-a-a https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. the arithmetic >>> semantics of a formal language of arithmetics do not permit a self-
reference.
G||del uses tricks for that.
Tarski used the same tricks.
https://www.researchgate.net/
publication/331859461_Minimal_Type_Theory_YACC_BNF
LP := ~True(LP)
It was enormously more complicated for G||del
to say this Olcott Minimal Type Theory Expression.
G := ((F re4 G) re? (F re4 -4G))-a // this one may be imperfect
Semantically these expressions are not truth bearers.
Neither the usual first order logic nor the arithmetic semantics
assingns any meaning to the symbols := and re4. Because G||del's
proof was about the Peano arithmetic he could only use the symbols
of the language of Peano arithmetic.
Yes he had to go though quite a mess so say the same thing.
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...
...We are therefore confronted with a proposition which asserts its
own unprovability. 15 ...
(G||del 1931:40-41)
Those are not parts of the theorem or its proof. They only become
important (to some extent) after the proof.
...We are therefore confronted with a proposition
which asserts its own unprovability. (G||del 1931:40-41)
That is, G||del proved that a particular sentence of Peano arithmetic
is provable only if it is arithmetically false.
This is the exactly correct conventional expression:
Incomplete(T) rao rea-a ((T re4 -a) reo (T re4 -4-a)).
Here one could use := instead of rao. But I think the conventional way
is simply to use words.
All of which is irrelevant to the tautology "Every sentence of logic
that is not tautology or dontradiction is true in some contexts and
false in others" and to your false response to it.
LP := ~True(LP) is a counter-example.
In usual formal languages that is not a sentence and therefore need
not be interpreted. In languages that allow := it is usually a syntax
error to have the symbol on the left in the expression on the right.
On 2025-10-02 10:07:33 +0000, olcott said:
On 10/2/2025 4:38 AM, Mikko wrote:
On 2025-10-01 15:40:06 +0000, olcott said:
On 10/1/2025 5:12 AM, Mikko wrote:
On 2025-10-01 01:46:15 +0000, olcott said:
On 9/30/2025 7:48 AM, Mikko wrote:
On 2025-09-29 12:21:25 +0000, olcott said:
On 9/27/2025 5:05 AM, Mikko wrote:
On 2025-09-26 01:08:45 +0000, olcott said:
On 9/25/2025 2:15 AM, Mikko wrote:
On 2025-09-24 14:27:00 +0000, olcott said:
On 9/24/2025 2:12 AM, Mikko wrote:
On 2025-09-23 16:04:38 +0000, olcott said:
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said:Prior to Pythagoras there was a universal consensus >>>>>>>>>>>>>> that the Earth is flat.
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said:
On 9/20/2025 4:31 AM, Mikko wrote:
G||del's sentence is not really self-referential. It >>>>>>>>>>>>>>>>>>> is a valid
sentence in the first order language of Peano >>>>>>>>>>>>>>>>>>> arithmetic. That
the value of an arithmetic expression in that >>>>>>>>>>>>>>>>>>> sentence evaluates
to the G||del number of the sentence has no arithmetic >>>>>>>>>>>>>>>>>>> significance.
Yes that is the moronic received view yet these stupid >>>>>>>>>>>>>>>>>> people stupidly ignore G||del's own words.
It is what G||del said and proved.
The most important aspect of G||del's 1931 >>>>>>>>>>>>>>>>>> Incompleteness theorem
are these plain English direct quotes of G||del from >>>>>>>>>>>>>>>>>> his paper:
...there is also a close relationship with the rCLliarrCY >>>>>>>>>>>>>>>>>> antinomy,14 ...
...14 Every epistemological antinomy can likewise be >>>>>>>>>>>>>>>>>> used for a similar undecidability proof... >>>>>>>>>>>>>>>>>> ...We are therefore confronted with a proposition >>>>>>>>>>>>>>>>>> which asserts its own unprovability. 15 ... >>>>>>>>>>>>>>>>>> (G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia >>>>>>>>>>>>>>>>>> Mathematica And Related Systems
The most important aspect is the theorem itself: every >>>>>>>>>>>>>>>>> theory that
has the symbols and axioms of the first order Peano >>>>>>>>>>>>>>>>> arithmetic is
either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important. >>>>>>>>>>>>>>
To think the Earth as flat is simpler and good enough for many >>>>>>>>>>>>> purposes. For a long time there was no need to think about the >>>>>>>>>>>>> shape of the Earth.
The point is that not even a universal consensus equates to >>>>>>>>>>>> truth.
No, but it is a significant aspect of culture. A question of >>>>>>>>>>> importance
is not a matter of truth but a matter of opinion.
Many poeple also
find it useful to know that any attempt to construct a >>>>>>>>>>>>>>> cmplete theory
of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is >>>>>>>>>>>>>> screwed up.
If you want to build a formal system that is not anchored >>>>>>>>>>>>>> in a
screwed up idea than this is straight forward.
That 2 + 3 = 5 has practical value even if the theory >>>>>>>>>>>>> around it
cannot be made complete.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply >>>>>>>>>>>>>> the truth preserving operation of semantic logical entailment >>>>>>>>>>>>>> to these basic facts.
It is generally accepted that the set of axioms can be >>>>>>>>>>>>> infinite
Not when we are representing the finite set of human general >>>>>>>>>>>> knowledge.
Once again you try to deceive with a change of topic. There >>>>>>>>>>> is no
need to prove the incompletenes of human general knowledge as >>>>>>>>>>> that
already is obvious. But G||del's and Tarski's theorems are about >>>>>>>>>>> natural number arithmetic and its extensions so they need to >>>>>>>>>>> cover
the possibility that there are infinitely many axioms.
Tarski admits that he anchor his whole proof on the
liar paradox and
He doesn't "anchor" it to the liar paradix. The liar paradox >>>>>>>>> has some
formal similarity to the sentence Tarski constructs but is not >>>>>>>>> a part
of the proof. Consequently anything said about the liar's
paracos is
irrelevant to the correctness of the proof.
Factually incorrect.
False. Tarski confirms what I said:
And I prove my point in the paragraph that you skipped.
Not relevant to Tarski's rerutation of your "Factually incorrect".
He anchored his whole proof in that he
needed an extra level of logic to do this:
You need metalogic if you want to say anything about logic.
X is any expression of language that is not
a truth bearer. It is true that X is not true.
You cannot say that in the plain language of logic. You need a
metatheory that can express and infer about expressions and
relate them to truth.
I proved otherwise
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
You didn't prove anything. If you could you would post here the
plain logic sentence that says what you said.
But Tarski proved about natural numbers that if there were a definition
of a predicate in terms of a formula in the language of Peano arithmetic
that accepts all numbers that encode a true sentence and rejects all
other numbers then that predicate would accept a number that encodes
a false sentence or reject a number that encodes a true sentence.
On 10/4/2025 5:25 AM, Mikko wrote:
On 2025-10-02 10:07:33 +0000, olcott said:
On 10/2/2025 4:38 AM, Mikko wrote:
On 2025-10-01 15:40:06 +0000, olcott said:
On 10/1/2025 5:12 AM, Mikko wrote:
On 2025-10-01 01:46:15 +0000, olcott said:
On 9/30/2025 7:48 AM, Mikko wrote:
On 2025-09-29 12:21:25 +0000, olcott said:
On 9/27/2025 5:05 AM, Mikko wrote:
On 2025-09-26 01:08:45 +0000, olcott said:
On 9/25/2025 2:15 AM, Mikko wrote:
On 2025-09-24 14:27:00 +0000, olcott said:
On 9/24/2025 2:12 AM, Mikko wrote:
On 2025-09-23 16:04:38 +0000, olcott said:
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said:Prior to Pythagoras there was a universal consensus >>>>>>>>>>>>>>> that the Earth is flat.
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said: >>>>>>>>>>>>>>>>>>> On 9/20/2025 4:31 AM, Mikko wrote:
It is what G||del said and proved.
G||del's sentence is not really self-referential. It is a valid
sentence in the first order language of Peano arithmetic. That
the value of an arithmetic expression in that sentence evaluates
to the G||del number of the sentence has no arithmetic significance.
Yes that is the moronic received view yet these stupid >>>>>>>>>>>>>>>>>>> people stupidly ignore G||del's own words. >>>>>>>>>>>>>>>>>>
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...
...We are therefore confronted with a proposition which asserts its own
unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
The most important aspect is the theorem itself: every theory that
has the symbols and axioms of the first order Peano arithmetic is
either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important. >>>>>>>>>>>>>>>
To think the Earth as flat is simpler and good enough for many >>>>>>>>>>>>>> purposes. For a long time there was no need to think about the >>>>>>>>>>>>>> shape of the Earth.
The point is that not even a universal consensus equates to truth.
No, but it is a significant aspect of culture. A question of importance
is not a matter of truth but a matter of opinion.
Not when we are representing the finite set of human general knowledge.Many poeple also
find it useful to know that any attempt to construct a cmplete theory
of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is screwed up.
If you want to build a formal system that is not anchored in a >>>>>>>>>>>>>>> screwed up idea than this is straight forward.
That 2 + 3 = 5 has practical value even if the theory around it >>>>>>>>>>>>>> cannot be made complete.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply >>>>>>>>>>>>>>> the truth preserving operation of semantic logical entailment >>>>>>>>>>>>>>> to these basic facts.
It is generally accepted that the set of axioms can be infinite >>>>>>>>>>>>>
Once again you try to deceive with a change of topic. There is no >>>>>>>>>>>> need to prove the incompletenes of human general knowledge as that >>>>>>>>>>>> already is obvious. But G||del's and Tarski's theorems are about >>>>>>>>>>>> natural number arithmetic and its extensions so they need to cover >>>>>>>>>>>> the possibility that there are infinitely many axioms.
Tarski admits that he anchor his whole proof on the
liar paradox and
He doesn't "anchor" it to the liar paradix. The liar paradox has some
formal similarity to the sentence Tarski constructs but is not a part
of the proof. Consequently anything said about the liar's paracos is >>>>>>>>>> irrelevant to the correctness of the proof.
Factually incorrect.
False. Tarski confirms what I said:
And I prove my point in the paragraph that you skipped.
Not relevant to Tarski's rerutation of your "Factually incorrect".
He anchored his whole proof in that he
needed an extra level of logic to do this:
You need metalogic if you want to say anything about logic.
X is any expression of language that is not
a truth bearer. It is true that X is not true.
You cannot say that in the plain language of logic. You need a
metatheory that can express and infer about expressions and
relate them to truth.
I proved otherwise
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
You didn't prove anything. If you could you would post here the
plain logic sentence that says what you said.
It explains a correction to an aspect of the
foundation of logic and it does this in plain
English and a tiny bit of Prolog.
But Tarski proved about natural numbers that if there were a definition
of a predicate in terms of a formula in the language of Peano arithmetic
that accepts all numbers that encode a true sentence and rejects all
other numbers then that predicate would accept a number that encodes
a false sentence or reject a number that encodes a true sentence.
Mine has a broader scope that can be applied to
any pathological self-reference(Olcott 2004) in
formal expressions and formalized natural language
expressions.
On 10/4/2025 5:11 AM, Mikko wrote:
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or dontradiction is >>>>>>>> true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words.
The syntax of formal logical languages allows
some expressions to be created having pathological
self-reference(Olcott 2004).
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string without meaning
does not refer.
Self-reference can be detected in a string with a name.
Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy of the liar >>> -a-a-a in the metalanguage, by forming in the language itself a sentence >>> -a-a-a x such that the sentence of the metalanguage which is correlated
-a-a-a with x asserts that x is not a true sentence.
-a-a-a https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. the arithmetic >>>> semantics of a formal language of arithmetics do not permit a self-
reference.
G||del uses tricks for that.
Tarski used the same tricks.
Yet they only actually boil down to
Incomplete(F) rao reaG ((F re4 G) reo (F re4 -4G)).
and this
LP := ~True(LP)
On 2025-10-04 13:34:07 +0000, olcott said:
On 10/4/2025 5:25 AM, Mikko wrote:
On 2025-10-02 10:07:33 +0000, olcott said:
On 10/2/2025 4:38 AM, Mikko wrote:
On 2025-10-01 15:40:06 +0000, olcott said:
On 10/1/2025 5:12 AM, Mikko wrote:
On 2025-10-01 01:46:15 +0000, olcott said:He anchored his whole proof in that he
On 9/30/2025 7:48 AM, Mikko wrote:
On 2025-09-29 12:21:25 +0000, olcott said:
On 9/27/2025 5:05 AM, Mikko wrote:
On 2025-09-26 01:08:45 +0000, olcott said:
On 9/25/2025 2:15 AM, Mikko wrote:
On 2025-09-24 14:27:00 +0000, olcott said:Tarski admits that he anchor his whole proof on the
On 9/24/2025 2:12 AM, Mikko wrote:
On 2025-09-23 16:04:38 +0000, olcott said:
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said:Prior to Pythagoras there was a universal consensus >>>>>>>>>>>>>>>> that the Earth is flat.
On 9/21/2025 4:22 AM, Mikko wrote:
On 2025-09-20 14:57:20 +0000, olcott said: >>>>>>>>>>>>>>>>>>>> On 9/20/2025 4:31 AM, Mikko wrote:
It is what G||del said and proved.
G||del's sentence is not really self-referential. It >>>>>>>>>>>>>>>>>>>>> is a valid
sentence in the first order language of Peano >>>>>>>>>>>>>>>>>>>>> arithmetic. That
the value of an arithmetic expression in that >>>>>>>>>>>>>>>>>>>>> sentence evaluates
to the G||del number of the sentence has no >>>>>>>>>>>>>>>>>>>>> arithmetic significance.
Yes that is the moronic received view yet these stupid >>>>>>>>>>>>>>>>>>>> people stupidly ignore G||del's own words. >>>>>>>>>>>>>>>>>>>
The most important aspect of G||del's 1931 >>>>>>>>>>>>>>>>>>>> Incompleteness theorem
are these plain English direct quotes of G||del from >>>>>>>>>>>>>>>>>>>> his paper:
...there is also a close relationship with the >>>>>>>>>>>>>>>>>>>> rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be >>>>>>>>>>>>>>>>>>>> used for a similar undecidability proof... >>>>>>>>>>>>>>>>>>>> ...We are therefore confronted with a proposition >>>>>>>>>>>>>>>>>>>> which asserts its own unprovability. 15 ... >>>>>>>>>>>>>>>>>>>> (G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia >>>>>>>>>>>>>>>>>>>> Mathematica And Related Systems
The most important aspect is the theorem itself: >>>>>>>>>>>>>>>>>>> every theory that
has the symbols and axioms of the first order Peano >>>>>>>>>>>>>>>>>>> arithmetic is
either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection
It is important because people consider it important. >>>>>>>>>>>>>>>>
To think the Earth as flat is simpler and good enough for >>>>>>>>>>>>>>> many
purposes. For a long time there was no need to think >>>>>>>>>>>>>>> about the
shape of the Earth.
The point is that not even a universal consensus equates >>>>>>>>>>>>>> to truth.
No, but it is a significant aspect of culture. A question >>>>>>>>>>>>> of importance
is not a matter of truth but a matter of opinion.
Many poeple also
find it useful to know that any attempt to construct a >>>>>>>>>>>>>>>>> cmplete theory
of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is >>>>>>>>>>>>>>>> screwed up.
If you want to build a formal system that is not >>>>>>>>>>>>>>>> anchored in a
screwed up idea than this is straight forward.
That 2 + 3 = 5 has practical value even if the theory >>>>>>>>>>>>>>> around it
cannot be made complete.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply >>>>>>>>>>>>>>>> the truth preserving operation of semantic logical >>>>>>>>>>>>>>>> entailment
to these basic facts.
It is generally accepted that the set of axioms can be >>>>>>>>>>>>>>> infinite
Not when we are representing the finite set of human >>>>>>>>>>>>>> general knowledge.
Once again you try to deceive with a change of topic. There >>>>>>>>>>>>> is no
need to prove the incompletenes of human general knowledge >>>>>>>>>>>>> as that
already is obvious. But G||del's and Tarski's theorems are >>>>>>>>>>>>> about
natural number arithmetic and its extensions so they need >>>>>>>>>>>>> to cover
the possibility that there are infinitely many axioms. >>>>>>>>>>>>
liar paradox and
He doesn't "anchor" it to the liar paradix. The liar paradox >>>>>>>>>>> has some
formal similarity to the sentence Tarski constructs but is >>>>>>>>>>> not a part
of the proof. Consequently anything said about the liar's >>>>>>>>>>> paracos is
irrelevant to the correctness of the proof.
Factually incorrect.
False. Tarski confirms what I said:
And I prove my point in the paragraph that you skipped.
Not relevant to Tarski's rerutation of your "Factually incorrect". >>>>>>
needed an extra level of logic to do this:
You need metalogic if you want to say anything about logic.
X is any expression of language that is not
a truth bearer. It is true that X is not true.
You cannot say that in the plain language of logic. You need a
metatheory that can express and infer about expressions and
relate them to truth.
I proved otherwise
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
You didn't prove anything. If you could you would post here the
plain logic sentence that says what you said.
It explains a correction to an aspect of the
foundation of logic and it does this in plain
English and a tiny bit of Prolog.
It is not correct to use the word "correction" when the thing to
be corrected is correct already.
But Tarski proved about natural numbers that if there were a definition
of a predicate in terms of a formula in the language of Peano arithmetic >>> that accepts all numbers that encode a true sentence and rejects all
other numbers then that predicate would accept a number that encodes
a false sentence or reject a number that encodes a true sentence.
Mine has a broader scope that can be applied to
any pathological self-reference(Olcott 2004) in
formal expressions and formalized natural language
expressions.
Tarstki's scope is wider, too, but the first order arithmetic of natural numbers is the most interesting part of the scope.
On 2025-10-04 13:30:22 +0000, olcott said:
On 10/4/2025 5:11 AM, Mikko wrote:
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or dontradiction is >>>>>>>>> true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words.
The syntax of formal logical languages allows
some expressions to be created having pathological
self-reference(Olcott 2004).
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string without meaning
does not refer.
Self-reference can be detected in a string with a name.
Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy of the liar >>>> -a-a-a in the metalanguage, by forming in the language itself a sentence >>>> -a-a-a x such that the sentence of the metalanguage which is correlated >>>> -a-a-a with x asserts that x is not a true sentence.
-a-a-a https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. the
arithmetic
semantics of a formal language of arithmetics do not permit a self-
reference.
G||del uses tricks for that.
Tarski used the same tricks.
Yet they only actually boil down to
Incomplete(F) rao reaG ((F re4 G) reo (F re4 -4G)).
and this
LP := ~True(LP)
The system they considered has no symbol for :=. Instead, they construct something like LP <-> ~True(LP). G||del then shows that that the expression that asserts its own unprovability is is not provable and therefore true.
Tarski shows that if there is there is a formula that is true if its
argument encodes a true sentence and false if its argument encodes a false statements (its value does not matter if the argument does not encode
a sentence) then it is possible to encode a sentence that says "the truth formula returns false if given my encoding" and give it to the truth
formula, which would then return the negation of the value it returns.
As that would be a contradiction there cannot be a truth formula and therefore no definition truth.
At least for some systems it is possible to have a truth predicate in
a metatheory even if not in the system itself.
On 10/5/2025 5:06 AM, Mikko wrote:
On 2025-10-04 13:34:07 +0000, olcott said:
On 10/4/2025 5:25 AM, Mikko wrote:
On 2025-10-02 10:07:33 +0000, olcott said:
On 10/2/2025 4:38 AM, Mikko wrote:
On 2025-10-01 15:40:06 +0000, olcott said:
On 10/1/2025 5:12 AM, Mikko wrote:
On 2025-10-01 01:46:15 +0000, olcott said:He anchored his whole proof in that he
On 9/30/2025 7:48 AM, Mikko wrote:
On 2025-09-29 12:21:25 +0000, olcott said:
On 9/27/2025 5:05 AM, Mikko wrote:
On 2025-09-26 01:08:45 +0000, olcott said:
On 9/25/2025 2:15 AM, Mikko wrote:
On 2025-09-24 14:27:00 +0000, olcott said:Tarski admits that he anchor his whole proof on the
On 9/24/2025 2:12 AM, Mikko wrote:
On 2025-09-23 16:04:38 +0000, olcott said:
On 9/23/2025 4:21 AM, Mikko wrote:
On 2025-09-23 00:56:19 +0000, olcott said: >>>>>>>>>>>>>>>>>>Prior to Pythagoras there was a universal consensus >>>>>>>>>>>>>>>>> that the Earth is flat.
On 9/21/2025 4:22 AM, Mikko wrote:It is important because people consider it important. >>>>>>>>>>>>>>>>>
On 2025-09-20 14:57:20 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>> On 9/20/2025 4:31 AM, Mikko wrote:
It is what G||del said and proved.
G||del's sentence is not really self-referential. It is a valid
sentence in the first order language of Peano arithmetic. That
the value of an arithmetic expression in that sentence evaluates
to the G||del number of the sentence has no arithmetic significance.
Yes that is the moronic received view yet these stupid >>>>>>>>>>>>>>>>>>>>> people stupidly ignore G||del's own words. >>>>>>>>>>>>>>>>>>>>
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...
...We are therefore confronted with a proposition which asserts its own
unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
The most important aspect is the theorem itself: every theory that
has the symbols and axioms of the first order Peano arithmetic is
either incomplete or inconsistent.
That never has been the important part.
That has always been bullshit misdirection >>>>>>>>>>>>>>>>>>
To think the Earth as flat is simpler and good enough for many >>>>>>>>>>>>>>>> purposes. For a long time there was no need to think about the >>>>>>>>>>>>>>>> shape of the Earth.
The point is that not even a universal consensus equates to truth.
No, but it is a significant aspect of culture. A question of importance
is not a matter of truth but a matter of opinion.
That 2 + 3 = 5 has practical value even if the theory around itMany poeple also
find it useful to know that any attempt to construct a cmplete theory
of arithemtic would be a waste of time.
Yet only when the architecture of the formal system is screwed up.
If you want to build a formal system that is not anchored in a
screwed up idea than this is straight forward. >>>>>>>>>>>>>>>>
cannot be made complete.
*Refuting G||del 1931 Incompleteness*
You begin with a finite list of basic facts and only apply >>>>>>>>>>>>>>>>> the truth preserving operation of semantic logical entailment >>>>>>>>>>>>>>>>> to these basic facts.
It is generally accepted that the set of axioms can be infinite
Not when we are representing the finite set of human general knowledge.
Once again you try to deceive with a change of topic. There is no
need to prove the incompletenes of human general knowledge as that
already is obvious. But G||del's and Tarski's theorems are about >>>>>>>>>>>>>> natural number arithmetic and its extensions so they need to cover
the possibility that there are infinitely many axioms. >>>>>>>>>>>>>
liar paradox and
He doesn't "anchor" it to the liar paradix. The liar paradox has some
formal similarity to the sentence Tarski constructs but is not a part
of the proof. Consequently anything said about the liar's paracos is
irrelevant to the correctness of the proof.
Factually incorrect.
False. Tarski confirms what I said:
And I prove my point in the paragraph that you skipped.
Not relevant to Tarski's rerutation of your "Factually incorrect". >>>>>>>
needed an extra level of logic to do this:
You need metalogic if you want to say anything about logic.
X is any expression of language that is not
a truth bearer. It is true that X is not true.
You cannot say that in the plain language of logic. You need a
metatheory that can express and infer about expressions and
relate them to truth.
I proved otherwise
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
You didn't prove anything. If you could you would post here the
plain logic sentence that says what you said.
It explains a correction to an aspect of the
foundation of logic and it does this in plain
English and a tiny bit of Prolog.
It is not correct to use the word "correction" when the thing to
be corrected is correct already.
G||del 1931 undecidability and Tarski Undefinability
only exist because they they not know to reject an
expression of language that is not a truth bearer.
Claude AI is quite hesitant at first, disagreeing
with me several times. Then it is finally convinced
that I am correct.
But Tarski proved about natural numbers that if there were a definition >>>> of a predicate in terms of a formula in the language of Peano arithmetic >>>> that accepts all numbers that encode a true sentence and rejects all
other numbers then that predicate would accept a number that encodes
a false sentence or reject a number that encodes a true sentence.
Mine has a broader scope that can be applied to
any pathological self-reference(Olcott 2004) in
formal expressions and formalized natural language
expressions.
Tarstki's scope is wider, too, but the first order arithmetic of natural
numbers is the most interesting part of the scope.
My scope is the entire body of human knowledge
that can be expressed in language.
On 10/5/2025 5:26 AM, Mikko wrote:
On 2025-10-04 13:30:22 +0000, olcott said:
On 10/4/2025 5:11 AM, Mikko wrote:
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or dontradiction is >>>>>>>>>> true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words.
The syntax of formal logical languages allows
some expressions to be created having pathological
self-reference(Olcott 2004).
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string without meaning
does not refer.
Self-reference can be detected in a string with a name.
Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy of the liar >>>>> -a-a-a in the metalanguage, by forming in the language itself a sentence >>>>> -a-a-a x such that the sentence of the metalanguage which is correlated >>>>> -a-a-a with x asserts that x is not a true sentence.
-a-a-a https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. the arithmetic >>>>>> semantics of a formal language of arithmetics do not permit a self- >>>>>> reference.
G||del uses tricks for that.
Tarski used the same tricks.
Yet they only actually boil down to
Incomplete(F) rao reaG ((F re4 G) reo (F re4 -4G)).
and this
LP := ~True(LP)
The system they considered has no symbol for :=. Instead, they construct
something like LP <-> ~True(LP). G||del then shows that that the expression >> that asserts its own unprovability is is not provable and therefore true.
Claude AI eventually agreed that both G||del's 1931
Incompleteness theorem and the Tarski Undefinability
theorem are anchored in liar paradox like expression
that should have been rejected as not a truth bearer.
On 2025-10-05 14:03:37 +0000, olcott said:
G||del 1931 undecidability and Tarski Undefinability
only exist because they they not know to reject an
expression of language that is not a truth bearer.
What expression of the language of the first order theory of the
first order Peano arithmetic is not a truth bearer? That you can't
determine the truth value of some expression does not mean that ir
has none. That you don't understand the proof does not mean that
the proofs are not sound.
Claude AI is quite hesitant at first, disagreeing
with me several times. Then it is finally convinced
that I am correct.
That you may convince an artificial idiot means nothing.
But Tarski proved about natural numbers that if there were a
definition
of a predicate in terms of a formula in the language of Peano
arithmetic
that accepts all numbers that encode a true sentence and rejects all >>>>> other numbers then that predicate would accept a number that encodes >>>>> a false sentence or reject a number that encodes a true sentence.
Mine has a broader scope that can be applied to
any pathological self-reference(Olcott 2004) in
formal expressions and formalized natural language
expressions.
Tarstki's scope is wider, too, but the first order arithmetic of natural >>> numbers is the most interesting part of the scope.
My scope is the entire body of human knowledge
that can be expressed in language.
Tarski's scope was only formal theories and their languages. Within that scope it is at least clear what constitutes a proof.
On 2025-10-05 14:09:37 +0000, olcott said:
On 10/5/2025 5:26 AM, Mikko wrote:
On 2025-10-04 13:30:22 +0000, olcott said:
On 10/4/2025 5:11 AM, Mikko wrote:
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or
dontradiction is
true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words.
The syntax of formal logical languages allows
some expressions to be created having pathological
self-reference(Olcott 2004).
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string without meaning
does not refer.
Self-reference can be detected in a string with a name.
Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy of the liar >>>>>> -a-a-a in the metalanguage, by forming in the language itself a sentence >>>>>> -a-a-a x such that the sentence of the metalanguage which is correlated >>>>>> -a-a-a with x asserts that x is not a true sentence.
-a-a-a https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. the
arithmetic
semantics of a formal language of arithmetics do not permit a self- >>>>>>> reference.
G||del uses tricks for that.
Tarski used the same tricks.
Yet they only actually boil down to
Incomplete(F) rao reaG ((F re4 G) reo (F re4 -4G)).
and this
LP := ~True(LP)
The system they considered has no symbol for :=. Instead, they construct >>> something like LP <-> ~True(LP). G||del then shows that that the
expression
that asserts its own unprovability is is not provable and therefore
true.
Claude AI eventually agreed that both G||del's 1931
Incompleteness theorem and the Tarski Undefinability
theorem are anchored in liar paradox like expression
that should have been rejected as not a truth bearer.
G||del proved that every sentence of a first order theory that is not
the negation of any sentnece of that theory is true in some model of
that theory. Therefore every sentence of every first order theory is
a truth-bearer.
As long as you don't understand that "The liar's paradox is not true"
is true and therefore a valid basis for a proof you cannot say anything
about Tarski's proof but are stuck to straw men.
On 10/6/2025 7:27 AM, Mikko wrote:
On 2025-10-05 14:03:37 +0000, olcott said:
G||del 1931 undecidability and Tarski Undefinability
only exist because they they not know to reject an
expression of language that is not a truth bearer.
What expression of the language of the first order theory of the
first order Peano arithmetic is not a truth bearer? That you can't
determine the truth value of some expression does not mean that ir
has none. That you don't understand the proof does not mean that
the proofs are not sound.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
It turns out that the essence of these two papers is much
simpler than that.
Claude AI is quite hesitant at first, disagreeing
with me several times. Then it is finally convinced
that I am correct.
That you may convince an artificial idiot means nothing.
It may seem to mean nothing until after you carefully
examine all of the details of how it pieces together all
of my ideas into a single cohesive whole.
But Tarski proved about natural numbers that if there were a definition >>>>>> of a predicate in terms of a formula in the language of Peano arithmetic >>>>>> that accepts all numbers that encode a true sentence and rejects all >>>>>> other numbers then that predicate would accept a number that encodes >>>>>> a false sentence or reject a number that encodes a true sentence.
Mine has a broader scope that can be applied to
any pathological self-reference(Olcott 2004) in
formal expressions and formalized natural language
expressions.
Tarstki's scope is wider, too, but the first order arithmetic of natural >>>> numbers is the most interesting part of the scope.
My scope is the entire body of human knowledge
that can be expressed in language.
Tarski's scope was only formal theories and their languages. Within that
scope it is at least clear what constitutes a proof.
What good would that be?
On 10/6/2025 7:36 AM, Mikko wrote:
On 2025-10-05 14:09:37 +0000, olcott said:
On 10/5/2025 5:26 AM, Mikko wrote:
On 2025-10-04 13:30:22 +0000, olcott said:Claude AI eventually agreed that both G||del's 1931
On 10/4/2025 5:11 AM, Mikko wrote:
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or dontradiction is >>>>>>>>>>>> true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words.
The syntax of formal logical languages allows
some expressions to be created having pathological
self-reference(Olcott 2004).
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string without meaning >>>>>> does not refer.
Self-reference can be detected in a string with a name.
Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy of the liar
-a-a-a in the metalanguage, by forming in the language itself a sentence
-a-a-a x such that the sentence of the metalanguage which is correlated >>>>>>> -a-a-a with x asserts that x is not a true sentence.
-a-a-a https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. the arithmetic
semantics of a formal language of arithmetics do not permit a self- >>>>>>>> reference.
G||del uses tricks for that.
Tarski used the same tricks.
Yet they only actually boil down to
Incomplete(F) rao reaG ((F re4 G) reo (F re4 -4G)).
and this
LP := ~True(LP)
The system they considered has no symbol for :=. Instead, they construct >>>> something like LP <-> ~True(LP). G||del then shows that that the expression
that asserts its own unprovability is is not provable and therefore true. >>>
Incompleteness theorem and the Tarski Undefinability
theorem are anchored in liar paradox like expression
that should have been rejected as not a truth bearer.
G||del proved that every sentence of a first order theory that is not
the negation of any sentnece of that theory is true in some model of
that theory. Therefore every sentence of every first order theory is
a truth-bearer.
As long as you don't understand that "The liar's paradox is not true"
is true and therefore a valid basis for a proof you cannot say anything
about Tarski's proof but are stuck to straw men.
*The Liar Paradox is rejected*
(thus unavailable for subsequent analysis)
True(English, "This sentence is not true")==INCORRECT
*I explained this in complete detail to Claude AI* https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ... ...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...
...We are therefore confronted with a proposition which asserts its own unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
https://monoskop.org/images/9/93/Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf
Basically Claude AI completely validated all of my work
on Tarski Undefinability and G||del 1931 Incompleteness. https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
On 2025-10-06 13:14:35 +0000, olcott said:
On 10/6/2025 7:27 AM, Mikko wrote:
On 2025-10-05 14:03:37 +0000, olcott said:
G||del 1931 undecidability and Tarski Undefinability
only exist because they they not know to reject an
expression of language that is not a truth bearer.
What expression of the language of the first order theory of the
first order Peano arithmetic is not a truth bearer? That you can't
determine the truth value of some expression does not mean that ir
has none. That you don't understand the proof does not mean that
the proofs are not sound.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
It turns out that the essence of these two papers is much
simpler than that.
Apparently not simple enough for you.
Claude AI is quite hesitant at first, disagreeing
with me several times. Then it is finally convinced
that I am correct.
That you may convince an artificial idiot means nothing.
It may seem to mean nothing until after you carefully
examine all of the details of how it pieces together all
of my ideas into a single cohesive whole.
That you may convince an artificial idiot really means nothing.
If a reliable automatic proof checker could confirm your proof
that might mean something.
But Tarski proved about natural numbers that if there were aMine has a broader scope that can be applied to
definition
of a predicate in terms of a formula in the language of Peano
arithmetic
that accepts all numbers that encode a true sentence and rejects all >>>>>>> other numbers then that predicate would accept a number that encodes >>>>>>> a false sentence or reject a number that encodes a true sentence. >>>>>>
any pathological self-reference(Olcott 2004) in
formal expressions and formalized natural language
expressions.
Tarstki's scope is wider, too, but the first order arithmetic of
natural
numbers is the most interesting part of the scope.
My scope is the entire body of human knowledge
that can be expressed in language.
Tarski's scope was only formal theories and their languages. Within that >>> scope it is at least clear what constitutes a proof.
What good would that be?
At the time the problem of the determination of arithmetic truth
was considered important. Mathematics has so much applications
that it was felt necessary to have a firm foundation for it. A
method to determine mathematial truth was therefore desidrable.
The arithmetic of natural numbers is a simple theory and the
most central one to much of mathematics, so it was a good starting
point for the search of powerful methods. If such methods could be
developed for natural numbers they might then be extensible to
other parts of mathematics.
On 2025-10-06 13:23:10 +0000, olcott said:
On 10/6/2025 7:36 AM, Mikko wrote:
On 2025-10-05 14:09:37 +0000, olcott said:
On 10/5/2025 5:26 AM, Mikko wrote:
On 2025-10-04 13:30:22 +0000, olcott said:
On 10/4/2025 5:11 AM, Mikko wrote:
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:The syntax of formal logical languages allows
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or
dontradiction is
true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words. >>>>>>>>>>
some expressions to be created having pathological
self-reference(Olcott 2004).
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string without meaning >>>>>>> does not refer.
Self-reference can be detected in a string with a name.
Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy of the >>>>>>>> liar
-a-a-a in the metalanguage, by forming in the language itself a >>>>>>>> sentence
-a-a-a x such that the sentence of the metalanguage which is
correlated
-a-a-a with x asserts that x is not a true sentence.
-a-a-a https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. the >>>>>>>>> arithmetic
semantics of a formal language of arithmetics do not permit a >>>>>>>>> self-
reference.
G||del uses tricks for that.
Tarski used the same tricks.
Yet they only actually boil down to
Incomplete(F) rao reaG ((F re4 G) reo (F re4 -4G)).
and this
LP := ~True(LP)
The system they considered has no symbol for :=. Instead, they
construct
something like LP <-> ~True(LP). G||del then shows that that the
expression
that asserts its own unprovability is is not provable and therefore >>>>> true.
Claude AI eventually agreed that both G||del's 1931
Incompleteness theorem and the Tarski Undefinability
theorem are anchored in liar paradox like expression
that should have been rejected as not a truth bearer.
G||del proved that every sentence of a first order theory that is not
the negation of any sentnece of that theory is true in some model of
that theory. Therefore every sentence of every first order theory is
a truth-bearer.
As long as you don't understand that "The liar's paradox is not true"
is true and therefore a valid basis for a proof you cannot say anything
about Tarski's proof but are stuck to straw men.
*The Liar Paradox is rejected*
(thus unavailable for subsequent analysis)
True(English, "This sentence is not true")==INCORRECT
*I explained this in complete detail to Claude AI*
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...
...We are therefore confronted with a proposition which asserts its
own unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
https://monoskop.org/images/9/93/
Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf
Basically Claude AI completely validated all of my work
on Tarski Undefinability and G||del 1931 Incompleteness.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
None of the above demonstrates any understanding of the fact that "The
liar's paradox is not true" is true and therefore a valid basis for a
proof. Consequently there is no reason to expect that you could say
anything about Tarski's work instead of your straw man.
On 9/27/2025 5:12 AM, Mikko wrote:
On 2025-09-26 15:28:52 +0000, olcott said:
On 9/26/2025 2:48 AM, Mikko wrote:
On 2025-09-26 01:19:50 +0000, olcott said:
On 9/25/2025 2:34 AM, Mikko wrote:
On 2025-09-24 14:36:46 +0000, olcott said:
On 9/24/2025 2:19 AM, Mikko wrote:
On 2025-09-23 15:39:53 +0000, olcott said:
On 9/23/2025 4:29 AM, Mikko wrote:
On 2025-09-23 00:59:54 +0000, olcott said:
On 9/21/2025 4:26 AM, Mikko wrote:
On 2025-09-20 14:58:33 +0000, olcott said:The meaning is that it is not a truth bearer
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said:In an infinitely recursive chain that you dishonestly >>>>>>>>>>>>> erased.
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said:
Tarski an otherwise profoundly brilliant man stupidly >>>>>>>>>>>>>>>>> anchored his whole Undefinability proof in the semantic >>>>>>>>>>>>>>>>> gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic gibberish.
This sentence is not true.
What it is not true about?
The sentence claims that it is not true about itself. >>>>>>>>>>>>>
No, that meaning can be found without considering any recursion. >>>>>>>>>>>
thus has no truth value.
If the sentence "This sentence is not true" has no truth value then >>>>>>>>>> it is not true.
And it is not false, thus must be rejected
as not a member of any formal logic system
thus cannot form a basis for any Undefinability proof.
The sentence "The sentence 'This sentence is not true' is not true" >>>>>>>> is true and can be used as an element of a proof.
Yes and likewise with this:
"The sentence 'What time is it?' is not true".
Thus in neither case does this prevent a Truth
predicate from being defined at the same logic level.
Not in any obvious way but turns out that if there is a definable truth >>>>>> predicate then there is a proof of a false sentence that asserts its >>>>>> own unprovability, i.e., the arithmetic with a definable truth predicate >>>>>> is provably inconsistent.
There is no true and unprovable.
G||del proved that if a first order theory is incomplete it has models >>>> where some unprovable sentence is true and other models where the same >>>> sentence is false.
That is only because he did not screen out sentences
that are not truth bearers like: "What time is it (yes or no)?"
"This sentence is not true", "This sentence cannot be proven".
He didn't need to screen out anything. His proof covers all first order
theories. In many theories your examples are unexpressible anyway, so
there is no need to screen them out.
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
I just showed you have Tarski expressed one
of these turds in his formal system.
x ree True if and only if p
On 10/7/2025 4:52 AM, Mikko wrote:
On 2025-10-06 13:23:10 +0000, olcott said:
On 10/6/2025 7:36 AM, Mikko wrote:
On 2025-10-05 14:09:37 +0000, olcott said:
On 10/5/2025 5:26 AM, Mikko wrote:
On 2025-10-04 13:30:22 +0000, olcott said:
On 10/4/2025 5:11 AM, Mikko wrote:
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:The syntax of formal logical languages allows
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or dontradiction is
true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words. >>>>>>>>>>>
some expressions to be created having pathological
self-reference(Olcott 2004).
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string without meaning >>>>>>>> does not refer.
Self-reference can be detected in a string with a name.
Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy of the liar
-a-a-a in the metalanguage, by forming in the language itself a sentence
-a-a-a x such that the sentence of the metalanguage which is correlated
-a-a-a with x asserts that x is not a true sentence.
-a-a-a https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. the arithmetic
semantics of a formal language of arithmetics do not permit a self- >>>>>>>>>> reference.
G||del uses tricks for that.
Tarski used the same tricks.
Yet they only actually boil down to
Incomplete(F) rao reaG ((F re4 G) reo (F re4 -4G)).
and this
LP := ~True(LP)
The system they considered has no symbol for :=. Instead, they construct >>>>>> something like LP <-> ~True(LP). G||del then shows that that the expression
that asserts its own unprovability is is not provable and therefore true.
Claude AI eventually agreed that both G||del's 1931
Incompleteness theorem and the Tarski Undefinability
theorem are anchored in liar paradox like expression
that should have been rejected as not a truth bearer.
G||del proved that every sentence of a first order theory that is not
the negation of any sentnece of that theory is true in some model of
that theory. Therefore every sentence of every first order theory is
a truth-bearer.
As long as you don't understand that "The liar's paradox is not true"
is true and therefore a valid basis for a proof you cannot say anything >>>> about Tarski's proof but are stuck to straw men.
*The Liar Paradox is rejected*
(thus unavailable for subsequent analysis)
True(English, "This sentence is not true")==INCORRECT
*I explained this in complete detail to Claude AI*
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ... >>> ...14 Every epistemological antinomy can likewise be used for a similar >>> undecidability proof...
...We are therefore confronted with a proposition which asserts its own >>> unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
https://monoskop.org/images/9/93/
Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf
Basically Claude AI completely validated all of my work
on Tarski Undefinability and G||del 1931 Incompleteness.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
None of the above demonstrates any understanding of the fact that "The
liar's paradox is not true" is true and therefore a valid basis for a
proof. Consequently there is no reason to expect that you could say
anything about Tarski's work instead of your straw man.
"What time is it (true or false)?" is also not true and
best rejected at the beginning.
On 2025-09-29 12:27:50 +0000, olcott said:
On 9/27/2025 5:12 AM, Mikko wrote:
On 2025-09-26 15:28:52 +0000, olcott said:
On 9/26/2025 2:48 AM, Mikko wrote:
On 2025-09-26 01:19:50 +0000, olcott said:
On 9/25/2025 2:34 AM, Mikko wrote:
On 2025-09-24 14:36:46 +0000, olcott said:
On 9/24/2025 2:19 AM, Mikko wrote:
On 2025-09-23 15:39:53 +0000, olcott said:
On 9/23/2025 4:29 AM, Mikko wrote:
On 2025-09-23 00:59:54 +0000, olcott said:
On 9/21/2025 4:26 AM, Mikko wrote:
On 2025-09-20 14:58:33 +0000, olcott said:
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said:In an infinitely recursive chain that you dishonestly >>>>>>>>>>>>>> erased.
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said:
Tarski an otherwise profoundly brilliant man stupidly >>>>>>>>>>>>>>>>>> anchored his whole Undefinability proof in the semantic >>>>>>>>>>>>>>>>>> gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not >>>>>>>>>>>>>>>>> semantic gibberish.
This sentence is not true.
What it is not true about?
The sentence claims that it is not true about itself. >>>>>>>>>>>>>>
No, that meaning can be found without considering any >>>>>>>>>>>>> recursion.
The meaning is that it is not a truth bearer
thus has no truth value.
If the sentence "This sentence is not true" has no truth >>>>>>>>>>> value then
it is not true.
And it is not false, thus must be rejected
as not a member of any formal logic system
thus cannot form a basis for any Undefinability proof.
The sentence "The sentence 'This sentence is not true' is not >>>>>>>>> true"
is true and can be used as an element of a proof.
Yes and likewise with this:
"The sentence 'What time is it?' is not true".
Thus in neither case does this prevent a Truth
predicate from being defined at the same logic level.
Not in any obvious way but turns out that if there is a definable >>>>>>> truth
predicate then there is a proof of a false sentence that asserts its >>>>>>> own unprovability, i.e., the arithmetic with a definable truth
predicate
is provably inconsistent.
There is no true and unprovable.
G||del proved that if a first order theory is incomplete it has models >>>>> where some unprovable sentence is true and other models where the same >>>>> sentence is false.
That is only because he did not screen out sentences
that are not truth bearers like: "What time is it (yes or no)?"
"This sentence is not true", "This sentence cannot be proven".
He didn't need to screen out anything. His proof covers all first order
theories. In many theories your examples are unexpressible anyway, so
there is no need to screen them out.
Any sentence that is neither true nor false
must be rejected from any system of logic.
Whether a sentence is true or false or neither depends on semantics.
In an uninterpreted formal theory a sentence has not meaning and
therefore no truth value so cannot be relejcted for a lack of truth
value.
Every consistent first order theory has a model where all
provable sentences are true and all other sentencese are either true
or false so every sentence is a truth-bearer. But it is possible to
use different semantics that does not assign a truth value to every
sentence.
Non-truth bearers in logic systems are like
turds in birthday cakes.
At least in first order logic there isn't any.
I just showed you have Tarski expressed one
of these turds in his formal system.
x ree True if and only if p
If you mean the sentence "The Liar's paradox is not true" then
that sentence is true and therefore is a truth-bearer. If you
mean something else then you are only talking about your straw
man.
On 2025-10-07 14:19:09 +0000, olcott said:
On 10/7/2025 4:52 AM, Mikko wrote:
On 2025-10-06 13:23:10 +0000, olcott said:
On 10/6/2025 7:36 AM, Mikko wrote:
On 2025-10-05 14:09:37 +0000, olcott said:
On 10/5/2025 5:26 AM, Mikko wrote:
On 2025-10-04 13:30:22 +0000, olcott said:
On 10/4/2025 5:11 AM, Mikko wrote:
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:The syntax of formal logical languages allows
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or >>>>>>>>>>>>>>> dontradiction is
true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words. >>>>>>>>>>>>
some expressions to be created having pathological
self-reference(Olcott 2004).
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string without meaning >>>>>>>>> does not refer.
Self-reference can be detected in a string with a name.
Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy of >>>>>>>>>> the liar
-a-a-a in the metalanguage, by forming in the language itself a >>>>>>>>>> sentence
-a-a-a x such that the sentence of the metalanguage which is >>>>>>>>>> correlated
-a-a-a with x asserts that x is not a true sentence.
-a-a-a https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. the >>>>>>>>>>> arithmetic
semantics of a formal language of arithmetics do not permit a >>>>>>>>>>> self-
reference.
G||del uses tricks for that.
Tarski used the same tricks.
Yet they only actually boil down to
Incomplete(F) rao reaG ((F re4 G) reo (F re4 -4G)).
and this
LP := ~True(LP)
The system they considered has no symbol for :=. Instead, they
construct
something like LP <-> ~True(LP). G||del then shows that that the >>>>>>> expression
that asserts its own unprovability is is not provable and
therefore true.
Claude AI eventually agreed that both G||del's 1931
Incompleteness theorem and the Tarski Undefinability
theorem are anchored in liar paradox like expression
that should have been rejected as not a truth bearer.
G||del proved that every sentence of a first order theory that is not >>>>> the negation of any sentnece of that theory is true in some model of >>>>> that theory. Therefore every sentence of every first order theory is >>>>> a truth-bearer.
As long as you don't understand that "The liar's paradox is not true" >>>>> is true and therefore a valid basis for a proof you cannot say
anything
about Tarski's proof but are stuck to straw men.
*The Liar Paradox is rejected*
(thus unavailable for subsequent analysis)
True(English, "This sentence is not true")==INCORRECT
*I explained this in complete detail to Claude AI*
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ... >>>> ...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...
...We are therefore confronted with a proposition which asserts its
own unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
https://monoskop.org/images/9/93/
Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf
Basically Claude AI completely validated all of my work
on Tarski Undefinability and G||del 1931 Incompleteness.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
None of the above demonstrates any understanding of the fact that "The
liar's paradox is not true" is true and therefore a valid basis for a
proof. Consequently there is no reason to expect that you could say
anything about Tarski's work instead of your straw man.
"What time is it (true or false)?" is also not true and
best rejected at the beginning.
A question is never true and should not be even mentioned in a
discussion about truth values.
Anyway, nice to see that you don't disagree.
On 10/7/2025 4:48 AM, Mikko wrote:
On 2025-10-06 13:14:35 +0000, olcott said:
On 10/6/2025 7:27 AM, Mikko wrote:
On 2025-10-05 14:03:37 +0000, olcott said:
G||del 1931 undecidability and Tarski Undefinability
only exist because they they not know to reject an
expression of language that is not a truth bearer.
What expression of the language of the first order theory of the
first order Peano arithmetic is not a truth bearer? That you can't
determine the truth value of some expression does not mean that ir
has none. That you don't understand the proof does not mean that
the proofs are not sound.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
It turns out that the essence of these two papers is much
simpler than that.
Apparently not simple enough for you.
Claude AI is quite hesitant at first, disagreeing
with me several times. Then it is finally convinced
that I am correct.
That you may convince an artificial idiot means nothing.
It may seem to mean nothing until after you carefully
examine all of the details of how it pieces together all
of my ideas into a single cohesive whole.
That you may convince an artificial idiot really means nothing.
If a reliable automatic proof checker could confirm your proof
that might mean something.
The proof is entirely semantic.
Claude AI verified that the meaning of my words
proved my point. You could to if you looked at
the dialogue.
But Tarski proved about natural numbers that if there were a definitionMine has a broader scope that can be applied to
of a predicate in terms of a formula in the language of Peano arithmetic
that accepts all numbers that encode a true sentence and rejects all >>>>>>>> other numbers then that predicate would accept a number that encodes >>>>>>>> a false sentence or reject a number that encodes a true sentence. >>>>>>>
any pathological self-reference(Olcott 2004) in
formal expressions and formalized natural language
expressions.
Tarstki's scope is wider, too, but the first order arithmetic of natural >>>>>> numbers is the most interesting part of the scope.
My scope is the entire body of human knowledge
that can be expressed in language.
Tarski's scope was only formal theories and their languages. Within that >>>> scope it is at least clear what constitutes a proof.
What good would that be?
True(Language, Expression) could be a reliable arbiter
of truth providing all of the reasoning why we can know
that a well crafted lie is not true.
At the time the problem of the determination of arithmetic truth
was considered important. Mathematics has so much applications
that it was felt necessary to have a firm foundation for it. A
method to determine mathematial truth was therefore desidrable.
The arithmetic of natural numbers is a simple theory and the
most central one to much of mathematics, so it was a good starting
point for the search of powerful methods. If such methods could be
developed for natural numbers they might then be extensible to
other parts of mathematics.
And he couldn't even get that right.
On 10/8/2025 5:54 AM, Mikko wrote:
On 2025-10-07 14:19:09 +0000, olcott said:
On 10/7/2025 4:52 AM, Mikko wrote:
On 2025-10-06 13:23:10 +0000, olcott said:
On 10/6/2025 7:36 AM, Mikko wrote:
On 2025-10-05 14:09:37 +0000, olcott said:
On 10/5/2025 5:26 AM, Mikko wrote:
On 2025-10-04 13:30:22 +0000, olcott said:
On 10/4/2025 5:11 AM, Mikko wrote:
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:The syntax of formal logical languages allows
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or dontradiction is
true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words. >>>>>>>>>>>>>
some expressions to be created having pathological
self-reference(Olcott 2004).
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string without meaning >>>>>>>>>> does not refer.
Self-reference can be detected in a string with a name.
Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy of the liar
-a-a-a in the metalanguage, by forming in the language itself a sentence
-a-a-a x such that the sentence of the metalanguage which is correlated
-a-a-a with x asserts that x is not a true sentence.
-a-a-a https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. the arithmetic
semantics of a formal language of arithmetics do not permit a self-
reference.
G||del uses tricks for that.
Tarski used the same tricks.
Yet they only actually boil down to
Incomplete(F) rao reaG ((F re4 G) reo (F re4 -4G)).
and this
LP := ~True(LP)
The system they considered has no symbol for :=. Instead, they construct
something like LP <-> ~True(LP). G||del then shows that that the expression
that asserts its own unprovability is is not provable and therefore true.
Claude AI eventually agreed that both G||del's 1931
Incompleteness theorem and the Tarski Undefinability
theorem are anchored in liar paradox like expression
that should have been rejected as not a truth bearer.
G||del proved that every sentence of a first order theory that is not >>>>>> the negation of any sentnece of that theory is true in some model of >>>>>> that theory. Therefore every sentence of every first order theory is >>>>>> a truth-bearer.
As long as you don't understand that "The liar's paradox is not true" >>>>>> is true and therefore a valid basis for a proof you cannot say anything >>>>>> about Tarski's proof but are stuck to straw men.
*The Liar Paradox is rejected*
(thus unavailable for subsequent analysis)
True(English, "This sentence is not true")==INCORRECT
*I explained this in complete detail to Claude AI*
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ... >>>>> ...14 Every epistemological antinomy can likewise be used for a similar >>>>> undecidability proof...
...We are therefore confronted with a proposition which asserts its own >>>>> unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
https://monoskop.org/images/9/93/
Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf
Basically Claude AI completely validated all of my work
on Tarski Undefinability and G||del 1931 Incompleteness.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
None of the above demonstrates any understanding of the fact that "The >>>> liar's paradox is not true" is true and therefore a valid basis for a
proof. Consequently there is no reason to expect that you could say
anything about Tarski's work instead of your straw man.
"What time is it (true or false)?" is also not true and
best rejected at the beginning.
A question is never true and should not be even mentioned in a
discussion about truth values.
Anyway, nice to see that you don't disagree.
Yet Tarski anchored his whole proof in this:
?- LP = not(true(LP)).
When it is rejected as not a truth-bearer
as Prolog does then Claude AI agree the
basis of his whole proof ceases to exist.
On 10/8/2025 5:52 AM, Mikko wrote:
On 2025-09-29 12:27:50 +0000, olcott said:
On 9/27/2025 5:12 AM, Mikko wrote:
On 2025-09-26 15:28:52 +0000, olcott said:
On 9/26/2025 2:48 AM, Mikko wrote:
On 2025-09-26 01:19:50 +0000, olcott said:
On 9/25/2025 2:34 AM, Mikko wrote:
On 2025-09-24 14:36:46 +0000, olcott said:
On 9/24/2025 2:19 AM, Mikko wrote:
On 2025-09-23 15:39:53 +0000, olcott said:
On 9/23/2025 4:29 AM, Mikko wrote:
On 2025-09-23 00:59:54 +0000, olcott said:
On 9/21/2025 4:26 AM, Mikko wrote:
On 2025-09-20 14:58:33 +0000, olcott said:The meaning is that it is not a truth bearer
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said:In an infinitely recursive chain that you dishonestly >>>>>>>>>>>>>>> erased.
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said: >>>>>>>>>>>>>>>>>>
Tarski an otherwise profoundly brilliant man stupidly >>>>>>>>>>>>>>>>>>> anchored his whole Undefinability proof in the semantic >>>>>>>>>>>>>>>>>>> gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic gibberish.
This sentence is not true.
What it is not true about?
The sentence claims that it is not true about itself. >>>>>>>>>>>>>>>
No, that meaning can be found without considering any recursion. >>>>>>>>>>>>>
thus has no truth value.
If the sentence "This sentence is not true" has no truth value then
it is not true.
And it is not false, thus must be rejected
as not a member of any formal logic system
thus cannot form a basis for any Undefinability proof.
The sentence "The sentence 'This sentence is not true' is not true" >>>>>>>>>> is true and can be used as an element of a proof.
Yes and likewise with this:
"The sentence 'What time is it?' is not true".
Thus in neither case does this prevent a Truth
predicate from being defined at the same logic level.
Not in any obvious way but turns out that if there is a definable truth
predicate then there is a proof of a false sentence that asserts its >>>>>>>> own unprovability, i.e., the arithmetic with a definable truth predicate
is provably inconsistent.
There is no true and unprovable.
G||del proved that if a first order theory is incomplete it has models >>>>>> where some unprovable sentence is true and other models where the same >>>>>> sentence is false.
That is only because he did not screen out sentences
that are not truth bearers like: "What time is it (yes or no)?"
"This sentence is not true", "This sentence cannot be proven".
He didn't need to screen out anything. His proof covers all first order >>>> theories. In many theories your examples are unexpressible anyway, so
there is no need to screen them out.
Any sentence that is neither true nor false
must be rejected from any system of logic.
Whether a sentence is true or false or neither depends on semantics.
Yes.
In an uninterpreted formal theory a sentence has not meaning and
therefore no truth value so cannot be relejcted for a lack of truth
value.
I have posited that it has always been a huge
mistake that semantics was divided away from
the syntax of every formal logic system since
the syllogism. It is the root cause of the
divergence of logic from correct reasoning.
Every consistent first order theory has a model where all
provable sentences are true and all other sentencese are either true
or false so every sentence is a truth-bearer. But it is possible to
use different semantics that does not assign a truth value to every
sentence.
Non-truth bearers in logic systems are like
turds in birthday cakes.
At least in first order logic there isn't any.
So G||del requires more than FOL?
From what I recall PA has one axiom that is SOL.
I just showed you have Tarski expressed one
of these turds in his formal system.
x ree True if and only if p
If you mean the sentence "The Liar's paradox is not true" then
No that sentence seems to be Tarski's way
of saying: ?- LP = not(true(LP)).
On 2025-10-07 14:16:11 +0000, olcott said:
On 10/7/2025 4:48 AM, Mikko wrote:
On 2025-10-06 13:14:35 +0000, olcott said:
On 10/6/2025 7:27 AM, Mikko wrote:
On 2025-10-05 14:03:37 +0000, olcott said:
G||del 1931 undecidability and Tarski Undefinability
only exist because they they not know to reject an
expression of language that is not a truth bearer.
What expression of the language of the first order theory of the
first order Peano arithmetic is not a truth bearer? That you can't
determine the truth value of some expression does not mean that ir
has none. That you don't understand the proof does not mean that
the proofs are not sound.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
It turns out that the essence of these two papers is much
simpler than that.
Apparently not simple enough for you.
Claude AI is quite hesitant at first, disagreeing
with me several times. Then it is finally convinced
that I am correct.
That you may convince an artificial idiot means nothing.
It may seem to mean nothing until after you carefully
examine all of the details of how it pieces together all
of my ideas into a single cohesive whole.
That you may convince an artificial idiot really means nothing.
If a reliable automatic proof checker could confirm your proof
that might mean something.
The proof is entirely semantic.
Claude AI verified that the meaning of my words
proved my point. You could to if you looked at
the dialogue.
As I already said, that does not mean anything.
But Tarski proved about natural numbers that if there were a >>>>>>>>> definitionMine has a broader scope that can be applied to
of a predicate in terms of a formula in the language of Peano >>>>>>>>> arithmetic
that accepts all numbers that encode a true sentence and
rejects all
other numbers then that predicate would accept a number that >>>>>>>>> encodes
a false sentence or reject a number that encodes a true sentence. >>>>>>>>
any pathological self-reference(Olcott 2004) in
formal expressions and formalized natural language
expressions.
Tarstki's scope is wider, too, but the first order arithmetic of >>>>>>> natural
numbers is the most interesting part of the scope.
My scope is the entire body of human knowledge
that can be expressed in language.
Tarski's scope was only formal theories and their languages. Within >>>>> that
scope it is at least clear what constitutes a proof.
What good would that be?
True(Language, Expression) could be a reliable arbiter
of truth providing all of the reasoning why we can know
that a well crafted lie is not true.
What does not exist is not useful for practical purposes.
At the time the problem of the determination of arithmetic truth
was considered important. Mathematics has so much applications
that it was felt necessary to have a firm foundation for it. A
method to determine mathematial truth was therefore desidrable.
The arithmetic of natural numbers is a simple theory and the
most central one to much of mathematics, so it was a good starting
point for the search of powerful methods. If such methods could be
developed for natural numbers they might then be extensible to
other parts of mathematics.
And he couldn't even get that right.
You have no evidence about that. What statement he made about these
topics that you thik is incorrect?
On 2025-10-09 03:13:41 +0000, olcott said:
On 10/8/2025 5:54 AM, Mikko wrote:
On 2025-10-07 14:19:09 +0000, olcott said:
On 10/7/2025 4:52 AM, Mikko wrote:
On 2025-10-06 13:23:10 +0000, olcott said:
On 10/6/2025 7:36 AM, Mikko wrote:
On 2025-10-05 14:09:37 +0000, olcott said:
On 10/5/2025 5:26 AM, Mikko wrote:
On 2025-10-04 13:30:22 +0000, olcott said:
On 10/4/2025 5:11 AM, Mikko wrote:
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:The syntax of formal logical languages allows
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false >>>>>>>>>>>>>>>>>> must be rejected from any system of logic. >>>>>>>>>>>>>>>>>> Non-truth bearers in logic systems are like >>>>>>>>>>>>>>>>>> turds in birthday cakes.
Every sentence of logic that is not tautology or >>>>>>>>>>>>>>>>> dontradiction is
true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words. >>>>>>>>>>>>>>
some expressions to be created having pathological >>>>>>>>>>>>>> self-reference(Olcott 2004).
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string without >>>>>>>>>>> meaning
does not refer.
Self-reference can be detected in a string with a name.
Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy of >>>>>>>>>>>> the liar
-a-a-a in the metalanguage, by forming in the language itself a >>>>>>>>>>>> sentence
-a-a-a x such that the sentence of the metalanguage which is >>>>>>>>>>>> correlated
-a-a-a with x asserts that x is not a true sentence.
-a-a-a https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. >>>>>>>>>>>>> the arithmetic
semantics of a formal language of arithmetics do not permit >>>>>>>>>>>>> a self-
reference.
G||del uses tricks for that.
Tarski used the same tricks.
Yet they only actually boil down to
Incomplete(F) rao reaG ((F re4 G) reo (F re4 -4G)).
and this
LP := ~True(LP)
The system they considered has no symbol for :=. Instead, they >>>>>>>>> construct
something like LP <-> ~True(LP). G||del then shows that that the >>>>>>>>> expression
that asserts its own unprovability is is not provable and
therefore true.
Claude AI eventually agreed that both G||del's 1931
Incompleteness theorem and the Tarski Undefinability
theorem are anchored in liar paradox like expression
that should have been rejected as not a truth bearer.
G||del proved that every sentence of a first order theory that is not >>>>>>> the negation of any sentnece of that theory is true in some model of >>>>>>> that theory. Therefore every sentence of every first order theory is >>>>>>> a truth-bearer.
As long as you don't understand that "The liar's paradox is not >>>>>>> true"
is true and therefore a valid basis for a proof you cannot say
anything
about Tarski's proof but are stuck to straw men.
*The Liar Paradox is rejected*
(thus unavailable for subsequent analysis)
True(English, "This sentence is not true")==INCORRECT
*I explained this in complete detail to Claude AI*
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
The most important aspect of G||del's 1931 Incompleteness theorem
are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...
...We are therefore confronted with a proposition which asserts
its own unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And >>>>>> Related Systems
https://monoskop.org/images/9/93/
Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf
Basically Claude AI completely validated all of my work
on Tarski Undefinability and G||del 1931 Incompleteness.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
None of the above demonstrates any understanding of the fact that "The >>>>> liar's paradox is not true" is true and therefore a valid basis for a >>>>> proof. Consequently there is no reason to expect that you could say
anything about Tarski's work instead of your straw man.
"What time is it (true or false)?" is also not true and
best rejected at the beginning.
A question is never true and should not be even mentioned in a
discussion about truth values.
Anyway, nice to see that you don't disagree.
Yet Tarski anchored his whole proof in this:
?- LP = not(true(LP)).
You anchor your counter-proof on this:
?- LP = not(true(LP)).
But an anchor is not a proof. Tarski had a complete proof. You have not.
When it is rejected as not a truth-bearer
as Prolog does then Claude AI agree the
basis of his whole proof ceases to exist.
When it is reject mothing is left of your proof.
On 2025-10-09 03:10:56 +0000, olcott said:
On 10/8/2025 5:52 AM, Mikko wrote:
On 2025-09-29 12:27:50 +0000, olcott said:
On 9/27/2025 5:12 AM, Mikko wrote:
On 2025-09-26 15:28:52 +0000, olcott said:
On 9/26/2025 2:48 AM, Mikko wrote:
On 2025-09-26 01:19:50 +0000, olcott said:
On 9/25/2025 2:34 AM, Mikko wrote:
On 2025-09-24 14:36:46 +0000, olcott said:
On 9/24/2025 2:19 AM, Mikko wrote:
On 2025-09-23 15:39:53 +0000, olcott said:
On 9/23/2025 4:29 AM, Mikko wrote:
On 2025-09-23 00:59:54 +0000, olcott said:
On 9/21/2025 4:26 AM, Mikko wrote:
On 2025-09-20 14:58:33 +0000, olcott said:
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said:In an infinitely recursive chain that you dishonestly >>>>>>>>>>>>>>>> erased.
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said: >>>>>>>>>>>>>>>>>>>
Tarski an otherwise profoundly brilliant man stupidly >>>>>>>>>>>>>>>>>>>> anchored his whole Undefinability proof in the semantic >>>>>>>>>>>>>>>>>>>> gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not >>>>>>>>>>>>>>>>>>> semantic gibberish.
This sentence is not true.
What it is not true about?
The sentence claims that it is not true about itself. >>>>>>>>>>>>>>>>
No, that meaning can be found without considering any >>>>>>>>>>>>>>> recursion.
The meaning is that it is not a truth bearer
thus has no truth value.
If the sentence "This sentence is not true" has no truth >>>>>>>>>>>>> value then
it is not true.
And it is not false, thus must be rejected
as not a member of any formal logic system
thus cannot form a basis for any Undefinability proof.
The sentence "The sentence 'This sentence is not true' is not >>>>>>>>>>> true"
is true and can be used as an element of a proof.
Yes and likewise with this:
"The sentence 'What time is it?' is not true".
Thus in neither case does this prevent a Truth
predicate from being defined at the same logic level.
Not in any obvious way but turns out that if there is a
definable truth
predicate then there is a proof of a false sentence that
asserts its
own unprovability, i.e., the arithmetic with a definable truth >>>>>>>>> predicate
is provably inconsistent.
There is no true and unprovable.
G||del proved that if a first order theory is incomplete it has >>>>>>> models
where some unprovable sentence is true and other models where the >>>>>>> same
sentence is false.
That is only because he did not screen out sentences
that are not truth bearers like: "What time is it (yes or no)?"
"This sentence is not true", "This sentence cannot be proven".
He didn't need to screen out anything. His proof covers all first
order
theories. In many theories your examples are unexpressible anyway, so >>>>> there is no need to screen them out.
Any sentence that is neither true nor false
must be rejected from any system of logic.
Whether a sentence is true or false or neither depends on semantics.
Yes.
In an uninterpreted formal theory a sentence has not meaning and
therefore no truth value so cannot be relejcted for a lack of truth
value.
I have posited that it has always been a huge
mistake that semantics was divided away from
the syntax of every formal logic system since
the syllogism. It is the root cause of the
divergence of logic from correct reasoning.
Logic has been shown to be useful. Your "correct reasoning" has not been.
Therefore there is a good reason to believe that the separation of the meaning from the form was a good idea.
Every consistent first order theory has a model where all
provable sentences are true and all other sentencese are either true
or false so every sentence is a truth-bearer. But it is possible to
use different semantics that does not assign a truth value to every
sentence.
Non-truth bearers in logic systems are like
turds in birthday cakes.
At least in first order logic there isn't any.
So G||del requires more than FOL?
G||del did require a metasystem that can relate expressions and
sequences of expressions of first order logic to numbers. That
can be done in the first order. The proof is covers all extenisions
of the first order theory of the first order Peano artihmetic.
That covers all orders.
-aFrom what I recall PA has one axiom that is SOL.
Peano's original presentation had. The first order theory needs
an axiom rule for infinitely many axioms. In addition it needs
axioms that define addition and multiplication, which could
be defined recursively in a system that supports recursive
definitions.
I just showed you have Tarski expressed one
of these turds in his formal system.
x ree True if and only if p
If you mean the sentence "The Liar's paradox is not true" then
No that sentence seems to be Tarski's way
of saying: ?- LP = not(true(LP)).
Anyway, you cannot reject anything that has been proven unless
you reject the idea of analytic truth.
On 10/9/2025 5:51 AM, Mikko wrote:
On 2025-10-07 14:16:11 +0000, olcott said:
On 10/7/2025 4:48 AM, Mikko wrote:
On 2025-10-06 13:14:35 +0000, olcott said:
On 10/6/2025 7:27 AM, Mikko wrote:
On 2025-10-05 14:03:37 +0000, olcott said:
G||del 1931 undecidability and Tarski Undefinability
only exist because they they not know to reject an
expression of language that is not a truth bearer.
What expression of the language of the first order theory of the
first order Peano arithmetic is not a truth bearer? That you can't >>>>>> determine the truth value of some expression does not mean that ir >>>>>> has none. That you don't understand the proof does not mean that
the proofs are not sound.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
It turns out that the essence of these two papers is much
simpler than that.
Apparently not simple enough for you.
Claude AI is quite hesitant at first, disagreeing
with me several times. Then it is finally convinced
that I am correct.
That you may convince an artificial idiot means nothing.
It may seem to mean nothing until after you carefully
examine all of the details of how it pieces together all
of my ideas into a single cohesive whole.
That you may convince an artificial idiot really means nothing.
If a reliable automatic proof checker could confirm your proof
that might mean something.
The proof is entirely semantic.
Claude AI verified that the meaning of my words
proved my point. You could to if you looked at
the dialogue.
As I already said, that does not mean anything.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The gist of it is that when the Liar Paradox
is first rejected as not a truth bearer then
Tarski's whole proof loses its entire basis.
Claude AI summed up the gist of each view
of the Liar Paradox from all of the papers
written on it.
It turn out that one of my best proposals
was already written by Saul Kripke
Outline of a Theory of Truth
Saul Kripke
The Journal of Philosophy, Vol. 72, No. 19,
Seventy-Second Annual Meeting American
Philosophical Association, Eastern Division.
(Nov. 6, 1975), pp. 690-716.
https://files.commons.gc.cuny.edu/wp-content/blogs.dir/1358/files/2019/04/Outline-of-a-Theory-of-Truth.pdf
On 10/9/2025 5:55 AM, Mikko wrote:
On 2025-10-09 03:13:41 +0000, olcott said:
On 10/8/2025 5:54 AM, Mikko wrote:
On 2025-10-07 14:19:09 +0000, olcott said:
On 10/7/2025 4:52 AM, Mikko wrote:
On 2025-10-06 13:23:10 +0000, olcott said:
On 10/6/2025 7:36 AM, Mikko wrote:
On 2025-10-05 14:09:37 +0000, olcott said:
On 10/5/2025 5:26 AM, Mikko wrote:
On 2025-10-04 13:30:22 +0000, olcott said:
On 10/4/2025 5:11 AM, Mikko wrote:
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:The syntax of formal logical languages allows
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false >>>>>>>>>>>>>>>>>>> must be rejected from any system of logic. >>>>>>>>>>>>>>>>>>> Non-truth bearers in logic systems are like >>>>>>>>>>>>>>>>>>> turds in birthday cakes.
Every sentence of logic that is not tautology or dontradiction is
true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words. >>>>>>>>>>>>>>>
some expressions to be created having pathological >>>>>>>>>>>>>>> self-reference(Olcott 2004).
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string without meaning >>>>>>>>>>>> does not refer.
Self-reference can be detected in a string with a name. >>>>>>>>>>>>> Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy of the liar
-a-a-a in the metalanguage, by forming in the language itself a sentence
-a-a-a x such that the sentence of the metalanguage which is correlated
-a-a-a with x asserts that x is not a true sentence. >>>>>>>>>>>>> -a-a-a https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x >>>>>>>>>>>>> https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. the arithmetic
semantics of a formal language of arithmetics do not permit a self-
reference.
G||del uses tricks for that.
Tarski used the same tricks.
Yet they only actually boil down to
Incomplete(F) rao reaG ((F re4 G) reo (F re4 -4G)).
and this
LP := ~True(LP)
The system they considered has no symbol for :=. Instead, they construct
something like LP <-> ~True(LP). G||del then shows that that the expression
that asserts its own unprovability is is not provable and therefore true.
Claude AI eventually agreed that both G||del's 1931
Incompleteness theorem and the Tarski Undefinability
theorem are anchored in liar paradox like expression
that should have been rejected as not a truth bearer.
G||del proved that every sentence of a first order theory that is not >>>>>>>> the negation of any sentnece of that theory is true in some model of >>>>>>>> that theory. Therefore every sentence of every first order theory is >>>>>>>> a truth-bearer.
As long as you don't understand that "The liar's paradox is not true" >>>>>>>> is true and therefore a valid basis for a proof you cannot say anything
about Tarski's proof but are stuck to straw men.
*The Liar Paradox is rejected*
(thus unavailable for subsequent analysis)
True(English, "This sentence is not true")==INCORRECT
*I explained this in complete detail to Claude AI*
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
The most important aspect of G||del's 1931 Incompleteness theorem >>>>>>> are these plain English direct quotes of G||del from his paper:
...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...
...We are therefore confronted with a proposition which asserts its own
unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And >>>>>>> Related Systems
https://monoskop.org/images/9/93/
Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf
Basically Claude AI completely validated all of my work
on Tarski Undefinability and G||del 1931 Incompleteness.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
None of the above demonstrates any understanding of the fact that "The >>>>>> liar's paradox is not true" is true and therefore a valid basis for a >>>>>> proof. Consequently there is no reason to expect that you could say >>>>>> anything about Tarski's work instead of your straw man.
"What time is it (true or false)?" is also not true and
best rejected at the beginning.
A question is never true and should not be even mentioned in a
discussion about truth values.
Anyway, nice to see that you don't disagree.
Yet Tarski anchored his whole proof in this:
?- LP = not(true(LP)).
You anchor your counter-proof on this:
?- LP = not(true(LP)).
But an anchor is not a proof. Tarski had a complete proof. You have not.
When we toss out his whole basis his proof
utterly fails.
On 10/9/2025 6:12 AM, Mikko wrote:
On 2025-10-09 03:10:56 +0000, olcott said:
On 10/8/2025 5:52 AM, Mikko wrote:
On 2025-09-29 12:27:50 +0000, olcott said:
On 9/27/2025 5:12 AM, Mikko wrote:
On 2025-09-26 15:28:52 +0000, olcott said:
On 9/26/2025 2:48 AM, Mikko wrote:
On 2025-09-26 01:19:50 +0000, olcott said:
On 9/25/2025 2:34 AM, Mikko wrote:
On 2025-09-24 14:36:46 +0000, olcott said:
On 9/24/2025 2:19 AM, Mikko wrote:
On 2025-09-23 15:39:53 +0000, olcott said:
On 9/23/2025 4:29 AM, Mikko wrote:The sentence "The sentence 'This sentence is not true' is not true"
On 2025-09-23 00:59:54 +0000, olcott said:
On 9/21/2025 4:26 AM, Mikko wrote:
On 2025-09-20 14:58:33 +0000, olcott said:
On 9/19/2025 4:22 AM, Mikko wrote:
On 2025-09-18 14:47:10 +0000, olcott said: >>>>>>>>>>>>>>>>>>In an infinitely recursive chain that you dishonestly >>>>>>>>>>>>>>>>> erased.
On 9/18/2025 4:26 AM, Mikko wrote:
On 2025-09-17 14:53:58 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
Tarski an otherwise profoundly brilliant man stupidly >>>>>>>>>>>>>>>>>>>>> anchored his whole Undefinability proof in the semantic >>>>>>>>>>>>>>>>>>>>> gibberish of the Liar Paradox.
The statement "Liar's paradox is not true" is not semantic gibberish.
This sentence is not true.
What it is not true about?
The sentence claims that it is not true about itself. >>>>>>>>>>>>>>>>>
No, that meaning can be found without considering any recursion.
The meaning is that it is not a truth bearer
thus has no truth value.
If the sentence "This sentence is not true" has no truth value then
it is not true.
And it is not false, thus must be rejected
as not a member of any formal logic system
thus cannot form a basis for any Undefinability proof. >>>>>>>>>>>>
is true and can be used as an element of a proof.
Yes and likewise with this:
"The sentence 'What time is it?' is not true".
Thus in neither case does this prevent a Truth
predicate from being defined at the same logic level.
Not in any obvious way but turns out that if there is a definable truth
predicate then there is a proof of a false sentence that asserts its >>>>>>>>>> own unprovability, i.e., the arithmetic with a definable truth predicate
is provably inconsistent.
There is no true and unprovable.
G||del proved that if a first order theory is incomplete it has models >>>>>>>> where some unprovable sentence is true and other models where the same >>>>>>>> sentence is false.
That is only because he did not screen out sentences
that are not truth bearers like: "What time is it (yes or no)?"
"This sentence is not true", "This sentence cannot be proven".
He didn't need to screen out anything. His proof covers all first order >>>>>> theories. In many theories your examples are unexpressible anyway, so >>>>>> there is no need to screen them out.
Any sentence that is neither true nor false
must be rejected from any system of logic.
Whether a sentence is true or false or neither depends on semantics.
Yes.
In an uninterpreted formal theory a sentence has not meaning and
therefore no truth value so cannot be relejcted for a lack of truth
value.
I have posited that it has always been a huge
mistake that semantics was divided away from
the syntax of every formal logic system since
the syllogism. It is the root cause of the
divergence of logic from correct reasoning.
Logic has been shown to be useful. Your "correct reasoning" has not been.
Because no one knows about it.
Therefore there is a good reason to believe that the separation of the
meaning from the form was a good idea.
There are all kinds of errors that are simply
invisible when semantics and rules of inference
are separated.
On 2025-10-09 13:18:28 +0000, olcott said:
On 10/9/2025 5:51 AM, Mikko wrote:
On 2025-10-07 14:16:11 +0000, olcott said:
On 10/7/2025 4:48 AM, Mikko wrote:
On 2025-10-06 13:14:35 +0000, olcott said:
On 10/6/2025 7:27 AM, Mikko wrote:
On 2025-10-05 14:03:37 +0000, olcott said:
G||del 1931 undecidability and Tarski Undefinability
only exist because they they not know to reject an
expression of language that is not a truth bearer.
What expression of the language of the first order theory of the >>>>>>> first order Peano arithmetic is not a truth bearer? That you can't >>>>>>> determine the truth value of some expression does not mean that ir >>>>>>> has none. That you don't understand the proof does not mean that >>>>>>> the proofs are not sound.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
It turns out that the essence of these two papers is much
simpler than that.
Apparently not simple enough for you.
Claude AI is quite hesitant at first, disagreeing
with me several times. Then it is finally convinced
that I am correct.
That you may convince an artificial idiot means nothing.
It may seem to mean nothing until after you carefully
examine all of the details of how it pieces together all
of my ideas into a single cohesive whole.
That you may convince an artificial idiot really means nothing.
If a reliable automatic proof checker could confirm your proof
that might mean something.
The proof is entirely semantic.
Claude AI verified that the meaning of my words
proved my point. You could to if you looked at
the dialogue.
As I already said, that does not mean anything.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The gist of it is that when the Liar Paradox
is first rejected as not a truth bearer then
Tarski's whole proof loses its entire basis.
No, it does not. Tarski's proof is based on the ordinary logic and
Peano arithmetic. Therefore it and its conclusion are parts of the
analytic knowledge.
However, the Liar's paradox is basis of your counter argument, which therefore loses its basis if the Liar's paradox is rejected.
Claude AI summed up the gist of each view
of the Liar Paradox from all of the papers
written on it.
It turn out that one of my best proposals
was already written by Saul Kripke
Outline of a Theory of Truth
Saul Kripke
The Journal of Philosophy, Vol. 72, No. 19,
Seventy-Second Annual Meeting American
Philosophical Association, Eastern Division.
(Nov. 6, 1975), pp. 690-716.
https://files.commons.gc.cuny.edu/wp-content/blogs.dir/1358/
files/2019/04/Outline-of-a-Theory-of-Truth.pdf
I don't think you mean this "important lesson: it would be fruitless to
look for an intrinsic criterion that will enable us to sieve out -- as meaningless, or ill-formed -- those sentences which lead to paradox.
This looks more relevant: "G||del put the issue of the legitimacy of self-referential sentences beyond doubt; he showed that they are as incontestably legitimate as arithmetic itself."
On 2025-10-09 13:21:15 +0000, olcott said:
On 10/9/2025 5:55 AM, Mikko wrote:
On 2025-10-09 03:13:41 +0000, olcott said:
On 10/8/2025 5:54 AM, Mikko wrote:
On 2025-10-07 14:19:09 +0000, olcott said:
On 10/7/2025 4:52 AM, Mikko wrote:
On 2025-10-06 13:23:10 +0000, olcott said:
On 10/6/2025 7:36 AM, Mikko wrote:
On 2025-10-05 14:09:37 +0000, olcott said:
On 10/5/2025 5:26 AM, Mikko wrote:
On 2025-10-04 13:30:22 +0000, olcott said:
On 10/4/2025 5:11 AM, Mikko wrote:
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:The syntax of formal logical languages allows
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said: >>>>>>>>>>>>>>>>>>>A mere false assumption
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false >>>>>>>>>>>>>>>>>>>> must be rejected from any system of logic. >>>>>>>>>>>>>>>>>>>> Non-truth bearers in logic systems are like >>>>>>>>>>>>>>>>>>>> turds in birthday cakes.
Every sentence of logic that is not tautology or >>>>>>>>>>>>>>>>>>> dontradiction is
true in some contexts and false in others. >>>>>>>>>>>>>>>>>>
No, it is true on the basis of the meanings of the words. >>>>>>>>>>>>>>>>
some expressions to be created having pathological >>>>>>>>>>>>>>>> self-reference(Olcott 2004).
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string without >>>>>>>>>>>>> meaning
does not refer.
Self-reference can be detected in a string with a name. >>>>>>>>>>>>>> Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy >>>>>>>>>>>>>> of the liar
-a-a-a in the metalanguage, by forming in the language itself >>>>>>>>>>>>>> a sentence
-a-a-a x such that the sentence of the metalanguage which is >>>>>>>>>>>>>> correlated
-a-a-a with x asserts that x is not a true sentence. >>>>>>>>>>>>>> -a-a-a https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x >>>>>>>>>>>>>> https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. >>>>>>>>>>>>>>> the arithmetic
semantics of a formal language of arithmetics do not >>>>>>>>>>>>>>> permit a self-
reference.
G||del uses tricks for that.
Tarski used the same tricks.
Yet they only actually boil down to
Incomplete(F) rao reaG ((F re4 G) reo (F re4 -4G)).
and this
LP := ~True(LP)
The system they considered has no symbol for :=. Instead, >>>>>>>>>>> they construct
something like LP <-> ~True(LP). G||del then shows that that >>>>>>>>>>> the expression
that asserts its own unprovability is is not provable and >>>>>>>>>>> therefore true.
Claude AI eventually agreed that both G||del's 1931
Incompleteness theorem and the Tarski Undefinability
theorem are anchored in liar paradox like expression
that should have been rejected as not a truth bearer.
G||del proved that every sentence of a first order theory that >>>>>>>>> is not
the negation of any sentnece of that theory is true in some >>>>>>>>> model of
that theory. Therefore every sentence of every first order
theory is
a truth-bearer.
As long as you don't understand that "The liar's paradox is not >>>>>>>>> true"
is true and therefore a valid basis for a proof you cannot say >>>>>>>>> anything
about Tarski's proof but are stuck to straw men.
*The Liar Paradox is rejected*
(thus unavailable for subsequent analysis)
True(English, "This sentence is not true")==INCORRECT
*I explained this in complete detail to Claude AI*
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
The most important aspect of G||del's 1931 Incompleteness theorem >>>>>>>> are these plain English direct quotes of G||del from his paper: >>>>>>>> ...there is also a close relationship with the rCLliarrCY
antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a >>>>>>>> similar undecidability proof...
...We are therefore confronted with a proposition which asserts >>>>>>>> its own unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica >>>>>>>> And Related Systems
https://monoskop.org/images/9/93/
Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf
Basically Claude AI completely validated all of my work
on Tarski Undefinability and G||del 1931 Incompleteness.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
None of the above demonstrates any understanding of the fact that >>>>>>> "The
liar's paradox is not true" is true and therefore a valid basis >>>>>>> for a
proof. Consequently there is no reason to expect that you could say >>>>>>> anything about Tarski's work instead of your straw man.
"What time is it (true or false)?" is also not true and
best rejected at the beginning.
A question is never true and should not be even mentioned in a
discussion about truth values.
Anyway, nice to see that you don't disagree.
Yet Tarski anchored his whole proof in this:
?- LP = not(true(LP)).
You anchor your counter-proof on this:
?- LP = not(true(LP)).
But an anchor is not a proof. Tarski had a complete proof. You have not.
When we toss out his whole basis his proof
utterly fails.
When you toss out "The liar paradox is not true" the liar paraxod
remains not ture and the fact still is a valid basis for proof.
On 2025-10-09 13:25:56 +0000, olcott said:
On 10/9/2025 6:12 AM, Mikko wrote:
On 2025-10-09 03:10:56 +0000, olcott said:
I have posited that it has always been a huge
mistake that semantics was divided away from
the syntax of every formal logic system since
the syllogism. It is the root cause of the
divergence of logic from correct reasoning.
Logic has been shown to be useful. Your "correct reasoning" has not
been.
Because no one knows about it.
Much about it has been known for as long time as anyone can remember.
Instances of "correct reasoning" and "incorrect reasoning" have been identified and many these identifications have been justified. But it
is true that what you call "correct reasoning" is different from what
others have called so and is indeed not known or asked about.
Therefore there is a good reason to believe that the separation of the
meaning from the form was a good idea.
There are all kinds of errors that are simply
invisible when semantics and rules of inference
are separated.
There are errors that are invisible until someone sees them. In particular, people tend to be blind to their own errors. Therefore it is useful that proofs can be checked without special knowledge.
On 10/10/2025 3:46 AM, Mikko wrote:
On 2025-10-09 13:18:28 +0000, olcott said:
On 10/9/2025 5:51 AM, Mikko wrote:
On 2025-10-07 14:16:11 +0000, olcott said:
On 10/7/2025 4:48 AM, Mikko wrote:
On 2025-10-06 13:14:35 +0000, olcott said:
On 10/6/2025 7:27 AM, Mikko wrote:
On 2025-10-05 14:03:37 +0000, olcott said:
G||del 1931 undecidability and Tarski Undefinability
only exist because they they not know to reject an
expression of language that is not a truth bearer.
What expression of the language of the first order theory of the >>>>>>>> first order Peano arithmetic is not a truth bearer? That you can't >>>>>>>> determine the truth value of some expression does not mean that ir >>>>>>>> has none. That you don't understand the proof does not mean that >>>>>>>> the proofs are not sound.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
It turns out that the essence of these two papers is much
simpler than that.
Apparently not simple enough for you.
Claude AI is quite hesitant at first, disagreeing
with me several times. Then it is finally convinced
that I am correct.
That you may convince an artificial idiot means nothing.
It may seem to mean nothing until after you carefully
examine all of the details of how it pieces together all
of my ideas into a single cohesive whole.
That you may convince an artificial idiot really means nothing.
If a reliable automatic proof checker could confirm your proof
that might mean something.
The proof is entirely semantic.
Claude AI verified that the meaning of my words
proved my point. You could to if you looked at
the dialogue.
As I already said, that does not mean anything.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The gist of it is that when the Liar Paradox
is first rejected as not a truth bearer then
Tarski's whole proof loses its entire basis.
No, it does not. Tarski's proof is based on the ordinary logic and
Peano arithmetic. Therefore it and its conclusion are parts of the
analytic knowledge.
However, the Liar's paradox is basis of your counter argument, which
therefore loses its basis if the Liar's paradox is rejected.
When the Liar Paradox is tossed out Tarski loses the
first line and third of his proof. This causes his
whole proof to fail to reach its conclusion.
On 10/10/2025 3:48 AM, Mikko wrote:
On 2025-10-09 13:21:15 +0000, olcott said:
On 10/9/2025 5:55 AM, Mikko wrote:
On 2025-10-09 03:13:41 +0000, olcott said:When we toss out his whole basis his proof
On 10/8/2025 5:54 AM, Mikko wrote:
On 2025-10-07 14:19:09 +0000, olcott said:
On 10/7/2025 4:52 AM, Mikko wrote:
On 2025-10-06 13:23:10 +0000, olcott said:
On 10/6/2025 7:36 AM, Mikko wrote:
On 2025-10-05 14:09:37 +0000, olcott said:
On 10/5/2025 5:26 AM, Mikko wrote:
On 2025-10-04 13:30:22 +0000, olcott said:
On 10/4/2025 5:11 AM, Mikko wrote:
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said: >>>>>>>>>>>>>>>>>>> On 9/30/2025 7:54 AM, Mikko wrote:The syntax of formal logical languages allows >>>>>>>>>>>>>>>>> some expressions to be created having pathological >>>>>>>>>>>>>>>>> self-reference(Olcott 2004).
On 2025-09-29 12:24:30 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>A mere false assumption
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false >>>>>>>>>>>>>>>>>>>>> must be rejected from any system of logic. >>>>>>>>>>>>>>>>>>>>> Non-truth bearers in logic systems are like >>>>>>>>>>>>>>>>>>>>> turds in birthday cakes.
Every sentence of logic that is not tautology or dontradiction is
true in some contexts and false in others. >>>>>>>>>>>>>>>>>>>
No, it is true on the basis of the meanings of the words. >>>>>>>>>>>>>>>>>
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string without meaning
does not refer.
Self-reference can be detected in a string with a name. >>>>>>>>>>>>>>> Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy of the liar
-a-a-a in the metalanguage, by forming in the language itself a sentence
-a-a-a x such that the sentence of the metalanguage which is correlated
-a-a-a with x asserts that x is not a true sentence. >>>>>>>>>>>>>>> -a-a-a https://liarparadox.org/Tarski_247_248.pdf >>>>>>>>>>>>>>>
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x >>>>>>>>>>>>>>> https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. the arithmetic
semantics of a formal language of arithmetics do not permit a self-
reference.
G||del uses tricks for that.
Tarski used the same tricks.
Yet they only actually boil down to
Incomplete(F) rao reaG ((F re4 G) reo (F re4 -4G)).
and this
LP := ~True(LP)
The system they considered has no symbol for :=. Instead, they construct
something like LP <-> ~True(LP). G||del then shows that that the expression
that asserts its own unprovability is is not provable and therefore true.
Claude AI eventually agreed that both G||del's 1931
Incompleteness theorem and the Tarski Undefinability
theorem are anchored in liar paradox like expression
that should have been rejected as not a truth bearer.
G||del proved that every sentence of a first order theory that is not
the negation of any sentnece of that theory is true in some model of >>>>>>>>>> that theory. Therefore every sentence of every first order theory is >>>>>>>>>> a truth-bearer.
As long as you don't understand that "The liar's paradox is not true"
is true and therefore a valid basis for a proof you cannot say anything
about Tarski's proof but are stuck to straw men.
*The Liar Paradox is rejected*
(thus unavailable for subsequent analysis)
True(English, "This sentence is not true")==INCORRECT
*I explained this in complete detail to Claude AI*
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275 >>>>>>>>>
The most important aspect of G||del's 1931 Incompleteness theorem >>>>>>>>> are these plain English direct quotes of G||del from his paper: >>>>>>>>> ...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...
...We are therefore confronted with a proposition which asserts its own
unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And >>>>>>>>> Related Systems
https://monoskop.org/images/9/93/
Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf
Basically Claude AI completely validated all of my work
on Tarski Undefinability and G||del 1931 Incompleteness.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
None of the above demonstrates any understanding of the fact that "The >>>>>>>> liar's paradox is not true" is true and therefore a valid basis for a >>>>>>>> proof. Consequently there is no reason to expect that you could say >>>>>>>> anything about Tarski's work instead of your straw man.
"What time is it (true or false)?" is also not true and
best rejected at the beginning.
A question is never true and should not be even mentioned in a
discussion about truth values.
Anyway, nice to see that you don't disagree.
Yet Tarski anchored his whole proof in this:
?- LP = not(true(LP)).
You anchor your counter-proof on this:
?- LP = not(true(LP)).
But an anchor is not a proof. Tarski had a complete proof. You have not. >>>
utterly fails.
When you toss out "The liar paradox is not true" the liar paraxod
remains not ture and the fact still is a valid basis for proof.
Non-truth bearers such as "What time is it?"
and "this sentence in not true" must be excluded
from formal proofs of we get the wacky results
that a Truth predicate cannot be defined or a
self-contradictory sentence is true when evaluated
by a metatheory outside the scope of self-contradiction.
On 10/10/2025 3:58 AM, Mikko wrote:
On 2025-10-09 13:25:56 +0000, olcott said:
On 10/9/2025 6:12 AM, Mikko wrote:
On 2025-10-09 03:10:56 +0000, olcott said:
Because no one knows about it.
I have posited that it has always been a huge
mistake that semantics was divided away from
the syntax of every formal logic system since
the syllogism. It is the root cause of the
divergence of logic from correct reasoning.
Logic has been shown to be useful. Your "correct reasoning" has not been. >>>
Much about it has been known for as long time as anyone can remember.
That Tarski and G||del were wrong has been known
for a long time? The actual truth is that Tarski
and G||del have been presumed to be correct on the
basis of false assumptions.
On 2025-10-10 14:38:17 +0000, olcott said:
On 10/10/2025 3:46 AM, Mikko wrote:
On 2025-10-09 13:18:28 +0000, olcott said:
On 10/9/2025 5:51 AM, Mikko wrote:
On 2025-10-07 14:16:11 +0000, olcott said:
On 10/7/2025 4:48 AM, Mikko wrote:
On 2025-10-06 13:14:35 +0000, olcott said:
On 10/6/2025 7:27 AM, Mikko wrote:
On 2025-10-05 14:03:37 +0000, olcott said:
G||del 1931 undecidability and Tarski Undefinability
only exist because they they not know to reject an
expression of language that is not a truth bearer.
What expression of the language of the first order theory of the >>>>>>>>> first order Peano arithmetic is not a truth bearer? That you can't >>>>>>>>> determine the truth value of some expression does not mean that ir >>>>>>>>> has none. That you don't understand the proof does not mean that >>>>>>>>> the proofs are not sound.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275
It turns out that the essence of these two papers is much
simpler than that.
Apparently not simple enough for you.
Claude AI is quite hesitant at first, disagreeing
with me several times. Then it is finally convinced
that I am correct.
That you may convince an artificial idiot means nothing.
It may seem to mean nothing until after you carefully
examine all of the details of how it pieces together all
of my ideas into a single cohesive whole.
That you may convince an artificial idiot really means nothing.
If a reliable automatic proof checker could confirm your proof
that might mean something.
The proof is entirely semantic.
Claude AI verified that the meaning of my words
proved my point. You could to if you looked at
the dialogue.
As I already said, that does not mean anything.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The gist of it is that when the Liar Paradox
is first rejected as not a truth bearer then
Tarski's whole proof loses its entire basis.
No, it does not. Tarski's proof is based on the ordinary logic and
Peano arithmetic. Therefore it and its conclusion are parts of the
analytic knowledge.
However, the Liar's paradox is basis of your counter argument, which
therefore loses its basis if the Liar's paradox is rejected.
When the Liar Paradox is tossed out Tarski loses the
first line and third of his proof. This causes his
whole proof to fail to reach its conclusion.
What do you mean with "first line" and "third line" of the proof?
Tarski did not break his text to lines. That was done by the
typesetter.
On 2025-10-10 14:45:22 +0000, olcott said:
On 10/10/2025 3:48 AM, Mikko wrote:
On 2025-10-09 13:21:15 +0000, olcott said:
On 10/9/2025 5:55 AM, Mikko wrote:
On 2025-10-09 03:13:41 +0000, olcott said:
On 10/8/2025 5:54 AM, Mikko wrote:
On 2025-10-07 14:19:09 +0000, olcott said:
On 10/7/2025 4:52 AM, Mikko wrote:
On 2025-10-06 13:23:10 +0000, olcott said:
On 10/6/2025 7:36 AM, Mikko wrote:None of the above demonstrates any understanding of the fact >>>>>>>>> that "The
On 2025-10-05 14:09:37 +0000, olcott said:
On 10/5/2025 5:26 AM, Mikko wrote:
On 2025-10-04 13:30:22 +0000, olcott said:
On 10/4/2025 5:11 AM, Mikko wrote:
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said: >>>>>>>>>>>>>>>>>>>> On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>A mere false assumption
On 9/27/2025 5:07 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>
Any sentence that is neither true nor false >>>>>>>>>>>>>>>>>>>>>> must be rejected from any system of logic. >>>>>>>>>>>>>>>>>>>>>> Non-truth bearers in logic systems are like >>>>>>>>>>>>>>>>>>>>>> turds in birthday cakes.
Every sentence of logic that is not tautology or >>>>>>>>>>>>>>>>>>>>> dontradiction is
true in some contexts and false in others. >>>>>>>>>>>>>>>>>>>>
No, it is true on the basis of the meanings of the >>>>>>>>>>>>>>>>>>> words.
The syntax of formal logical languages allows >>>>>>>>>>>>>>>>>> some expressions to be created having pathological >>>>>>>>>>>>>>>>>> self-reference(Olcott 2004).
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string >>>>>>>>>>>>>>> without meaning
does not refer.
Self-reference can be detected in a string with a name. >>>>>>>>>>>>>>>> Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the >>>>>>>>>>>>>>>> antinomy of the liar
-a-a-a in the metalanguage, by forming in the language >>>>>>>>>>>>>>>> itself a sentence
-a-a-a x such that the sentence of the metalanguage which >>>>>>>>>>>>>>>> is correlated
-a-a-a with x asserts that x is not a true sentence. >>>>>>>>>>>>>>>> -a-a-a https://liarparadox.org/Tarski_247_248.pdf >>>>>>>>>>>>>>>>
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x >>>>>>>>>>>>>>>> https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For >>>>>>>>>>>>>>>>> example. the arithmetic
semantics of a formal language of arithmetics do not >>>>>>>>>>>>>>>>> permit a self-
reference.
G||del uses tricks for that.
Tarski used the same tricks.
Yet they only actually boil down to
Incomplete(F) rao reaG ((F re4 G) reo (F re4 -4G)). >>>>>>>>>>>>>> and this
LP := ~True(LP)
The system they considered has no symbol for :=. Instead, >>>>>>>>>>>>> they construct
something like LP <-> ~True(LP). G||del then shows that that >>>>>>>>>>>>> the expression
that asserts its own unprovability is is not provable and >>>>>>>>>>>>> therefore true.
Claude AI eventually agreed that both G||del's 1931
Incompleteness theorem and the Tarski Undefinability
theorem are anchored in liar paradox like expression
that should have been rejected as not a truth bearer.
G||del proved that every sentence of a first order theory that >>>>>>>>>>> is not
the negation of any sentnece of that theory is true in some >>>>>>>>>>> model of
that theory. Therefore every sentence of every first order >>>>>>>>>>> theory is
a truth-bearer.
As long as you don't understand that "The liar's paradox is >>>>>>>>>>> not true"
is true and therefore a valid basis for a proof you cannot >>>>>>>>>>> say anything
about Tarski's proof but are stuck to straw men.
*The Liar Paradox is rejected*
(thus unavailable for subsequent analysis)
True(English, "This sentence is not true")==INCORRECT
*I explained this in complete detail to Claude AI*
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275 >>>>>>>>>>
The most important aspect of G||del's 1931 Incompleteness theorem >>>>>>>>>> are these plain English direct quotes of G||del from his paper: >>>>>>>>>> ...there is also a close relationship with the rCLliarrCY >>>>>>>>>> antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for >>>>>>>>>> a similar undecidability proof...
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica >>>>>>>>>> And Related Systems
https://monoskop.org/images/9/93/
Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf
Basically Claude AI completely validated all of my work
on Tarski Undefinability and G||del 1931 Incompleteness.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275 >>>>>>>>>
liar's paradox is not true" is true and therefore a valid basis >>>>>>>>> for a
proof. Consequently there is no reason to expect that you could >>>>>>>>> say
anything about Tarski's work instead of your straw man.
"What time is it (true or false)?" is also not true and
best rejected at the beginning.
A question is never true and should not be even mentioned in a
discussion about truth values.
Anyway, nice to see that you don't disagree.
Yet Tarski anchored his whole proof in this:
?- LP = not(true(LP)).
You anchor your counter-proof on this:
?- LP = not(true(LP)).
But an anchor is not a proof. Tarski had a complete proof. You have >>>>> not.
When we toss out his whole basis his proof
utterly fails.
When you toss out "The liar paradox is not true" the liar paraxod
remains not ture and the fact still is a valid basis for proof.
Non-truth bearers such as "What time is it?"
and "this sentence in not true" must be excluded
from formal proofs of we get the wacky results
that a Truth predicate cannot be defined or a
self-contradictory sentence is true when evaluated
by a metatheory outside the scope of self-contradiction.
Can you proove that Tarski made an error without mentioning any sentence
that you said must be excluded?
On 2025-10-10 15:02:34 +0000, olcott said:
On 10/10/2025 3:58 AM, Mikko wrote:
On 2025-10-09 13:25:56 +0000, olcott said:
On 10/9/2025 6:12 AM, Mikko wrote:
On 2025-10-09 03:10:56 +0000, olcott said:
I have posited that it has always been a huge
mistake that semantics was divided away from
the syntax of every formal logic system since
the syllogism. It is the root cause of the
divergence of logic from correct reasoning.
Logic has been shown to be useful. Your "correct reasoning" has not >>>>> been.
Because no one knows about it.
Much about it has been known for as long time as anyone can remember.
That Tarski and G||del were wrong has been known
for a long time? The actual truth is that Tarski
and G||del have been presumed to be correct on the
basis of false assumptions.
Your "correct reasoning" was not invented by G||del or Tarski.
On 10/11/2025 4:57 AM, Mikko wrote:
On 2025-10-10 14:38:17 +0000, olcott said:
On 10/10/2025 3:46 AM, Mikko wrote:
On 2025-10-09 13:18:28 +0000, olcott said:
On 10/9/2025 5:51 AM, Mikko wrote:
On 2025-10-07 14:16:11 +0000, olcott said:
On 10/7/2025 4:48 AM, Mikko wrote:
On 2025-10-06 13:14:35 +0000, olcott said:
On 10/6/2025 7:27 AM, Mikko wrote:
On 2025-10-05 14:03:37 +0000, olcott said:
G||del 1931 undecidability and Tarski Undefinability
only exist because they they not know to reject an
expression of language that is not a truth bearer.
What expression of the language of the first order theory of the >>>>>>>>>> first order Peano arithmetic is not a truth bearer? That you can't >>>>>>>>>> determine the truth value of some expression does not mean that ir >>>>>>>>>> has none. That you don't understand the proof does not mean that >>>>>>>>>> the proofs are not sound.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275 >>>>>>>>> It turns out that the essence of these two papers is much
simpler than that.
Apparently not simple enough for you.
Claude AI is quite hesitant at first, disagreeing
with me several times. Then it is finally convinced
that I am correct.
That you may convince an artificial idiot means nothing.
It may seem to mean nothing until after you carefully
examine all of the details of how it pieces together all
of my ideas into a single cohesive whole.
That you may convince an artificial idiot really means nothing. >>>>>>>> If a reliable automatic proof checker could confirm your proof >>>>>>>> that might mean something.
The proof is entirely semantic.
Claude AI verified that the meaning of my words
proved my point. You could to if you looked at
the dialogue.
As I already said, that does not mean anything.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The gist of it is that when the Liar Paradox
is first rejected as not a truth bearer then
Tarski's whole proof loses its entire basis.
No, it does not. Tarski's proof is based on the ordinary logic and
Peano arithmetic. Therefore it and its conclusion are parts of the
analytic knowledge.
However, the Liar's paradox is basis of your counter argument, which
therefore loses its basis if the Liar's paradox is rejected.
When the Liar Paradox is tossed out Tarski loses the
first line and third of his proof. This causes his
whole proof to fail to reach its conclusion.
What do you mean with "first line" and "third line" of the proof?
Tarski did not break his text to lines. That was done by the
typesetter.
So you are saying the he jumbled all of his
proof steps together?
On 10/11/2025 5:01 AM, Mikko wrote:
On 2025-10-10 14:45:22 +0000, olcott said:
On 10/10/2025 3:48 AM, Mikko wrote:
On 2025-10-09 13:21:15 +0000, olcott said:
On 10/9/2025 5:55 AM, Mikko wrote:
On 2025-10-09 03:13:41 +0000, olcott said:When we toss out his whole basis his proof
On 10/8/2025 5:54 AM, Mikko wrote:
On 2025-10-07 14:19:09 +0000, olcott said:
On 10/7/2025 4:52 AM, Mikko wrote:
On 2025-10-06 13:23:10 +0000, olcott said:
On 10/6/2025 7:36 AM, Mikko wrote:None of the above demonstrates any understanding of the fact that "The
On 2025-10-05 14:09:37 +0000, olcott said:
On 10/5/2025 5:26 AM, Mikko wrote:G||del proved that every sentence of a first order theory that is not
On 2025-10-04 13:30:22 +0000, olcott said:
On 10/4/2025 5:11 AM, Mikko wrote:
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>> On 9/30/2025 7:54 AM, Mikko wrote:The syntax of formal logical languages allows >>>>>>>>>>>>>>>>>>> some expressions to be created having pathological >>>>>>>>>>>>>>>>>>> self-reference(Olcott 2004).
On 2025-09-29 12:24:30 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>A mere false assumption
On 9/27/2025 5:07 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>
Any sentence that is neither true nor false >>>>>>>>>>>>>>>>>>>>>>> must be rejected from any system of logic. >>>>>>>>>>>>>>>>>>>>>>> Non-truth bearers in logic systems are like >>>>>>>>>>>>>>>>>>>>>>> turds in birthday cakes.
Every sentence of logic that is not tautology or dontradiction is
true in some contexts and false in others. >>>>>>>>>>>>>>>>>>>>>
No, it is true on the basis of the meanings of the words. >>>>>>>>>>>>>>>>>>>
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string without meaning
does not refer.
Self-reference can be detected in a string with a name. >>>>>>>>>>>>>>>>> Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy of the liar
-a-a-a in the metalanguage, by forming in the language itself a sentence
-a-a-a x such that the sentence of the metalanguage which is correlated
-a-a-a with x asserts that x is not a true sentence. >>>>>>>>>>>>>>>>> -a-a-a https://liarparadox.org/Tarski_247_248.pdf >>>>>>>>>>>>>>>>>
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x >>>>>>>>>>>>>>>>> https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. the arithmetic
semantics of a formal language of arithmetics do not permit a self-
reference.
G||del uses tricks for that.
Tarski used the same tricks.
Yet they only actually boil down to
Incomplete(F) rao reaG ((F re4 G) reo (F re4 -4G)). >>>>>>>>>>>>>>> and this
LP := ~True(LP)
The system they considered has no symbol for :=. Instead, they construct
something like LP <-> ~True(LP). G||del then shows that that the expression
that asserts its own unprovability is is not provable and therefore true.
Claude AI eventually agreed that both G||del's 1931
Incompleteness theorem and the Tarski Undefinability >>>>>>>>>>>>> theorem are anchored in liar paradox like expression >>>>>>>>>>>>> that should have been rejected as not a truth bearer. >>>>>>>>>>>>
the negation of any sentnece of that theory is true in some model of
that theory. Therefore every sentence of every first order theory is
a truth-bearer.
As long as you don't understand that "The liar's paradox is not true"
is true and therefore a valid basis for a proof you cannot say anything
about Tarski's proof but are stuck to straw men.
*The Liar Paradox is rejected*
(thus unavailable for subsequent analysis)
True(English, "This sentence is not true")==INCORRECT
*I explained this in complete detail to Claude AI*
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275 >>>>>>>>>>>
The most important aspect of G||del's 1931 Incompleteness theorem >>>>>>>>>>> are these plain English direct quotes of G||del from his paper: >>>>>>>>>>> ...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...
...We are therefore confronted with a proposition which asserts its own
unprovability. 15 ...
(G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And >>>>>>>>>>> Related Systems
https://monoskop.org/images/9/93/
Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf
Basically Claude AI completely validated all of my work
on Tarski Undefinability and G||del 1931 Incompleteness. >>>>>>>>>>> https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275 >>>>>>>>>>
liar's paradox is not true" is true and therefore a valid basis for a
proof. Consequently there is no reason to expect that you could say >>>>>>>>>> anything about Tarski's work instead of your straw man.
"What time is it (true or false)?" is also not true and
best rejected at the beginning.
A question is never true and should not be even mentioned in a >>>>>>>> discussion about truth values.
Anyway, nice to see that you don't disagree.
Yet Tarski anchored his whole proof in this:
?- LP = not(true(LP)).
You anchor your counter-proof on this:
?- LP = not(true(LP)).
But an anchor is not a proof. Tarski had a complete proof. You have not. >>>>>
utterly fails.
When you toss out "The liar paradox is not true" the liar paraxod
remains not ture and the fact still is a valid basis for proof.
Non-truth bearers such as "What time is it?"
and "this sentence in not true" must be excluded
from formal proofs of we get the wacky results
that a Truth predicate cannot be defined or a
self-contradictory sentence is true when evaluated
by a metatheory outside the scope of self-contradiction.
Can you proove that Tarski made an error without mentioning any sentence
that you said must be excluded?
That was his only mistake.
Can you count to five without using any numbers?
On 10/11/2025 5:02 AM, Mikko wrote:
On 2025-10-10 15:02:34 +0000, olcott said:
On 10/10/2025 3:58 AM, Mikko wrote:
On 2025-10-09 13:25:56 +0000, olcott said:
On 10/9/2025 6:12 AM, Mikko wrote:
On 2025-10-09 03:10:56 +0000, olcott said:
I have posited that it has always been a huge
mistake that semantics was divided away from
the syntax of every formal logic system since
the syllogism. It is the root cause of the
divergence of logic from correct reasoning.
Logic has been shown to be useful. Your "correct reasoning" has not been.
Because no one knows about it.
Much about it has been known for as long time as anyone can remember.
That Tarski and G||del were wrong has been known
for a long time? The actual truth is that Tarski
and G||del have been presumed to be correct on the
basis of false assumptions.
Your "correct reasoning" was not invented by G||del or Tarski.
Apparently the seed of my correct reasoning system
was created by Saul Kripke.
https://files.commons.gc.cuny.edu/wp-content/blogs.dir/1358/files/2019/04/Outline-of-a-Theory-of-Truth.pdf
My system is simpler and may work a little
differently.
On 2025-10-11 13:26:16 +0000, olcott said:
On 10/11/2025 4:57 AM, Mikko wrote:
On 2025-10-10 14:38:17 +0000, olcott said:
On 10/10/2025 3:46 AM, Mikko wrote:
On 2025-10-09 13:18:28 +0000, olcott said:
On 10/9/2025 5:51 AM, Mikko wrote:
On 2025-10-07 14:16:11 +0000, olcott said:
On 10/7/2025 4:48 AM, Mikko wrote:
On 2025-10-06 13:14:35 +0000, olcott said:
On 10/6/2025 7:27 AM, Mikko wrote:
On 2025-10-05 14:03:37 +0000, olcott said:
G||del 1931 undecidability and Tarski Undefinability
only exist because they they not know to reject an
expression of language that is not a truth bearer.
What expression of the language of the first order theory of the >>>>>>>>>>> first order Peano arithmetic is not a truth bearer? That you >>>>>>>>>>> can't
determine the truth value of some expression does not mean >>>>>>>>>>> that ir
has none. That you don't understand the proof does not mean that >>>>>>>>>>> the proofs are not sound.
https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275 >>>>>>>>>> It turns out that the essence of these two papers is much
simpler than that.
Apparently not simple enough for you.
Claude AI is quite hesitant at first, disagreeing
with me several times. Then it is finally convinced
that I am correct.
That you may convince an artificial idiot means nothing.
It may seem to mean nothing until after you carefully
examine all of the details of how it pieces together all
of my ideas into a single cohesive whole.
That you may convince an artificial idiot really means nothing. >>>>>>>>> If a reliable automatic proof checker could confirm your proof >>>>>>>>> that might mean something.
The proof is entirely semantic.
Claude AI verified that the meaning of my words
proved my point. You could to if you looked at
the dialogue.
As I already said, that does not mean anything.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The gist of it is that when the Liar Paradox
is first rejected as not a truth bearer then
Tarski's whole proof loses its entire basis.
No, it does not. Tarski's proof is based on the ordinary logic and
Peano arithmetic. Therefore it and its conclusion are parts of the
analytic knowledge.
However, the Liar's paradox is basis of your counter argument, which >>>>> therefore loses its basis if the Liar's paradox is rejected.
When the Liar Paradox is tossed out Tarski loses the
first line and third of his proof. This causes his
whole proof to fail to reach its conclusion.
What do you mean with "first line" and "third line" of the proof?
Tarski did not break his text to lines. That was done by the
typesetter.
So you are saying the he jumbled all of his
proof steps together?
No, I asked a question that you failed to answer, apparently because
you cannot answer without revealing that you lied.
On 2025-10-11 13:28:02 +0000, olcott said:
On 10/11/2025 5:01 AM, Mikko wrote:
On 2025-10-10 14:45:22 +0000, olcott said:>>>> Non-truth bearers such as "What time is it?"
and "this sentence in not true" must be excluded
from formal proofs of we get the wacky results
that a Truth predicate cannot be defined or a
self-contradictory sentence is true when evaluated
by a metatheory outside the scope of self-contradiction.
Can you proove that Tarski made an error without mentioning any sentence >>> that you said must be excluded?
That was his only mistake.
Can you count to five without using any numbers?
I needn't. Nobody ever asks without using numbers to count to five.
On 2025-10-11 13:34:42 +0000, olcott said:
On 10/11/2025 5:02 AM, Mikko wrote:
On 2025-10-10 15:02:34 +0000, olcott said:
On 10/10/2025 3:58 AM, Mikko wrote:
On 2025-10-09 13:25:56 +0000, olcott said:That Tarski and G||del were wrong has been known
On 10/9/2025 6:12 AM, Mikko wrote:
On 2025-10-09 03:10:56 +0000, olcott said:
I have posited that it has always been a huge
mistake that semantics was divided away from
the syntax of every formal logic system since
the syllogism. It is the root cause of the
divergence of logic from correct reasoning.
Logic has been shown to be useful. Your "correct reasoning" has >>>>>>> not been.
Because no one knows about it.
Much about it has been known for as long time as anyone can remember. >>>>
for a long time? The actual truth is that Tarski
and G||del have been presumed to be correct on the
basis of false assumptions.
Your "correct reasoning" was not invented by G||del or Tarski.
Apparently the seed of my correct reasoning system
was created by Saul Kripke.
That's possible if you had read Kripke shortly before you started
to use the term.
https://files.commons.gc.cuny.edu/wp-content/blogs.dir/1358/
files/2019/04/Outline-of-a-Theory-of-Truth.pdf
My system is simpler and may work a little
differently.
Your system only looks simpler because you have not yet thought about
it more than superficieally.