olcott kirjoitti 2.12.2025 klo 16.00:
On 12/2/2025 2:53 AM, Mikko wrote:
olcott kirjoitti 1.12.2025 klo 19.15:
On 12/1/2025 5:02 AM, Mikko wrote:
olcott kirjoitti 29.11.2025 klo 23.59:
G := (F re4 G) // G says of itself that it is unprovable in F
With a reasonable type system that is a type error:
- the symbol re4 requires a sentence on the right side
- the value of the re4 operation is a truth value
- the symbol := requires the same type on both sides
- thus G must be both a sentence and a truth value
But G cannot be both. A sentence has a truth value but it isn't one. >>>>>
% This sentence cannot be proven in F
?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
It is an expression of language having no truth value
because it is not a logic sentence.
https://en.wikipedia.org/wiki/Sentence_(mathematical_logic)
Yes, that is the exxential difference between the two G's.
The expession F re4 G has a truth value because it is either
true or false
I propose that is a false assumption.
If you want to propose anygthng like that you should
(a) specify what is the assumption you want to propose as false
(b) why should that assumption be considered false
(c) what assumption would be true or at least less obviously false
On 12/3/2025 4:41 AM, Mikko wrote:
olcott kirjoitti 2.12.2025 klo 16.00:
On 12/2/2025 2:53 AM, Mikko wrote:
olcott kirjoitti 1.12.2025 klo 19.15:
On 12/1/2025 5:02 AM, Mikko wrote:
olcott kirjoitti 29.11.2025 klo 23.59:
G := (F re4 G) // G says of itself that it is unprovable in F
With a reasonable type system that is a type error:
- the symbol re4 requires a sentence on the right side
- the value of the re4 operation is a truth value
- the symbol := requires the same type on both sides
- thus G must be both a sentence and a truth value
But G cannot be both. A sentence has a truth value but it isn't one. >>>>>>
% This sentence cannot be proven in F
?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
It is an expression of language having no truth value
because it is not a logic sentence.
https://en.wikipedia.org/wiki/Sentence_(mathematical_logic)
Yes, that is the exxential difference between the two G's.
The expession F re4 G has a truth value because it is either
true or false
I propose that is a false assumption.
If you want to propose anygthng like that you should
(a) specify what is the assumption you want to propose as false
(b) why should that assumption be considered false
(c) what assumption would be true or at least less obviously false
?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
G is neither True nor False its resolution remains stuck
in an infinite loop.
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)
On 12/2/2025 3:49 AM, Mikko wrote:
dbush kirjoitti 29.11.2025 klo 20.19:
On 11/29/2025 1:07 PM, olcott wrote:
On 11/29/2025 11:53 AM, Kaz Kylheku wrote:
On 2025-11-29, olcott <polcott333@gmail.com> wrote:
Any expression of language that is proven true entirely
on the basis of its meaning expressed in language is
a semantic tautology.
A tautology is an expression of logic which is true for all
combinations of the truth values of its variables and propositions,
which is, of course, regardless of what they mean/represent.
I did not say tautology. I said semantic tautology.
I am defining a new thing under the Sun.
*Semantic tautology is stipulated to mean*
Any expression of language that is proven true entirely
on the basis of its meaning expressed in language.
So in other words, "semantic tautology" is just another term for
"definition".
A definition gives a new word for something.
A semantic tautology is a verbose expression that may take some effort
to understand but once understood is onderstood to say nothing.
A semantic tautology might be considered the
complete definition of a a word by providing
the complete definition of every word in this
definition recursively all the way down until
every one of these words is completely defined.
As even (a) is not answered we must interprete the above to mean
that you retracted your proposal.
olcott kirjoitti 3.12.2025 klo 17.59:
On 12/3/2025 4:41 AM, Mikko wrote:
olcott kirjoitti 2.12.2025 klo 16.00:
On 12/2/2025 2:53 AM, Mikko wrote:
olcott kirjoitti 1.12.2025 klo 19.15:
On 12/1/2025 5:02 AM, Mikko wrote:
olcott kirjoitti 29.11.2025 klo 23.59:
G := (F re4 G) // G says of itself that it is unprovable in F
With a reasonable type system that is a type error:
- the symbol re4 requires a sentence on the right side
- the value of the re4 operation is a truth value
- the symbol := requires the same type on both sides
- thus G must be both a sentence and a truth value
But G cannot be both. A sentence has a truth value but it isn't one. >>>>>>>
% This sentence cannot be proven in F
?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
It is an expression of language having no truth value
because it is not a logic sentence.
https://en.wikipedia.org/wiki/Sentence_(mathematical_logic)
Yes, that is the exxential difference between the two G's.
The expession F re4 G has a truth value because it is either
true or false
I propose that is a false assumption.
If you want to propose anygthng like that you should
(a) specify what is the assumption you want to propose as false
(b) why should that assumption be considered false
(c) what assumption would be true or at least less obviously false
?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
G is neither True nor False its resolution remains stuck
in an infinite loop.
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)
As even (a) is not answered we must interprete the above to mean
that you retracted your proposal.
olcott kirjoitti 2.12.2025 klo 17.26:
On 12/2/2025 3:49 AM, Mikko wrote:
dbush kirjoitti 29.11.2025 klo 20.19:
On 11/29/2025 1:07 PM, olcott wrote:
On 11/29/2025 11:53 AM, Kaz Kylheku wrote:
On 2025-11-29, olcott <polcott333@gmail.com> wrote:
Any expression of language that is proven true entirely
on the basis of its meaning expressed in language is
a semantic tautology.
A tautology is an expression of logic which is true for all
combinations of the truth values of its variables and propositions, >>>>>> which is, of course, regardless of what they mean/represent.
I did not say tautology. I said semantic tautology.
I am defining a new thing under the Sun.
*Semantic tautology is stipulated to mean*
Any expression of language that is proven true entirely
on the basis of its meaning expressed in language.
So in other words, "semantic tautology" is just another term for
"definition".
A definition gives a new word for something.
A semantic tautology is a verbose expression that may take some effort
to understand but once understood is onderstood to say nothing.
A semantic tautology might be considered the
complete definition of a a word by providing
the complete definition of every word in this
definition recursively all the way down until
every one of these words is completely defined.
A semantic tautology needn't define any words and usually doesn't.
It
can be and usually is expressed with words that already have meanings.
The definition of "semantic logical tautology" presented above doesn't require that it define any of its word.
On 12/5/2025 2:48 AM, Mikko wrote:
olcott kirjoitti 3.12.2025 klo 17.59:
On 12/3/2025 4:41 AM, Mikko wrote:
olcott kirjoitti 2.12.2025 klo 16.00:
On 12/2/2025 2:53 AM, Mikko wrote:
olcott kirjoitti 1.12.2025 klo 19.15:
On 12/1/2025 5:02 AM, Mikko wrote:
olcott kirjoitti 29.11.2025 klo 23.59:
G := (F re4 G) // G says of itself that it is unprovable in F
With a reasonable type system that is a type error:
- the symbol re4 requires a sentence on the right side
- the value of the re4 operation is a truth value
- the symbol := requires the same type on both sides
- thus G must be both a sentence and a truth value
But G cannot be both. A sentence has a truth value but it isn't >>>>>>>> one.
% This sentence cannot be proven in F
?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
It is an expression of language having no truth value
because it is not a logic sentence.
https://en.wikipedia.org/wiki/Sentence_(mathematical_logic)
Yes, that is the exxential difference between the two G's.
The expession F re4 G has a truth value because it is either
true or false
I propose that is a false assumption.
If you want to propose anygthng like that you should
(a) specify what is the assumption you want to propose as false
(b) why should that assumption be considered false
(c) what assumption would be true or at least less obviously false
?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
G is neither True nor False its resolution remains stuck
in an infinite loop.
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)
As even (a) is not answered we must interprete the above to mean
that you retracted your proposal.
If you understood the above you would understand
that I already answered (a) in 100% complete detail.
The assumption that is false is that G is not
semantically incoherent.
On 12/5/2025 2:57 AM, Mikko wrote:
olcott kirjoitti 2.12.2025 klo 17.26:
On 12/2/2025 3:49 AM, Mikko wrote:
dbush kirjoitti 29.11.2025 klo 20.19:
On 11/29/2025 1:07 PM, olcott wrote:
On 11/29/2025 11:53 AM, Kaz Kylheku wrote:
On 2025-11-29, olcott <polcott333@gmail.com> wrote:
Any expression of language that is proven true entirely
on the basis of its meaning expressed in language is
a semantic tautology.
A tautology is an expression of logic which is true for all
combinations of the truth values of its variables and propositions, >>>>>>> which is, of course, regardless of what they mean/represent.
I did not say tautology. I said semantic tautology.
I am defining a new thing under the Sun.
*Semantic tautology is stipulated to mean*
Any expression of language that is proven true entirely
on the basis of its meaning expressed in language.
So in other words, "semantic tautology" is just another term for
"definition".
A definition gives a new word for something.
A semantic tautology is a verbose expression that may take some effort >>>> to understand but once understood is onderstood to say nothing.
A semantic tautology might be considered the
complete definition of a a word by providing
the complete definition of every word in this
definition recursively all the way down until
every one of these words is completely defined.
A semantic tautology needn't define any words and usually doesn't.
[semantic tautology] is my term thus giving me absolute
authority over its meaning.
I stipulate that it derives
all of its meaning from the base meaning of its constituents
composed together.
It
can be and usually is expressed with words that already have meanings.
The definition of "semantic logical tautology" presented above doesn't
require that it define any of its word.
"I will be going to the grocery store in a few minutes"
Is not typically construed as any king of logic sentence
so I am expressly enlarging the scope of the-a the term
"tautology" and expressly removing the notion of any
syntactic basis by stipulating a "semantic" basis.
https://en.wikipedia.org/wiki/Tautology_(logic)
olcott kirjoitti 5.12.2025 klo 18.41:
On 12/5/2025 2:48 AM, Mikko wrote:
olcott kirjoitti 3.12.2025 klo 17.59:
On 12/3/2025 4:41 AM, Mikko wrote:
olcott kirjoitti 2.12.2025 klo 16.00:
On 12/2/2025 2:53 AM, Mikko wrote:
olcott kirjoitti 1.12.2025 klo 19.15:
On 12/1/2025 5:02 AM, Mikko wrote:
olcott kirjoitti 29.11.2025 klo 23.59:
G := (F re4 G) // G says of itself that it is unprovable in F >>>>>>>>>
With a reasonable type system that is a type error:
- the symbol re4 requires a sentence on the right side
- the value of the re4 operation is a truth value
- the symbol := requires the same type on both sides
- thus G must be both a sentence and a truth value
But G cannot be both. A sentence has a truth value but it isn't >>>>>>>>> one.
% This sentence cannot be proven in F
?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
It is an expression of language having no truth value
because it is not a logic sentence.
https://en.wikipedia.org/wiki/Sentence_(mathematical_logic)
Yes, that is the exxential difference between the two G's.
The expession F re4 G has a truth value because it is either
true or false
I propose that is a false assumption.
If you want to propose anygthng like that you should
(a) specify what is the assumption you want to propose as false
(b) why should that assumption be considered false
(c) what assumption would be true or at least less obviously false
?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
G is neither True nor False its resolution remains stuck
in an infinite loop.
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)
As even (a) is not answered we must interprete the above to mean
that you retracted your proposal.
If you understood the above you would understand
that I already answered (a) in 100% complete detail.
Apparently "that" in your "I propopose that is a false assumption"
refers to my "yes" response to your previous posting. But that
response does not oresent any assumption.
As everyone can see, you did not indentify the assumption.
The assumption that is false is that G is not
semantically incoherent.
That assumption is not present in any plase that the word "that"
could refer to.
olcott kirjoitti 5.12.2025 klo 19.30:
On 12/5/2025 2:57 AM, Mikko wrote:
olcott kirjoitti 2.12.2025 klo 17.26:
On 12/2/2025 3:49 AM, Mikko wrote:
dbush kirjoitti 29.11.2025 klo 20.19:
On 11/29/2025 1:07 PM, olcott wrote:
On 11/29/2025 11:53 AM, Kaz Kylheku wrote:
On 2025-11-29, olcott <polcott333@gmail.com> wrote:
Any expression of language that is proven true entirely
on the basis of its meaning expressed in language is
a semantic tautology.
A tautology is an expression of logic which is true for all
combinations of the truth values of its variables and propositions, >>>>>>>> which is, of course, regardless of what they mean/represent.
I did not say tautology. I said semantic tautology.
I am defining a new thing under the Sun.
*Semantic tautology is stipulated to mean*
Any expression of language that is proven true entirely
on the basis of its meaning expressed in language.
So in other words, "semantic tautology" is just another term for
"definition".
A definition gives a new word for something.
A semantic tautology is a verbose expression that may take some effort >>>>> to understand but once understood is onderstood to say nothing.
A semantic tautology might be considered the
complete definition of a a word by providing
the complete definition of every word in this
definition recursively all the way down until
every one of these words is completely defined.
A semantic tautology needn't define any words and usually doesn't.
[semantic tautology] is my term thus giving me absolute
authority over its meaning.
No, you have not. The word "tautology" already has a meaning. Therefore
you are restricted to subtypes of taotology.
I stipulate that it derives
all of its meaning from the base meaning of its constituents
composed together.
That is teh exac meaning when I used the expression above and below.
It
can be and usually is expressed with words that already have meanings.
The definition of "semantic logical tautology" presented above doesn't
require that it define any of its word.
"I will be going to the grocery store in a few minutes"
Aristotle has a long discussion on whther sentences about future
events, like your example above, have a truth value. He concluded
that they don't but modern ligicians often think they do. Either
way, the above is not any kind of tautology.
Is not typically construed as any king of logic sentence
so I am expressly enlarging the scope of the-a the term
"tautology" and expressly removing the notion of any
syntactic basis by stipulating a "semantic" basis.
If you want to extend the scope you must define what "tautology"
or at least "semantic tautology" means in the extended scope. But
the generalized meaning must be equivalent to the conventional
meaning when applied to sentences of ordinary logic.
https://en.wikipedia.org/wiki/Tautology_(logic)
That page says that tautology is a sentence that is true independently
of its semantics.
On 12/6/2025 2:37 AM, Mikko wrote:
olcott kirjoitti 5.12.2025 klo 18.41:
On 12/5/2025 2:48 AM, Mikko wrote:
olcott kirjoitti 3.12.2025 klo 17.59:
On 12/3/2025 4:41 AM, Mikko wrote:
olcott kirjoitti 2.12.2025 klo 16.00:
On 12/2/2025 2:53 AM, Mikko wrote:
olcott kirjoitti 1.12.2025 klo 19.15:
On 12/1/2025 5:02 AM, Mikko wrote:
olcott kirjoitti 29.11.2025 klo 23.59:
G := (F re4 G) // G says of itself that it is unprovable in F >>>>>>>>>>
With a reasonable type system that is a type error:
- the symbol re4 requires a sentence on the right side
- the value of the re4 operation is a truth value
- the symbol := requires the same type on both sides
- thus G must be both a sentence and a truth value
But G cannot be both. A sentence has a truth value but it >>>>>>>>>> isn't one.
% This sentence cannot be proven in F
?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
It is an expression of language having no truth value
because it is not a logic sentence.
https://en.wikipedia.org/wiki/Sentence_(mathematical_logic)
Yes, that is the exxential difference between the two G's.
The expession F re4 G has a truth value because it is either
true or false
I propose that is a false assumption.
If you want to propose anygthng like that you should
(a) specify what is the assumption you want to propose as false
(b) why should that assumption be considered false
(c) what assumption would be true or at least less obviously false
?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
G is neither True nor False its resolution remains stuck
in an infinite loop.
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)
As even (a) is not answered we must interprete the above to mean
that you retracted your proposal.
If you understood the above you would understand
that I already answered (a) in 100% complete detail.
Apparently "that" in your "I propopose that is a false assumption"
refers to my "yes" response to your previous posting. But that
response does not oresent any assumption.
As everyone can see, you did not indentify the assumption.
The assumption that is false is that G is not
semantically incoherent.
That assumption is not present in any plase that the word "that"
could refer to.
I explained all of the details of how G is
semantically incoherent and you understood none of it.
On 12/6/2025 2:53 AM, Mikko wrote:
olcott kirjoitti 5.12.2025 klo 19.30:
On 12/5/2025 2:57 AM, Mikko wrote:
olcott kirjoitti 2.12.2025 klo 17.26:
On 12/2/2025 3:49 AM, Mikko wrote:
dbush kirjoitti 29.11.2025 klo 20.19:
On 11/29/2025 1:07 PM, olcott wrote:
On 11/29/2025 11:53 AM, Kaz Kylheku wrote:
On 2025-11-29, olcott <polcott333@gmail.com> wrote:
Any expression of language that is proven true entirely
on the basis of its meaning expressed in language is
a semantic tautology.
A tautology is an expression of logic which is true for all
combinations of the truth values of its variables and
propositions,
which is, of course, regardless of what they mean/represent. >>>>>>>>>
I did not say tautology. I said semantic tautology.
I am defining a new thing under the Sun.
*Semantic tautology is stipulated to mean*
Any expression of language that is proven true entirely
on the basis of its meaning expressed in language.
So in other words, "semantic tautology" is just another term for >>>>>>> "definition".
A definition gives a new word for something.
A semantic tautology is a verbose expression that may take some
effort
to understand but once understood is onderstood to say nothing.
A semantic tautology might be considered the
complete definition of a a word by providing
the complete definition of every word in this
definition recursively all the way down until
every one of these words is completely defined.
A semantic tautology needn't define any words and usually doesn't.
[semantic tautology] is my term thus giving me absolute
authority over its meaning.
No, you have not. The word "tautology" already has a meaning. Therefore
you are restricted to subtypes of taotology.
I stipulate that it derives
all of its meaning from the base meaning of its constituents
composed together.
That is teh exac meaning when I used the expression above and below.
No one ever understands that my mathematical formal
system includes the entire body of human general
knowledge encoded in formalized English.
olcott kirjoitti 6.12.2025 klo 14.33:
No one ever understands that my mathematical formal
system includes the entire body of human general
knowledge encoded in formalized English.
Maybe because it is well understood that no formal system that can
be presented includes the entire body of human general knowledge.
On 07/12/2025 10:42, Mikko wrote:
olcott kirjoitti 6.12.2025 klo 14.33:
No one ever understands that my mathematical formal
system includes the entire body of human general
knowledge encoded in formalized English.
Liar.
Maybe because it is well understood that no formal system that can
be presented includes the entire body of human general knowledge.
Unless it also includes everything that is not of human general
knowledge. Infinite monkeys and so forth.
Olcott already said it was a semantic tautology, after all. Which is a
fancy way of saying that it's a system for universal semantic analysis
so it contains all possible meaning associations including those that
are of the body of human general knowledge.
Once he said it was a semantic tautology it was not possible to be surprising.
The difficult bit is as for a sculptor; to carve away those things that
are /not/ wanted.
On 07/12/2025 10:42, Mikko wrote:
olcott kirjoitti 6.12.2025 klo 14.33:
No one ever understands that my mathematical formal
system includes the entire body of human general
knowledge encoded in formalized English.
Liar.
Maybe because it is well understood that no formal system that can
be presented includes the entire body of human general knowledge.
Unless it also includes everything that is not of human general
knowledge. Infinite monkeys and so forth.
Olcott already said it was a semantic tautology, after all. Which is a
fancy way of saying that it's a system for universal semantic analysis
so it contains all possible meaning associations including those that
are of the body of human general knowledge.
Once he said it was a semantic tautology it was not possible to be surprising.
The difficult bit is as for a sculptor; to carve away those things that
are /not/ wanted.
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