Any expression of language that is proven true entirely
on the basis of its meaning expressed in language is
a semantic tautology.
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.
For instance "P or not P".
A deductive argument is tautological; its deduction is true
for all interpretations of the propositions it contains,
in all possible universes of discourse.
You would need to have tremendous stature in logic to
be able to dictate a redefinition of a deeply entrenched,
standard term.
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.
Any expression of language that is proven true entirely
on the basis of its meaning expressed in language is
a semantic tautology.
I also call this Analytic(Olcott)
https://plato.stanford.edu/entries/analytic-synthetic/
Two Dogmas of Empiricism
Willard Van Orman Quine
https://www.theologie.uzh.ch/dam/jcr:ffffffff- fbd6-1538-0000-000070cf64bc/Quine51.pdf
It overcomes Quine's objections by encoding basic facts
of the world as Rudolf Carnap Meaning Postulates organized
as a knowledge ontology inheritance hierarchy
-a In information science, an ontology encompasses a
-a representation, formal naming, and definitions of
-a the categories, properties, and relations between
-a the concepts...
-a https://en.wikipedia.org/wiki/Ontology_(information_science)
-a That is essentially Kurt G||del's "theory of simple types" By
-a the theory of simple types I mean the doctrine which says
-a that the objects of thought ... are divided into types,
-a namely: individuals, properties of individuals, relations
-a between individuals, properties of such relations, etc.
-a https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
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.
You would need to have tremendous stature in logic to
be able to dictate a redefinition of a deeply entrenched,
standard term.
Or I could simply prove that I am correct on the
basis of the meaning of my words, thus anyone
disagreeing is merely proving that they are too
full of themselves.
On 2025-11-29, olcott <polcott333@gmail.com> 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.
The existing tautology is already semantic. You have to know the
semantics (the truth tables of the logical operators used in the
formula, and the workings of quantifiers and whatnot) to be able to
conclude whether a formula is a tautology.
Pick another word. Since only dimwitted crackpots like yourself will
want to discuss anything using that word, keep the syllable count low
and make sure there aren't too many off-centre vowels.
*Semantic tautology is stipulated to mean*
Reject; call it something else.
Any expression of language that is proven true entirely
on the basis of its meaning expressed in language.
You are gonna need to supply an example.
You would need to have tremendous stature in logic to
be able to dictate a redefinition of a deeply entrenched,
standard term.
Or I could simply prove that I am correct on the
Your intellectual track record shows that you couldn't prove correct
your way out of a wet paper bag.
basis of the meaning of my words, thus anyone
disagreeing is merely proving that they are too
full of themselves.
You are already wrong. The definition of word is neither correct
nor incorrect. It's just accepted or not. A bad definition ahs
some issue like circularty or inconsistency, but if there is no
such problem, then the rest is just a matter of convention.
I'm informing you that there is a convention already which assigns
a meaning to "tautology". It is a semantic concept and therefore
"semantic tautology" isn't readily distinguishable.
On 11/29/2025 2:23 PM, Kaz Kylheku wrote:
On 2025-11-29, olcott <polcott333@gmail.com> 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.
The existing tautology is already semantic. You have to know the
semantics (the truth tables of the logical operators used in the
formula, and the workings of quantifiers and whatnot) to be able to
conclude whether a formula is a tautology.
Try and show how G||del incompleteness can be
specified in a language that can directly encode
self-reference and has its own provability operator
without hiding the actual semantics using G||del numbers.
Pick another word. Since only dimwitted crackpots like yourself will
want to discuss anything using that word, keep the syllable count low
and make sure there aren't too many off-centre vowels.
Ad hominem the first choice of losers.
*Semantic tautology is stipulated to mean*
Reject; call it something else.
Any expression of language that is proven true entirely
on the basis of its meaning expressed in language.
You are gonna need to supply an example.
The key is that a counter-example is categorically
impossible.
You would need to have tremendous stature in logic to
be able to dictate a redefinition of a deeply entrenched,
standard term.
Or I could simply prove that I am correct on the
Your intellectual track record shows that you couldn't prove correct
your way out of a wet paper bag.
Ad hominem the first choice of losers.
basis of the meaning of my words, thus anyone
disagreeing is merely proving that they are too
full of themselves.
You are already wrong. The definition of word is neither correct
nor incorrect. It's just accepted or not. A bad definition ahs
some issue like circularty or inconsistency, but if there is no
such problem, then the rest is just a matter of convention.
There you go, you are getting it now.
circularity, inconsistency, and incoherence.
I'm informing you that there is a convention already which assigns
a meaning to "tautology". It is a semantic concept and therefore
"semantic tautology" isn't readily distinguishable.
On 11/29/2025 2:23 PM, Kaz Kylheku wrote:
On 2025-11-29, olcott <polcott333@gmail.com> 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.
The existing tautology is already semantic. You have to know the
semantics (the truth tables of the logical operators used in the
formula, and the workings of quantifiers and whatnot) to be able to
conclude whether a formula is a tautology.
Try and show how G||del incompleteness can be
specified in a language that can directly encode
self-reference and has its own provability operator
without hiding the actual semantics using G||del numbers.
Pick another word. Since only dimwitted crackpots like yourself will
want to discuss anything using that word, keep the syllable count low
and make sure there aren't too many off-centre vowels.
Ad hominem the first choice of losers.
*Semantic tautology is stipulated to mean*
Reject; call it something else.
Any expression of language that is proven true entirely
on the basis of its meaning expressed in language.
You are gonna need to supply an example.
The key is that a counter-example is categorically
impossible.
You would need to have tremendous stature in logic to
be able to dictate a redefinition of a deeply entrenched,
standard term.
Or I could simply prove that I am correct on the
Your intellectual track record shows that you couldn't prove correct
your way out of a wet paper bag.
Ad hominem the first choice of losers.
You are already wrong. The definition of word is neither correct
nor incorrect. It's just accepted or not. A bad definition ahs
some issue like circularty or inconsistency, but if there is no
such problem, then the rest is just a matter of convention.
There you go, you are getting it now.
circularity, inconsistency, and incoherence.
On 2025-11-29, olcott <polcott333@gmail.com> wrote:
On 11/29/2025 2:23 PM, Kaz Kylheku wrote:
On 2025-11-29, olcott <polcott333@gmail.com> 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.
The existing tautology is already semantic. You have to know the
semantics (the truth tables of the logical operators used in the
formula, and the workings of quantifiers and whatnot) to be able to
conclude whether a formula is a tautology.
Try and show how G||del incompleteness can be
specified in a language that can directly encode
self-reference and has its own provability operator
without hiding the actual semantics using G||del numbers.
The numbers are essential, because G||del Incompleteness is
about number theory.
The G||del Theorem involves a proof in which a certain number,
the "G||del number" that may be called G, is asserted to have
a number-theoretical property.
An example of a number-theoretical property is "25 is a perfect
square". Except we need it in more formal language.
G||del discovered that you can encode statements of number theory as integers, and manipulate them (e.g. do derivation) by arithmetic.
Then it became obvious that whether or not a formula is a theorem
is a property of its G||del number: a number-theoretical property.
There are theorem-numbers and non-theorem-numbrers.
The G||del sentence says somethng like "The G||del number
calculated by the expression G is not a theorem-number."
But G turns out to be the G||del number of that very sentence
itself.
Pick another word. Since only dimwitted crackpots like yourself will
want to discuss anything using that word, keep the syllable count low
and make sure there aren't too many off-centre vowels.
Ad hominem the first choice of losers.
I'm not making an argument; I'm suggesting a way of choosing
an alternative word, since "tautology" is taken.
*Semantic tautology is stipulated to mean*
Reject; call it something else.
Any expression of language that is proven true entirely
on the basis of its meaning expressed in language.
You are gonna need to supply an example.
The key is that a counter-example is categorically
impossible.
So you are saying every expression in a certain language
is proven true, so that its syntax admits no false sentences?
What language is that, and what are examples? What happens
when you try to make a false sentence?
Is it possible to utter conjectures which later turn out false;
and if so, then what happens?
You would need to have tremendous stature in logic to
be able to dictate a redefinition of a deeply entrenched,
standard term.
Or I could simply prove that I am correct on the
Your intellectual track record shows that you couldn't prove correct
your way out of a wet paper bag.
Ad hominem the first choice of losers.
But anyway, your intellectual track record shows that you couldn't prove correct
your way out of a wet paper bag.
This is entirely relevant.
You've never proven anything and never will.
That contradicts your above claim that "I could simply prove ...".
All evidence points to: no, you couldn't.
You are already wrong. The definition of word is neither correct
nor incorrect. It's just accepted or not. A bad definition ahs
some issue like circularty or inconsistency, but if there is no
such problem, then the rest is just a matter of convention.
There you go, you are getting it now.
circularity, inconsistency, and incoherence.
The existing definition of "tautology" doesn't have these issues.
On 11/29/2025 3:39 PM, Kaz Kylheku wrote:
On 2025-11-29, olcott <polcott333@gmail.com> wrote:
On 11/29/2025 2:23 PM, Kaz Kylheku wrote:
On 2025-11-29, olcott <polcott333@gmail.com> 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.
The existing tautology is already semantic. You have to know the
semantics (the truth tables of the logical operators used in the
formula, and the workings of quantifiers and whatnot) to be able to
conclude whether a formula is a tautology.
Try and show how G||del incompleteness can be
specified in a language that can directly encode
self-reference and has its own provability operator
without hiding the actual semantics using G||del numbers.
The numbers are essential, because G||del Incompleteness is
about number theory.
The generalization G||del incompleteness applies to
every formal system that has arithmetic or better.
The G||del Theorem involves a proof in which a certain number,
the "G||del number" that may be called G, is asserted to have
a number-theoretical property.
G := (F re4 G) // G says of itself that it is unprovable in F
An example of a number-theoretical property is "25 is a perfect
square". Except we need it in more formal language.
G||del discovered that you can encode statements of number theory as
integers, and manipulate them (e.g. do derivation) by arithmetic.
That simply abstracts away the underlying semantics.
G is unprovable in F because G is semantically unsound,
We can't see that with G||del numbers.
Then it became obvious that whether or not a formula is a theorem
is a property of its G||del number: a number-theoretical property.
There are theorem-numbers and non-theorem-numbrers.
The G||del sentence says somethng like "The G||del number
calculated by the expression G is not a theorem-number."
But G turns out to be the G||del number of that very sentence
itself.
Pick another word. Since only dimwitted crackpots like yourself will
want to discuss anything using that word, keep the syllable count low
and make sure there aren't too many off-centre vowels.
Ad hominem the first choice of losers.
I'm not making an argument; I'm suggesting a way of choosing
an alternative word, since "tautology" is taken.
*Semantic tautology is stipulated to mean*
Reject; call it something else.
Any expression of language that is proven true entirely
on the basis of its meaning expressed in language.
You are gonna need to supply an example.
The key is that a counter-example is categorically
impossible.
So you are saying every expression in a certain language
is proven true, so that its syntax admits no false sentences?
It syntax admits anything that any human can
say in any language comprised of symbols.
What language is that, and what are examples? What happens
when you try to make a false sentence?
English, Second Order Predicate logic, C++...
Is it possible to utter conjectures which later turn out false;
and if so, then what happens?
Conjectures are not elements of the body of knowledge.
On 2025-11-29, olcott <polcott333@gmail.com> wrote:
On 11/29/2025 3:39 PM, Kaz Kylheku wrote:
On 2025-11-29, olcott <polcott333@gmail.com> wrote:
On 11/29/2025 2:23 PM, Kaz Kylheku wrote:
On 2025-11-29, olcott <polcott333@gmail.com> 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.
The existing tautology is already semantic. You have to know the
semantics (the truth tables of the logical operators used in the
formula, and the workings of quantifiers and whatnot) to be able to
conclude whether a formula is a tautology.
Try and show how G||del incompleteness can be
specified in a language that can directly encode
self-reference and has its own provability operator
without hiding the actual semantics using G||del numbers.
The numbers are essential, because G||del Incompleteness is
about number theory.
The generalization G||del incompleteness applies to
every formal system that has arithmetic or better.
And there you are, trying to take the numbers out of it.
The G||del Theorem involves a proof in which a certain number,
the "G||del number" that may be called G, is asserted to have
a number-theoretical property.
G := (F re4 G) // G says of itself that it is unprovable in F
No, it doesn't; that is an outside interpretation of what it is saying.
G||del's sentence says that a certain number isn't a theorem-number.
Godel proved that such a system can't exist if it can represent the properties of the Natural Number.
On 11/29/2025 1:27 PM, Richard Damon wrote:
[...]
Godel proved that such a system can't exist if it can represent the
properties of the Natural Number.
I hope this can exist. Sorry for any typos with the n-ary tree, n=2
here. Can you notice any errors I missed?-a natural number in the tree
has two unique children. I can derive these children from any natural number. I can get at a child's parent just from its mapped natural. It's 100% full circle.
-a-a-a-a-a 0
-a-a-a-a / \
-a-a-a /-a-a \
-a-a 1-a-a-a-a 2
-a / \-a-a / \
-a3-a-a 4 5-a-a 6
...........
The children of 1 are:
c[0] = 1 * 2 + 1 = 3
c[1] = c[0] + 1-a = 4
Nice! Now, to map back
The parent of 3 is:
p = ceil(3 / 2) - 1 = 1
The parent of 4 is:
p = 4 / 2 - 1 = 1
The parent of 5 is:
p = ceil(5 / 2) - 1 = 2
The parent of 6 is:
p = 6 / 2 - 1 = 2
Notice I do not have to use ceil in the case of 2-ary when the natural number in question is even? Premature optimization? ;^)
It works even with using ceil all the time:
Take the parent of 3 and 4:
p = ceil(3 / 2) - 1 = 1
p = ceil(4 / 2) - 1 = 1
Lets try a parent at zero with its 2-ary children of 1 and 2:
p = ceil(1 / 2) - 1 = 0
p = ceil(2 / 2) - 1 = 0
;^D
I need to adapt it for negative numbers. Think of the following 2-ary tree:
-1-a-a -2
-a \ /
-a-a 0
-a / \
+1-a-a +2
So, lets try it out... The children on the negative side of zero. Flip things wrt +1 becomes -1:
c[0] = 0 * 2 - 1 = -1
c[1] = c[0] - 1-a = -2
Well, that works! Let's get the parent of -2, and flip the sign on the
-1 to +1, should be zero: Also, lets flip ceil to floor:
p = floor(-2 / 2) + 1 = 0
Nice, lets try -1:
p = floor(-1 / 2) + 1 = 0
It works... Interesting to me.
Lets try -3, its parent should be -1:
p = floor(-3 / 2) + 1 = -1
Also, -4's parent should be -1:
p = floor(-4 / 2) + 1 = -1
Nice!
-5 and -6 should both have a parent of -2:
p = floor(-5 / 2) + 1 = -2
p = floor(-6 / 2) + 1 = -2
perfect.
On 11/29/2025 4:44 PM, Kaz Kylheku wrote:
On 2025-11-29, olcott <polcott333@gmail.com> wrote:
On 11/29/2025 3:39 PM, Kaz Kylheku wrote:
On 2025-11-29, olcott <polcott333@gmail.com> wrote:
On 11/29/2025 2:23 PM, Kaz Kylheku wrote:
On 2025-11-29, olcott <polcott333@gmail.com> 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.
The existing tautology is already semantic. You have to know the
semantics (the truth tables of the logical operators used in the
formula, and the workings of quantifiers and whatnot) to be able to >>>>>> conclude whether a formula is a tautology.
Try and show how G||del incompleteness can be
specified in a language that can directly encode
self-reference and has its own provability operator
without hiding the actual semantics using G||del numbers.
The numbers are essential, because G||del Incompleteness is
about number theory.
The generalization G||del incompleteness applies to
every formal system that has arithmetic or better.
And there you are, trying to take the numbers out of it.
The G||del Theorem involves a proof in which a certain number,
the "G||del number" that may be called G, is asserted to have
a number-theoretical property.
G := (F re4 G) // G says of itself that it is unprovable in F
No, it doesn't; that is an outside interpretation of what it is saying.
That is EXACTLY what the above expression says.
G||del's sentence says that a certain number isn't a theorem-number.
Which he says is merely his enormously convoluted way of saying this
...We are therefore confronted with a proposition which asserts its own unprovability. 15 rCa (G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
If you think that I am wrong then don't fucking guess
show exactly what his sentence actually says without
the ruse of G||del numbers in a language has its own
self-reference operator and provability operator.
I say it says this:
G := (F re4 G) // G says of itself that it is unprovable in F
On 11/29/25 6:53 PM, Chris M. Thomasson wrote:
On 11/29/2025 1:27 PM, Richard Damon wrote:
[...]
Godel proved that such a system can't exist if it can represent the
properties of the Natural Number.
So, where do you have a "provability operator" that will tell you if a
given theory is in fact provable.
That is what he showed can't exist.
The problem is that there are an infinite number of possible proofs to
see if any of them reach the desired statement.
You can CHECK if a proof is validly proving the statement, but not
determine if there exist such a proof, as the negative result requires infinite work.
On 11/29/2025 4:17 PM, Richard Damon wrote:
On 11/29/25 6:53 PM, Chris M. Thomasson wrote:
On 11/29/2025 1:27 PM, Richard Damon wrote:
[...]
Godel proved that such a system can't exist if it can represent the
properties of the Natural Number.
So, where do you have a "provability operator" that will tell you if a
given theory is in fact provable.
Nope. That is not possible. Think of the integer 0. I can prove that it
has, wrt n-ary, n positive children, and n negative children. For
example, 2-ary, two (+) and two (-). Say n is a natural number:
-1-a-a-a-a -2
-a \-a-a /
-a-a \ /
-a (-0+) = the root of all? ;^)
-a-a / \
-a /-a-a \
+1-a-a-a-a +2
But that is just for this n-ary case. I cannot just magically
extrapolate it our to some programming logic for some random program.
That is what he showed can't exist.
The problem is that there are an infinite number of possible proofs to
see if any of them reach the desired statement.
You can CHECK if a proof is validly proving the statement, but not
determine if there exist such a proof, as the negative result requires
infinite work.
On 11/29/25 7:35 PM, Chris M. Thomasson wrote:
On 11/29/2025 4:17 PM, Richard Damon wrote:
On 11/29/25 6:53 PM, Chris M. Thomasson wrote:
On 11/29/2025 1:27 PM, Richard Damon wrote:
[...]
Godel proved that such a system can't exist if it can represent the >>>>> properties of the Natural Number.
So, where do you have a "provability operator" that will tell you if
a given theory is in fact provable.
Nope. That is not possible. Think of the integer 0. I can prove that
it has, wrt n-ary, n positive children, and n negative children. For
example, 2-ary, two (+) and two (-). Say n is a natural number:
And that was the pre-condition Olcott made of his logic system, that it
have a provability operator.
Just like you can build a Halt Decider if you assume you have a correct
halt decider (and ignore that it make the system inconsistant).
-1-a-a-a-a -2
-a-a \-a-a /
-a-a-a \ /
-a-a (-0+) = the root of all? ;^)
-a-a-a / \
-a-a /-a-a \
+1-a-a-a-a +2
But that is just for this n-ary case. I cannot just magically
extrapolate it our to some programming logic for some random program.
That is what he showed can't exist.
The problem is that there are an infinite number of possible proofs
to see if any of them reach the desired statement.
You can CHECK if a proof is validly proving the statement, but not
determine if there exist such a proof, as the negative result
requires infinite work.
On 11/29/25 7:35 PM, Chris M. Thomasson wrote:[...]
On 11/29/2025 4:17 PM, Richard Damon wrote:
On 11/29/25 6:53 PM, Chris M. Thomasson wrote:
On 11/29/2025 1:27 PM, Richard Damon wrote:
[...]
Godel proved that such a system can't exist if it can represent the >>>>> properties of the Natural Number.
So, where do you have a "provability operator" that will tell you if
a given theory is in fact provable.
Nope. That is not possible. Think of the integer 0. I can prove that
it has, wrt n-ary, n positive children, and n negative children. For
example, 2-ary, two (+) and two (-). Say n is a natural number:
And that was the pre-condition Olcott made of his logic system, that it
have a provability operator.
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".
On 29/11/2025 18:19, dbush wrote:
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".
I think not. I think it's an analytic framework for language. I expect
it's standard. I never got told of it at university but, knowing what I
know now, its description sounds like it's just a way of saying "I do
formal analysis of language continua via something resembling
factorisation" because, well, what else would a semantic tautology be?
Frankly I think Olcott is careful to say only definitely true things and
he is already aware that lambda calculus has been used for language
analysis for a very long time. He ought to be informed that
computational linguists know about it, what it can do, how to use it to analyse, how to form tautologies wrt. relations between strings and
models, etc.
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.
Try and show how G||del incompleteness can be
specified in a language that can directly encode
self-reference and has its own provability operator
without hiding the actual semantics using G||del numbers.
On 29/11/2025 20:51, olcott wrote:
Try and show how G||del incompleteness can be
specified in a language that can directly encode
self-reference and has its own provability operator
without hiding the actual semantics using G||del numbers.
An outline how I'd go about this kind of thing (not complete by far, and
also not checked properly, though I have thought about it a bit). I've
done this about Olcott's paraphrasing of Goedel's outline in PM rather
than the challenge stated above because Goedel's system P is weird and I don't trust it at all. IMPORTANT! Goedels outline and Olcott's
paraphrase use a self-referential definition rather than universal quantification! I'll have to cogitate more to waffle about that.
Note, it involves a formal system /extension/ rather than an /episystem/
and that's how we may interpret the challenge to do our task "in [the] language".
Thinking about it a touch more carefully than before, assuming Olcott
very carefully formulated his G definition (I think F is nothing to do
with Goedel's system P, but is more akin to a modernisation of PM which goedel used for his similar outline). Note I have this time interpreted
F to refer to a basic system rather than the definition extension that I previously supposed. This way we have a few points in the space of
systems to reason more clearly with.
You have to take this all with a pinch of salt, we're using ":=" and it
will take some formalisation which I'm not doing (and so will |/-).
Then consider Olcott's paraphrasing
G := (F |/- G)
The above must be an axiom of a definition extension I'll call "I" that
also adjoins G and I to the objects of F and we'll assume we've already formalised extension within F. I'll call the resulting extended system
"I(F)" and suppose that's the form by which statements in F may name a
system "F" extended by I.
In that case I(F) is consistent: G is not derived of F.
We'd have a problem if I use a definition extension "J" that adjoins, instead, objects G and J and an axiom
G := (J(F) |/- G).
"J(F)" names what I assumed Olcott had meant "F" to name previously. I kind-of-conjecture that J(F) is contradictory because it seems obvious
that we can derive both |- G and |/- G which is how we'll recognise contradiction. I hesitate to use the term "inconsistent" because I don't trust the concept having found "indiscriminate" to be satisfactory and
more general for simpler systems.
Having drawn a very faint line on a block of stone before spending eons carving and polishing and looking up to see what it took to do so
little, it is obvious why Olcott has not been swayed by the
conversations in these newsgroups.
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
If you think that I am wrong then don't fucking guess
show exactly what his sentence actually says without
the ruse of G||del numbers in a language has its own
self-reference operator and provability operator.
I say it says this:
G := (F re4 G) // G says of itself that it is unprovable in F
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
On 29/11/2025 23:19, olcott wrote:
G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
Do you have a reference to the original and also English translation of
his 1938 paper "On Formally Undecidable Propositions of Principia
Mathematica And Related Systems II"?
^^
His 1931 paper says he'll followup with a completed proof and
generalisation to more systems - so I think that's what we have to look
at to understand what people refer to as his first incompleteness proof
and theorem. I've been told (albeit by a chatbot) that the title and
year above is what I should look for.
If you think that I am wrong then don't fucking guess
show exactly what his sentence actually says without
the ruse of G||del numbers in a language has its own
self-reference operator and provability operator.
You've gone off the deep end there.
I say it says this:
G := (F re4 G) // G says of itself that it is unprovable in F
It says that G is not a theorem of F, and perhaps it does so
epitheoretically because of the use of ":=" which often nominates a substitution to apply to get an object of F, and that would /almost/ trivially make it true, albeit not for all possible F.
"[fact] in [a system]" conventionally can mean [fact] for all definition extensions of [a system] when mathematicians are talking because they
add definitions when using the system and examine the consequences "/in/
the system". The prepositions are ambiguous across specialisms, clearly.
There are some more ambiguities so reflecting and responding usefully on Olcott's expression is difficult and nondeterministic.
The problem is that there are an infinite number of possible proofs to
see if any of them reach the desired statement.
You can CHECK if a proof is validly proving the statement, but not
determine if there exist such a proof, as the negative result requires infinite work.
On 01/12/2025 11:02, 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
If we're using it in its normal epitheoretic meaning. I think Olcott is
using it as a predicative object of a logistic F so it requires a
formula on the right? That's not unreasonable since we take
A |- B
as a shorthand for
|-A => |-B
leaving us with "B is a formula" to which the unary predicate |- may be applied to make a statement.
It's the epitheoretic "=>" that takes a statement on the right, but
clearly it's more complex because systems and lists of statements can be
used on the left. Olcott's use of |- as a predicative object of F is
clearly awkwardly ambiguous, as tempting as it may be.
The extra awkward thing here is that F is capable of using |- in its own formulae, making its (normal) use as a unary predicate redundant and
perhaps obstructive leaving us with a system whose statements are
exactly its formulas unless we have a unary predicative with no visible elements, if it's not nonsense for any other reasons.
I wonder if that may not be done for some reason. There are lots of
reasons to be concerned about it.
- the value of the re4 operation is a truth value
/Should/ we take re4 to be an operation here? or just a predicative object
of F?
- the symbol := requires the same type on both sides
Unless it's an operation (as in, an action to be done to generate sentences/formulas of the system being analysed). When G is an
epitheoretic object rather than an object of a definition extension of F
then I think it /must/ be such an operation.
On 30/11/2025 00:17, Richard Damon wrote:
The problem is that there are an infinite number of possible proofs to
see if any of them reach the desired statement.
You can CHECK if a proof is validly proving the statement, but not
determine if there exist such a proof, as the negative result requires
infinite work.
The infinite number of possible proofs isn't the reason why because you
are allowed induction in preference to enumeration.
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)
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".
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
that G is no provable in F, and the same truth
value is given to G in the expression G := (F re4 G). The
Prolog term not(provable(F, G)) does not have a truth value.
After G = not(provable(F, G)) the value of G is that data
structure, so it has no truth value, unlike the G in
G := (F re4 G).
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.
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.
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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