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On 2025-10-05 14:09:37 +0000, olcott said:
On 10/5/2025 5:26 AM, Mikko wrote:
On 2025-10-04 13:30:22 +0000, olcott said:
On 10/4/2025 5:11 AM, Mikko wrote:
On 2025-10-02 10:15:13 +0000, olcott said:
On 10/2/2025 5:03 AM, Mikko wrote:
On 2025-10-01 16:33:46 +0000, olcott said:
On 10/1/2025 5:13 AM, Mikko wrote:
On 2025-10-01 01:48:56 +0000, olcott said:
On 9/30/2025 7:54 AM, Mikko wrote:
On 2025-09-29 12:24:30 +0000, olcott said:
On 9/27/2025 5:07 AM, Mikko wrote:
Any sentence that is neither true nor false
must be rejected from any system of logic.
Non-truth bearers in logic systems are like
turds in birthday cakes.
Every sentence of logic that is not tautology or
dontradiction is
true in some contexts and false in others.
A mere false assumption
No, it is true on the basis of the meanings of the words.
The syntax of formal logical languages allows
some expressions to be created having pathological
self-reference(Olcott 2004).
No syntax is enough for self-reference.
Syntax is enough for self-reference.
No, self-reference is a semantic feature. A string without meaning
does not refer.
Self-reference can be detected in a string with a name.
Tarski's Liar Paradox from page 248
-a-a-a It would then be possible to reconstruct the antinomy of the liar >>>>>> -a-a-a in the metalanguage, by forming in the language itself a sentence >>>>>> -a-a-a x such that the sentence of the metalanguage which is correlated >>>>>> -a-a-a with x asserts that x is not a true sentence.
-a-a-a https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ree True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
The semantics determines whether
any syntactic construct is a self-reference. For example. the
arithmetic
semantics of a formal language of arithmetics do not permit a self- >>>>>>> reference.
G||del uses tricks for that.
Tarski used the same tricks.
Yet they only actually boil down to
Incomplete(F) rao reaG ((F re4 G) reo (F re4 -4G)).
and this
LP := ~True(LP)
The system they considered has no symbol for :=. Instead, they construct >>> something like LP <-> ~True(LP). G||del then shows that that the
expression
that asserts its own unprovability is is not provable and therefore
true.
Claude AI eventually agreed that both G||del's 1931
Incompleteness theorem and the Tarski Undefinability
theorem are anchored in liar paradox like expression
that should have been rejected as not a truth bearer.
G||del proved that every sentence of a first order theory that is not
the negation of any sentnece of that theory is true in some model of
that theory. Therefore every sentence of every first order theory is
a truth-bearer.
As long as you don't understand that "The liar's paradox is not true"
is true and therefore a valid basis for a proof you cannot say anything
about Tarski's proof but are stuck to straw men.
On 2025-10-09 13:25:56 +0000, olcott said:
On 10/9/2025 6:12 AM, Mikko wrote:
On 2025-10-09 03:10:56 +0000, olcott said:
I have posited that it has always been a huge
mistake that semantics was divided away from
the syntax of every formal logic system since
the syllogism. It is the root cause of the
divergence of logic from correct reasoning.
Logic has been shown to be useful. Your "correct reasoning" has not
been.
Because no one knows about it.
Much about it has been known for as long time as anyone can remember.
Instances of "correct reasoning" and "incorrect reasoning" have been identified and many these identifications have been justified. But it
is true that what you call "correct reasoning" is different from what
others have called so and is indeed not known or asked about.
Therefore there is a good reason to believe that the separation of the
meaning from the form was a good idea.
There are all kinds of errors that are simply
invisible when semantics and rules of inference
are separated.
There are errors that are invisible until someone sees them. In particular, people tend to be blind to their own errors. Therefore it is useful that proofs can be checked without special knowledge.