On 2023-12-17 02:23:12 +0000, olcott said:
*This is true by definition* Within the body of analytical truth of the analytic/synthetic distinction every element of the body of analytic knowledge (BOAK) is true entirely on the basis of its connection to the semantic meanings that make it true.
This proves that Gödel's 1931 Incompleteness and Tarski's Undefinability Theorem cannot apply to the body of analytical knowledge (BOAK). Lacking
this connection excludes an expression from the BOAK, thus undecidable expressions cannot exist within the BOAK.
True(x) is defined by the above, within the BOAK thus refuting Tarski.
Every element of the BOAK has a provability connection to its semantic meanings truthmaker within the BOAK thus refuting both Tarski and Gödel
that say this cannot correctly and consistently accomplished.
Tarski and Gödel don't claim that the arithmetic of natural numbers
is a part of BOAK as defined above. Therefore your argument does not
apply.
There are known sentences that could be, as far as is known, provable,
but are not proven. They are well formed sentences as their syntactic correctness is provable (and faily easy to prove).
If Gödel or Tarski could be refuted the way to do that wold be to
construct an algorithm that determines whether a string is a true
or false or meaningless (the last option for strings that are not
syntactically correct sentences). You can't construct such algorithm
so you can't refute Gödel or Tarski.
Mikko
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