Specification of the requirements of a counter-example for my refutation of Tarski

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PeteOlcott
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Specification of the requirements of a counter-example for my refutation of Tarski

Post by PeteOlcott »

We define the set of [computable knowledge]:
(possibly identical to the set of analytical knowledge)
(a) All the knowledge that can be fully expressed as relations between expressions of language.

(b) These relations between expression of language can be represented as relations between finite strings.

(c) Truth is defined as the satisfaction of these relations.
In such a system True(P) := Satisfied(P) := Provable(P)

There are two fundamental building blocks to this system:

(1) Expressions of language are stipulated to be true.≅ AXIOMS

(2) Relations between expressions of language stipulated to be truth preserving. ≅ rules-of-inference: Valid deduction expressed as relations between finite strings.

All of the above seems self-evidently correct. The key missing pieces is the expressive power of such a system.

If the above system can encode the full set of analytical knowledge then Tarski and Gödel are proven to be incorrect because every expression of language that is not provable is only not provable because it is not true.

THIS IS THE CRUX (the only way to prove me wrong)
What counter example of analytical knowledge can be provided of that cannot be expressed as relations between expressions of language?


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