experchange > comp.theory

peteolcott (05-23-19, 05:42 PM)
Sound deductive inference necessitates true conclusions
therefore sound deductive inference applied to formal
proofs of mathematical logic necessitates true consequences.


Tautology, in logic, a statement so framed that it cannot
be denied without inconsistency.

In other words it is a tautology that sound deduction would
partition the exhaustively complete set of finite strings
(or expressions of language) into True(x) and ¬True(x).

Since the Tarski Undefinability Theorem essentially concluded
that this cannot be done, Tarski is refuted by the above tautology.
peteolcott (05-23-19, 05:46 PM)
On 5/23/2019 10:42 AM, peteolcott wrote:
[..]
> (or expressions of language) into True(x) and ¬True(x).
> Since the Tarski Undefinability Theorem essentially concluded
> that this cannot be done, Tarski is refuted by the above tautology.


When we specify that True(x) is the consequences of the subset
of the of conventional formal proofs of mathematical logic having
true premises then True(x) is always defined and never undefinable.
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