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Tarski Undefinability Theorem refuted (step-by-step)
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peteolcott
2018-11-08 03:04:41 UTC
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Pages 275-276 are the heart of Tarski's 1936 Undefinability Theorem proof:
http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf

Direct quote from page 275
We can construct a sentence x which satisfies the following condition:
It is not true that x ∈ Pr if and only if p

(1) x ∉ Pr ↔ p
Where the symbol 'p' represents the whole sentence x.

In other words:
p ∉ Pr ↔ p

In other words:
p ∉ Provable ↔ p

In other words:
p ↔ ~Provable(p)

Copyright 2018 Pete Olcott
peteolcott
2018-11-08 04:18:41 UTC
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Post by peteolcott
http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
Direct quote from page 275
It is not true that x ∈ Pr if and only if p
(1) x ∉ Pr ↔ p
Where the symbol 'p' represents the whole sentence x.
p ∉ Pr ↔ p
p ∉ Provable ↔ p
p ↔ ~Provable(p)
Copyright 2018 Pete Olcott
Does anyone here have more than a dogmatic belief in the following?

Page 273
A. For every formalized language a formally correct and materially
adequate definition of true sentence can be constructed in the
metalanguage with the help only of general logical expressions, of
expressions of the language itself, and of terms from the morphology
of language – but under the condition that the metalanguage possesses
a higher order than the language which is the object of investigation.
B. If the order of the metalanguage is at most equal to that of the
language itself, such a definition cannot be constructed.

I propose that any reasoning that attempts to show the above referenced
Truth predicate cannot be implemented directly in the object language is
incorrect. If anyone knows this material well enough to try to show that
the metalanguage / object language distinction is required I will point
out their error.
Franz Gnaedinger
2018-11-08 08:16:59 UTC
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Post by peteolcott
Copyright 2018 Pete Olcott
Peter Olcott knows the absolute and complete and total truth, he is the author
of life and creator of life, he has hundred reasons to believe that he is God,
he creates our future minds in order that we can go on existing, he is a human
being and God in personal union, he is the one Creator of the Universe (claims
he made in sci.lang) while he can't even write a modest but useful language
program.

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