Discussion:
Refuting Incompleteness and Undefinability Version(17)
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peteolcott
2018-11-08 05:52:34 UTC
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I will keep the exact same naming convention and stick to the
general subject of this name. I provide a new Version number.
In this thread I switch from the 1931 GIT to Tarski 1936,
the Undefinability aspect of the name of this thread.

Does anyone here have more than a dogmatic belief in the following?
Can anyone provide the details of the reasoning proving that it
is necessary?

The best way for me to prove that it is not necessary is to provide
a correct rebuttal to any proof that it is necessary. I can do that
with reasoning, I cannot do that with dogma.

The Concept of Truth in Formalized Languages, Tarski 1936
The the Tarski Undefinability Theorem in is postscript on pages 268-278
http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf

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.
peteolcott
2018-11-08 05:56:00 UTC
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Post by peteolcott
I will keep the exact same naming convention and stick to the
general subject of this name. I provide a new Version number.
In this thread I switch from the 1931 GIT to Tarski 1936,
the Undefinability aspect of the name of this thread.
Does anyone here have more than a dogmatic belief in the following?
Can anyone provide the details of the reasoning proving that it
is necessary?
The best way for me to prove that it is not necessary is to provide
a correct rebuttal to any proof that it is necessary. I can do that
with reasoning, I cannot do that with dogma.
The Concept of Truth in Formalized Languages, Tarski 1936
The the Tarski Undefinability Theorem in is postscript on pages 268-278
http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
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.
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

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