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Topic: How can NO LOGICIAN follow this argument??
Replies: 13   Last Post: Mar 5, 2013 11:06 AM

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Graham Cooper

Posts: 4,495
Registered: 5/20/10
How can NO LOGICIAN follow this argument??
Posted: Mar 3, 2013 12:43 AM
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Look for the phrase CONSTRUCT-A-SENTENCE

> Fix a coding for arithmetic, that is, a way to associate a unique
> natural number with each statement of arithmetic. In terms of this
> coding, a truth predicate Tr(x) is a formula with the following
> property: For any statement S in the language of arithmetic,
> Tr(#S) <-> S
> holds (where #S means the natural number coding the sentence S).
> If Tr(x) is a formula of arithmetic, then using techniques
> developed by Godel, we can construct a sentence L such that
> L <-> ~Tr(#L)
> Goedel *explicitly* constructed a formula P and showed
> that both (1) and (2) were true of P.


"We can construct a formula"
"We can construct *ANY* formula"

T |- any formula

ex contradictione sequitur quodlibet
from a contradiction, anything follows


Godel and Tarski proofs were PRE AXIOMATIC SET THEORY!

TOM: You can't agree with this!
BETTY: That's right!
PAMMY: I don't agree!


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