Re: Torkel Franzén is dead


Aatu Koskensilta wrote:
The Gödel sentence of a theory T is also
self-referential in a specific and clear sense; a Gödel sentence makes
an assertion about a particular natural number, and that natural number
is the code of the sentence itself.

SEZ WHO?
You cannot force any particular godel-numbering
to "be" "real".
PA, as a first-order language, or even as a first-order theory,
does NOT have ANY "preferred" models. ALL interpretations,
INCLUDING ones in which numbers get interpreted as OTHER
formulas, are valid. There is a sense in which the proof of
Godel's Theorem REQUIRES us to be thinking about the
standard model, DESPITE the fact that there is nothing going
on (in the first-order presentation) that can distinguish it.

.

Relevant Pages

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