Re: what makes it true?

Timothy Little wrote:
Torkel Franzen wrote: 
 All models (of PA or some other theory, not of "the natural
numbers") are of course equally real. What does this have to do with
the observation - which is a simple mathematical theorem - that if
GC is undecidable in PA (or in the much weaker theory Q), it is
true?

I may be mistaken, but isn't it a theorem that an undecidable
proposition has both models where it is true and models where it is
false?  Why do you accept only the models in which it is true?


In this context, the word 'true' is understood (or is supposed
to be understood) to mean 'true in the standard model'---you know,
the set of objects that PA is supposed to be enabling you to
reason about. The point is that PA fails to enable you to
prove all the true statements about those objects.
.

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