[FOM] First-order arithmetical truth
mario
chiari.hm at flashnet.it
Mon Oct 30 13:50:20 EST 2006
Tim,
On Mon, 2006-10-16 at 18:16 -0400, Timothy Y. Chow wrote:
> Francis Davey wrote:
...
> You misunderstand Arnon Avron's point. Goedel's theorems are about formal
> systems. But what is a formal system? How can I tell the "intended"
> formal systems (the ones that deal with proofs of "finite" length, in a
> certain "intended" sense of the word "finite") from the unintended formal
> systems whose proofs are "finite" only in an "unintended" sense of the
> word "finite"?
>
> If [1] you lack the ability to distinguish the intended model of PA from
> another model, it would seem that [3] you also lack the ability to distinguish
> the intended meaning of the term "formal system" from some other meaning.
1. Do you argue for [1]->[3] above along the following (one line longer)
sketch:
if (1) somebody lacks the ability to distinguish the intended model
of PA from another model,
then (2) (s)he lacks the ability to distinguish the intended model of
meta-PM from another model,
then (3) (s)he lacks the ability to distinguish the intended meaning of
the term "formal system" from some other meaning.
Say meta-PM is any theory which is sufficient to axiomatize
metamathematical results about Principia Mathematica and/or ZFC.
2. How do you argue for (2)->(3)?
thanks
mario
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