# [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

```