# [FOM] First-order arithmetical truth

Timothy Y. Chow tchow at alum.mit.edu
Sat Oct 28 16:09:13 EDT 2006

```Vladimir Sazonov wrote:
>> However, I believe that I've said all I can say on the original topic
>> (namely, the point that Arnon Avron was trying to make to Francis
>> Davey).  You and I also appear to be in agreement on that point.
>
>I understand that style of reasoning and can follow it, but cannot
>agree with it because it is based on a vicious circle inherent to any
>reasoning based on a belief.

This remark of yours baffles me.  As I understand it, there are four
kinds of things that you think are relevant to this discussion:

Naive numbers     |  Naive formal systems
--------------------+---------------------------
Abstract numbers  |  Abstract formal systems

As far as I could tell, Francis Davey was implicitly driving a wedge
between the left and the right, thinking that formal systems are clear
whereas numbers aren't.  I, along with Arnon Avron I think, was trying to
show that one can freely pass between left and right, and any skepticism
on one side translates directly to skepticism on the other.

I thought you agreed with this.  You're telling me now that you don't?

I understand that you insist on driving a wedge between the top and the
bottom.  While I don't agree with all your views on this, I don't care to
argue the point, and will grant you that wedge if you want it.  It seems
to me to be orthogonal to the left-right wedge, which is what I care more