[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 
about elucidating.

>NAIVE formal systems are NOT more real than NAIVE numbers.

O.K., then I agree that I misunderstood you as saying that naive
formal systems *are* more real than naive numbers.  Now that that 
misunderstanding is cleared up, I have no argument with you.

Tim Chow

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