[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
>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.
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