[FOM] Deflationism and the Godel phenomena

[Timothy Y. Chow]

On Fri, 18 Feb 2005, Jeffrey Ketland wrote:
> (3) I will not accept 0=1
[...]
> (A: Self-Consistency)
> Possibly: A reasoner may assume his own (arithmetic) consistency
> (as in (3) above).

I think there is quite a large difference between unwillingness to assert 
0=1 and assuming one's own arithmetic consistency.  The latter seems to 
presuppose something like, "The arithmetic sentences I'm willing to assert 
form a sufficiently precise structure that they can be modeled as a 
logical theory."  This is implausible.  The things I'm willing to assert, 
for example, are not closed under logical consequence; prior to seeing a 
proof of (say) the prime number theorem, I was willing to assert all the 
relevant axioms but I wasn't willing to assert the prime number theorem, 
even though the prime number theorem is (and always has been) a logical 
consequence of those axioms.

Tim