[FOM] Truth and Consistency
Neil Tennant
neilt at mercutio.cohums.ohio-state.edu
Mon Jun 2 10:18:56 EDT 2003
On Sun, 1 Jun 2003, Lucas Wiman wrote:
> While I agree that [the fact that ZFC has been amply tested by
> "mathematical experience"---Parsons] is a good reason to keep using ZFC,
> I don't think that this tells us that ZFC is consistent. This tells us
> that if ZFC has any inconsistencies, then they are probably extremely
> non-obvious. They might have been missed by mathematicians and set
> theorists for so long because they're extremely weird or long or
> something like that. This is thus a contingent fact about human
> psychology.
Surely it would not be a contingent fact about human psychology if it
turned out to be the case that the shortest proof of an inconsistency in
ZF is extremely long? Wouldn't it be a mathematical fact?
> I am uncertain whether
[Dummett's criticism of Field's inductivist justification of the
consistency of ZF]
> is correct; we have no non-inductive
> verification of the facts of physics, yet they are generally considered
> inductively verified. If we take Popper's falsification view, then
> clearly it's quite reasonable to conjecture that ZF is consistent since
> so little disproof exists of it, though accepting it as a verified fact
> may be too strong.
Did Popper ever intend his falsificationist view of empirical theorizing
to apply also to such claims as that ZF is consistent?
Neil Tennant
More information about the FOM
mailing list