[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

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