Timothy Y. Chow tchow at alum.mit.edu
Thu Jun 6 13:49:57 EDT 2013

On Wed, 5 Jun 2013, Joe Shipman wrote:
> It's not a pointless semantic debate if we care about which statements 
> of arithmetic are "true". SOL will not only guarantee the meaningfulness 
> of statements of arithmetic, it will recognize a distinction between 
> Con(PA) which is a consequence of logical validities and can be thought 
> of as unqualifiedly "true", and Con(Z) which is a consequence of set 
> existence axioms that are not part of "logic".
> The question of "justifying the axioms" then goes away for most math 
> because logic comes "for free".

It's hard for me to imagine that this line of argumentation---i.e., X is 
true because X is logic and logic is true---would convince many people 
today when it comes to, say, X = Con(PA).  There's such a widespread 
feeling that logical truth is what you get by syntactic manipulation that 
you'd be fighting an uphill battle to convince people that Con(PA) is 
logically true.


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