[FOM] "Mathematician in the street" on AC

Bob Clark rc514 at york.ac.uk
Tue Aug 18 04:45:08 EDT 2009

Timothy Y. Chow wrote:
> When doing math, as opposed to when they have their guard up in a 
> conversation that is perceived to be philosophical,

I wonder how this distinction between truth when doing maths and when 
philosophising about maths relates to Carnap's internal/external 
distinction (eg in 'Empiricism, semantics and ontology'), and/or to 
Wittgenstein's 'two kinds of responsibility' maths has (eg LFM xxv) that 
give us, according to him, a view of 'the reality to which mathematics, 
in a sense, does correspond'.

Does anyone but me think there's still philosophical mileage in these 
dichotomies? I know John Burgess used a tentative version of the Carnap 
one to attack mathematical fictionalism a couple of years ago, and I 
know George Boolos described the internal/external thing as 'rubbish'. 
Anything else?


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