[FOM] Semantical realism without ontological realism in mathematics

[praatika@mappi.helsinki.fi]

Lainaus Bill Taylor <W.Taylor at math.canterbury.ac.nz>:

> -> platonist about mathematical objects but nevertheless deny 
> -> that they have any properties
> -> other than those we are capable of recognizing,
> 
> I presume this means "capable of recognizing fairly quickly". 

Certainly not! it only means "capable of recognizing in principle"

> OC if he means...
>   "capable of recognizing EVER, by means we may not even know about
> yet",
>                   ...then this is so vague as to be virtually useless.

I am actually inclined to agree, it is unclear, but nevertheless the two 
realisms are arguably independent. 


> So these views are close to being incoherent, IMHO.

I am not convinced of that...


> But having said that, I must also admit that all this debate
> (including mine) is "mere" philosophical arguments, so has very little, 
>(no?), significance.  This "mereness" is given away by the observation 
> that, whichever side we come down on, it will have NO EFFECT on our 
> mathematics, thus is all a non-issue.
> 
> But please tell me where I'm wrong.

I would have thought that the choice between intuitionistic and classical 
mathematics has some effect to our mathematics...

Best

Panu


Panu Raatikainen

PhD., Docent in Theoretical Philosophy
Fellow, Helsinki Collegium for Advanced Studies
University of Helsinki
 
Address: 
Helsinki Collegium for Advanced Studies
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E-mail: panu.raatikainen at helsinki.fi
 
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