[FOM] MacLane

praatika@mappi.helsinki.fi praatika at mappi.helsinki.fi
Wed May 20 01:22:47 EDT 2009

"Bas Spitters" <b.spitters at cs.ru.nl>:

> Second, that "apprehension" of sets is pretty
> obscure, since abstract sets are not apprehended by our usual senses.

This is, of course, a reasonable worry. However, one should not  
exaggerate the difference with intuitionism here. The latter is based  
on rather abstract notion of proof (or, more generally, of  
construction) which cannot be captured by any formalized system (and  
worse: the axiomhood is nowhere in the arithmetical hierarchy (if you  
accept these notions as intelligible); but in any case: no finitary  
representation is sufficient). I think it is fair to wonder just how  
well we apprehend such a notion of proof...

All the Best, Panu

Panu Raatikainen

Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy

Department of Philosophy
University of Helsinki

E-mail: panu.raatikainen at helsinki.fi


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