[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
Finland
E-mail: panu.raatikainen at helsinki.fi
http://www.mv.helsinki.fi/home/praatika/
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