[FOM] Paradoxes and Platonism
laureanoluna at yahoo.es
Mon May 19 11:14:47 EDT 2008
It is often said that set theoretic paradoxes show that Platonism is incompatible with naive comprehension (e.g. Antonelli 'Conceptions and
Paradoxes of Sets', Philosophia Mathematica 7, 2, 136-163). If we choose to keep naive comprehension, we cannot have the realm of sets given as an objective reality once for all, and vice versa.
But suppose we take the set theoretic universe as an objective and intemporally given reality so that, for instance, it is an objective fact for any set S whether S is in S. Then if I define a set R s.t. for any set S, S is in R iff S is not in S, I'm defining R only by reference to objective facts: for any set S it should be a fact either that S is in R or that it isn't.
So, on what not ad hoc, not a posteriori, grounds could I reject R? How could it be ill-defined? How could it not exist?
Have set theoretic paradoxes ever been regarded as simply disproving Platonism?
Comments, references and links welcome.
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