[FOM] Paradoxes and Platonism
vladimir.sazonov at yahoo.com
Tue May 20 08:29:50 EDT 2008
> From: laureano luna laureanoluna at yahoo.es
> So, on what not ad hoc, not a posteriori, grounds could I reject R
[Russel's paradoxical set - VS]? How could it
> be ill-defined? How could it not exist?
> Have set theoretic paradoxes ever been regarded as simply disproving Platonism?
Why to expect at all that our fantasies would behave in an objective way?
Of course, we can impose formal tools such as formal logic and axioms
on these fantasies, and then we will observe objective behaviour of these
"mechanical" tools (giving rise to illusions on an objective character
of our fantasies). These tools can be somewhat coherent with our subjective
ideas, but subjective ideas still remain subjective, and there is no hope
to have a complete coherence. (Again, coherence with what? with something
subjective? Thus no hope even on the meaningfulness of the "complete
coherence"! Thus any kind of paradoxes and incompleteness phenomena are
fully expectable!) Also our subjective ideas and dreams can remind (or be
induced from) something from our real world (and formal tools can help
in applying these ideas to the real world through formal imitating the
latter and using algorithms), but again, this does not make them genuinely
objective. However, it is indeed miraculously fruitful the interplay between
subjective and objective (or between subjective and subjective in the pure
mathematics) through mathematical formalisms, and this is another way to say
what is the essence of mathematics (and what is the formalist view on mathematics).
More information about the FOM