[FOM] Paradoxes and Platonism

[Vladimir Sazonov]

> 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). 
Vladimir Sazonov