[FOM] CH and platonism

[Arnon Avron]

Already the identity of PN is not absolute, and depends 
on the identity of the universe of sets, to say nothing 
about PPN. So although formally there is a difference between
third-degree platonism and stronger forms of platonism,
I do not see the essential big difference. 

   An informative question: do smallists (to adopt your name)
stop at PPN, and if so - why there, and not, say, at PPPPN?

Arnon

On Fri, Oct 28, 2016 at 07:38:02PM +0100, Paul B Levy wrote:
> 
> 
> > Date: Thu, 27 Oct 2016 22:54:53 +0300
> > From: aa at tau.ac.il (Arnon Avron)
> > To: Foundations of Mathematics <fom at cs.nyu.edu>
> > Cc: Arnon Avron <aa at tau.ac.il>
> > Subject: Re: [FOM] 729: Consistency of Mathematics/1
> > Message-ID: <20161027195453.GB10352 at localhost.localdomain>
> > Content-Type: text/plain; charset=us-ascii
> 
> > 3. Is the continuum hypothesis true or false? 
> > 
> >  This question presumes platonic views about an absolute, unique
> > universe of "sets". 
> 
> No, CH is a statement of third-order arithmetic.  It doesn't quantify
> over the universe of sets.  GCH, on the other hand, does.  For
> smallists, who take a platonic view of PPN (powerset of powerset of the
> naturals) but not of the universe of sets, this is a big difference.
> 
> Paul
> 
> 
> 
> -- 
> Paul Blain Levy
> School of Computer Science, University of Birmingham
> http://www.cs.bham.ac.uk/~pbl
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