[FOM] 729: Consistency of Mathematics/1

[Paul B Levy]

> 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