[FOM] Improving set theory

[Paul Blain Levy]

Dear Harvey,
> Date: Thu, 9 Jan 2020 13:10:02 -0500
> From: Harvey Friedman <hmflogic at gmail.com>
> To: Foundations of Mathematics <fom at cs.nyu.edu>
> Subject: [FOM] Improving Set Theory
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> ZFC has become the standard foundation for mathematics since about
> 1920. Alternatives have been proposed but not widely endorsed at least
> not yet.
You are right.  We critics of ZFC have work to do.
> I am particularly interested in what people think is lacking or is
> flawed about ZFC.
Nothing is lacking.  ZFC is not too weak but too strong.  The problem is 
that its language allows quantification over the entire totality of 
sets.  In my view (and others have said the same), that totality does 
not exist, so the language is not really meaningful.

Paul