The Universe (matthias)

Josef Urban josef.urban at
Mon Jul 13 05:32:53 EDT 2020

I guess very direct examples like the existence of Dedekind-infinite sets
are somehow (implicitly?) excluded?

I.e.: exists A, B st B is a proper subset of A & A,B are equipotent .

(I haven't read the paper)

On Mon, Jul 13, 2020 at 1:24 AM Timothy Y. Chow <tchow at>

> Oystein Linnebo wrote:
> >
> > In a recent paper, "Actual and potential infinity" (Nous 2018),
> >, Stewart
> > Shapiro and I take issue with the skeptical attitude illustrated by
> > Niebergall (as Adrian Mathias reminds us). Using the resources of modal
> > logic, we show how to articulate a clear and interesting distinction
> > between actual and potential infinity, which can be applied both to
> > arithmetical and set-theoretic potentialism.
> I found a draft version here---
> ---and skimmed it.  Here's a question.  Suppose Alice believes in actual
> infinity but Paul believes only in potential infinity.  Is there an
> example of a mathematical statement that both Alice and Paul regard as
> meaningful but that only Alice can prove, because the proof relies in an
> essential way on the assumption that an actual infinity exists?
> Tim
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