The Universe (matthias)

[Timothy Y. Chow]

Oystein Linnebo wrote:
>
> In a recent paper, "Actual and potential infinity" (Nous 2018), 
> https://onlinelibrary.wiley.com/doi/abs/10.1111/nous.12208, 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---

https://www.duo.uio.no/handle/10852/59120

---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