## 2 thoughts on “Potentialism and implicit actualism in the foundations of mathematics, Jowett Society lecture, Oxford, February 2019”

1. Very nice slide presentation. I do have a question regarding a set-theoretic potentialist’s view of $V$, the universe of all sets and its relation to the Kunen Inconsistency in $ZFC$. As is known, what Kunen proved in his paper, “Elementary embeddings and Infinitary Combinatorics”, is the following, for $j$: $V$ $\rightarrow$ $M$, assuming $AC$:

$\mathscr P$($\lambda$) $nsubseteq$ $M$

where $\lambda$ = { $j^n$($\kappa$): $n$ $\lt$ $\omega$}.

My question is simply this: If, for a set-theoretic potentialist, $V$ is the limit structure of all models of $ZFC$ (and it would seem that it would be, given your comments in the slide presentation regarding the limit structure), does the Kunen Inconsistency prove the set-theoretic potentialist’s point of view (since, according to what is written on the slide presentation, “the actual limit structure does not exist”) ?