I was given a photocopy of an article: "In Defense of Alain Badiou" by Robert Michael Ruehl, published in Philosophy Now. The article is behind a paywall, but here's the idea that caught my attention:
Against more traditional evaluations of it, Badiou argues that ontology is not an area of philosophical specialization: he argues that mathematicians specialize in ontological thought without knowing so, and philosophers are left to explain the radical implications of the mathematicians' thinking.
The article goes on to describe arguments that Badiou makes about what set theory shows about the world (e.g. "there is no transcendent unity to the world.")
I didn't know that this was... allowed, to extract information about the world from a formal system in this way.
Further reading (Wikipedia) reveals that Badiou has been criticized by some mathematicians and others who say he misuses set theory.
If I'm going to read "Being and Event", where Badiou first (?) makes his set theory arguments, I would be interested to know about other philosophers who have made similar kinds of arguments, or any other contextual information that might be relevant to evaluating this kind of argument in general.
[EDITED to get rid of a paywalled link and to add words]