Abstract
A recent position in the foundations of mathematics borrows its terminology from physics, namely the Multiverse View. This position states that there is not one universe containing all the sets, but rather many. At first glance, it looks like this view doesn't share so much with the view in physics beyond somehow involving talk of multiple universes. For a start, the set-theoretic multiverse (realistically understood) is composed of mathematical abstracta, whereas the physical multiverse contains many concreta.
In this talk, I want to explore the extent to which this idea is more than a mere similarity of catchy terminology. In particular, I'll suggest that an important motivation of each is fine-tuning; the idea that if there was just one universe, then it would be (seemingly without good grounds!) set up with very precise anthropocentric constraints. I'll use these observations to explore what each view can learn from the other and whether there are common pitfalls to be mindful of.