Countless have asked, but Gabriel Uzquiano sought to answer: How many angels can dance on the point of a needle?
The question asks not what is the case, but rather what can be the case. Some philosophers take what can be the case to be the same as what is the case in alternate universes, which they call possible worlds. For them, the actual world is only one of a plurality of concrete universes.
The angels-on-the-head-of-a-pin question is often used to parody medieval scholastics, but it turns out to pose a problem for that view.
“When you combine various tools from logic and set theory with a certain picture of modality, you find yourself in trouble,” Uzquiano said. “You have to say that there is some infinite cardinal number — although you know not which — so that there can be that many angels, but there cannot be any more than that many angels.”
A recent paper he coauthored in Mind, a tongue-in-cheek discussion of Thomas Aquinas, the 13th-century Italian philosopher and theologian, leads to a predicament for modal metaphysicists who believe the possible existence of angels boils down to the existence of merely possible angels in alternate universes.
Uzquiano likes to approach his research and teaching in new ways.
“I think what makes my research distinctive is the way in which I use formal methods in my approach to certain problems in metaphysics.”
And how many angels can dance on the point of a needle?
According to Uzquiano, no matter how large an infinite cardinal number may be, there can be at least that many angels.