Parts of Classes

by David Kellogg Lewis

Does the notion of part and whole have any application to classes? Lewis argues that it does, and that the smallest parts of any class are its one-membered "singleton" subclasses. That results in a reconception of set theory. The set-theoretical making of one out of many is just the composition of one whole out of many parts. But first, one singleton must be made out of its one member - this is the distinctively set-theoretical primitive operation. Thus set theory is entangled, with mereology: the theory of parts and wholes.

Genres: Philosophy, Logic, Mathematics

155 pages, Paperback

First published December 1, 1990

About the author

David Kellogg Lewis was a 20th century philosopher. Lewis taught briefly at UCLA and then at Princeton from 1970 until his death. He is also closely associated with Australia, whose philosophical community he visited almost annually for more than thirty years. He has made ground-breaking contributions in philosophy of language, philosophy of mind, metaphysics, epistemology, and philosophical logic. He is probably best known for his controversial modal realist stance: that there exist infinitely many concretely existing and causally isolated parallel universes, of which ours is just one, and which play the role of possible worlds in the analysis of necessity and possibility.

-wikipedia

Reviews

[J.]

To me, a weird, frustrating book. And that's about all I want to say.

[Axel Barceló · Rating 3 out of 5]

As usual, Lewis is very insightful, but stubborn. He believes that not everything is a set and thus his theory cannot account for the relation between sets and not sets in a non0mereological way. But this was to be expected. Instead, we should accept that there are nothign but sets, i.e., that the difference between an object and its singleton is metaphysically illusory.