A legacy post originally published on November 8, 2007 at 12:58 PM
🔗 Existence is a Predicate by Alexander Pruss
Let ‘w‘ refer to any world. Then “exists in” expresses a perfectly fine relation between entities and worlds. Let S be the set of worlds in which history ends in 30 BC. Then, there are some members w of S such that Aristotle exists in w, but for every member w of S it is the case that Charlemagne does not exist in w (assuming essentiality of approximate time of conception). Thus, for any given w, some entities are related by “existing in” to w and some are not. Call this relation “E”.
Now, we can define two “exists” predicates. Let ‘@’ rigidly refer to our world. Then, we can say “x exists” provided xE(the actual world) and that “x exists*” provided xE@. For any relation term R and any referring term t, “___Rt” is a predicate. So “exists” and “exists*” are predicates.
Interesting post! Can the actual world be said to exist on this model? If so, what sense of “exists” would we be using?
Hey Josh, thanks for the interesting question. As I understand Pruss’ argument, we can define “exists” in terms of world-membership and actuality. And in Pruss’ previous work, he characterizes the actual world as being “the aggregate of all actually existing things.” He adds that, “If one is fine with arbitrary mereological sums, one can take that aggregate to be a mereological sum […] If one is worried about the existence of this mereological sum, one should be able to paraphrase talk of the cosmos, universe, and other aggregates, into plurally quantified talk.” So, worlds are aggregates of their constituents.
Thanks, yes, that seems plausible. I guess I’m wondering about the specific proposal in the blog post, though: namely, that we can explicate “exists” as a relation between entities and worlds. How do we paraphrase the English sentence “The actual world exists”? Surely not by saying that the actual world bears the relation of “existing in” (E) the actual world. Right? Seems like we would have to paraphrase it differently, perhaps as “the actual world is identical to the actual world.” And that’s true, of course, but it doesn’t seem to be what we mean in English when we say that the actual world exists. Self-identity is not existence.
I think the Kantian-inclined among us will push and say that the relevant sense of “exists”–the one that isn’t a predicate–is being smuggled in here in the difference between actual and possible worlds in the first place. Once you have that difference, then sure, you can talk about world membership, etc. But without explicating the difference between actual and possible worlds, we haven’t yet confronted Kant.
Sorry for the rambling–thanks again for the thoughts.