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.
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
Alex,
Suppose you think that the domain of existing things includes all actual things and all possible things, as Lewis seems to have done. In that case, regarding non-actual objects, you might hold that they exist simpliciter, and not just possibly exist (and certainly not actually exist). Neither predicate seems appropriate in this case.
Alex,
Could you also comment on this problem:
A J Ayer claimed that, if ‘existing’ and ‘non-existent’ are predicates then all existential propositions are tautologies and all negative existential propositions are self-contradictory. This view is based on the assumption that a thing must exist for anything to be predicated of it. It could be asserted that there is no reason to make this assumption. On that basis, the particular quantifier need not have existential import. However, the rejection of Ayer’s (Russell's, Quine's) assumption leads to the problem that there is no principled reason that non-existent things should not have their identities along with their properties. Once this is allowed then pandora’s box is opened. For example, some thing a exists and some thing c exists. a is not (numerically or merely qualitatively) identical to c. Some thing b is identical to a and to c. Not surprisingly, b does not exist. Yet, because both a and c are identical to b, by the transitivity of identity, a is identical to c. So, a is both identical to and not identical to c. Examples can then be multiplied so that all ontological contradictions of the kind relating to identity and non-identity are entailed. That is, everything is identical to everything else.
Hi Alex,
So here's an argument that 'exists' isn't a predicate. Replace what you say about "exists in" with "is a member of". Then we can express all the same ideas without a predicate for existence. If something’s wrong with this argument then I think there's a problem with the original.
Dear Ted:
Are you assuming here that worlds are sets of entities or something like that?
Anyway, supposing we can show that we can define "exists" in terms of world-membership and actuality, I do not see how that shows "exists" is not a predicate. It only shows that "exists" is not a primitive predicate.
Alex,
I just meant to show that you do all the work that 'exists in' does with 'is a member of' and an actuality operator, which I took to be more sympathetic to the Russell-Quine view of 'exists' than the predicate view.
Alex,
I'm a bit worried because I'm not sure exactly what thesis you're defending in your post. I take it that you want to defend something like the thesis that the English word "exists" expresses a property.
(Personally, I don't think that this thesis should be described as the thesis that existence is a predicate (or that "exists" is a predicate, for that matter), since it is not a thesis concerning the syntactic features of existence (or "exists") and I take it that to say that something is a predicate is to describe its features. However, I understand that philosophers have often described the thesis that "exists" expresses a property in this way, and that it has become common to do so. So I won't press you on this relatively minor point.)
So, is that the thesis that you wished to defend? If so, then it doesn't seem to me that your remarks constitute much of a defense of it. What you have shown is that we can define two predicates, "exists" and "exists*", in terms of the binary predicate "exists in". Now these two binary predicates, I agree, express (relational) properties. But, so far as I can tell, you have not provided any argument for the claim that the English word "exists" is to be defined in one of these ways.
That seems about right. Perhaps we can also make use of essences and define existence in that "x exists if and only if given some Platonic essence y, x exemplifies y." We can, as you do, utilize possible world semantics.