Wolfgang Schwarz

What is Counterpart Theory?

Well, I know what Counterpart Theory is not: it is not a theory according to which ordinary things do not really exist at other possible worlds.

There are two readings of "ordinary things do not exist at other worlds". The first is a neutral reading on which things exist at another world in the way they sleep at another world or win elections at another world: whatever possible worlds are, they somehow represent things as existing and sleeping and winning. In this sense, something exists at a world iff the world represents it as existing. Anyone who accepts possible worlds talk at all accepts that ordinary things exist at other worlds in this sense.

On the second reading, existing at a world means being a mereological part of the world. On this reading, almost everybody rejects the claim that ordinary things exist at other possible worlds. Lewis rejects it because he rejects overlapping worlds. Others reject it because they conceive of worlds as abstract entities, sets of sentences or propositions perhaps, and ordinary material things are not parts of such entities. (Even if the sentences are Lagadonian, they do not contain ordinary objects as parts, unless, oddly, the Lagadonian sentences are construed mereologically rather than set-theoretically. Similarly for worlds understood as propositions or properties or states of affairs.)

So on one reading, everyone accepts that things exist at other worlds, and on the other reading, (almost) everyone denies it. So this does not distinguish proponents of Counterpart Theory from their opponents.

Here is another suggestion. Counterpart Theory says what it means for things to exist at another world in the first sense, and generally, what it means for them to be such-and-such at another world. Roughly,

something x has property P at world w iff w contains (as a part) something y which sufficiently resembles x and has P.

The problem with this suggestion is that it entails (extreme) Modal Realism, which is supposed to be far stronger than Counterpart Theory. Philosophers like Stalnaker, Hazen, Heller and Sider reject Modal Realism, but accept Counterpart Theory. Here is a weaker version (still rough):

x has P at w iff at w, there is something y which sufficiently resembles x and has P.

The right-hand side contains the de dicto clause "at w, there is a y which has P". Modal Realism holds that this is true iff w has a part that has P, but now we leave its interpretation open. It may instead be true because w is a set of sentences that entails "something has P", or because w is an abstract state of affairs such that if w were actual, something would have P.

However, the right-hand side also contains "x" which is bound by the hidden quantifier at the very beginning, so the proposal looks somewhat circular as an analysis of de re modality. More importantly, y should not be compared with how x is at w, but with how x is at our world. The counterpart relation is a cross-world similarity relation, not an intra-world similarity relation. So:

x has P at w iff at w, there is something y which sufficiently resembles how x actually is.

Unfortunately, some ersatzists appear to lack the ressources for cross-world comparisons. How does Plantinga, for example, interpret "there are worlds w1, w2 such that something at w1 is greater than anything at w2"? I don't know. Perhaps as "there is a level of greatness G such that if w1 were actual, something with greatness G would exist, whereas if w2 were actual, everything's greatness would be below G"? Along these lines, the previous proposal could perhaps be understood as follows:

x has P at w iff there is a property Q such that being Q means (or entails) resembling x and at w, there is something y which has both P and Q.

That looks ugly. Perhaps there is a better solution. At any rate, cross-world comparisons seem intuitive enough, and are needed even for the interpretation of ordinary modal sentences, so I assume that all parties can somehow understand them.

The current proposal is still very rough: it applies for suitable P only, and one should probably add that nothing at w ought to resemble x more closely than y. A more serious problem is that the proposal is very weak, in particular if resemblance is not tied to off-hand, intuitive judgments of overall similarity. And Lewis says it must not: the relevant kind of similarity can be mainly similarity in origin, or similarity in satisfying some theoretical role.

We should add, however, that the relevant kind of similarity is qualitative similarity. Then at least one family of theories is clearly ruled out: haecceitism. More precisely, it is ruled out that there are qualitatively identical worlds w1 and w2 such that for some qualitative property P, x has P at w1 but not at w2.

But isn't Counterpart Theory more than the negation of haecceitism? We might add that the relevant similarity relation is not a function: that there can be ties in similarity. But I don't see how a relation of qualitative similarity could possibly rule out ties. (Think of worlds of eternal recurrence.) So this is not a real addition. We might add that the relevant kind of similarity relation is not transitive. This would rule out e.g. that all and only perfect intrinsic duplicates count as similar. But should such counterpart relations be ruled out? Lewis says we should not stipulate that the counterpart relation is transitive, but he doesn't stipulate that it is not.

The greatest advantage of Counterpart Theory is of course that it allows for vagueness and context-dependence of modal properties. So perhaps we should add this to the characterization of Counterpart Theory. That would definitely rule out some conceptions of possible worlds, like Modal Realism with Overlap and some versions of linguistic ersatzism where names of actual things are contained in other worlds.

On the other hand, the vagueness and context-dependence seems to be a welcome possibility offered by Counterpart Theory, not an essential part of the theory itself.

Perhaps accepting Counterpart Theory is best characterized as accepting a theory of modality that a) allows for cross-world comparisons of individuals, b) rejects (a certain kind of) haecceitism, and c) would not require great modification to allow for vagueness and context-dependence of modal properties.