Cross-World Identity and Counterpart Theory

Core Idea

Cross-world identity principles specify which objects in different possible worlds are the same object. Approaches include essentialist principles (identity preserves essential properties), counterpart theory (objects related by similarity without strict identity), and direct identity (identity is primitive across worlds). These choices fundamentally affect modal semantics and metaphysics.

How It's Best Learned

Compare theories' handling of modal intuitions about identity: must an object have all its actual properties in every world where it exists? Can an object be different in essential ways across worlds while remaining identical?

Common Misconceptions

Assuming direct identity across worlds is obviously correct without argument. Thinking the debate is purely semantic rather than substantive for modal metaphysics and the metaphysics of modality.

Explainer

You know from possible-worlds semantics that modal claims—claims about what could or must be the case—are analyzed in terms of possible worlds: "possibly P" is true if P holds at some possible world, "necessarily P" if P holds at every world. And from modal realism you know that David Lewis treats possible worlds as genuine, concrete spatiotemporal realities comparable to our own. Once you accept a plurality of concrete worlds, a new question immediately arises: when we say "this very chair could have been red instead of green," are we saying something about *this exact chair* existing in another world with different properties, or about a *different but similar* chair in that world? This is the problem of cross-world identity.

The most intuitive view is direct identity: objects literally exist in multiple possible worlds, and when we say Nixon could have lost the election, we are talking about Nixon himself—the very same individual—in a world where the election went differently. This view requires that objects be trans-world individuals, numerically identical across distinct worlds. The problem is that Leibniz's Law (if A and B are identical, they share all properties) seems to threaten this: Nixon has the property *actually winning the 1968 election* and also the property *possibly losing the 1968 election*. These look like contradictory properties unless we are very careful about how to characterize them (typically by relativizing properties to worlds: Nixon has *winning at the actual world* and *losing at some other world*, which don't conflict).

David Lewis rejected direct identity in favor of counterpart theory. On his view, no individual exists in more than one possible world; all objects are world-bound. When we say Nixon could have lost, we are not saying Nixon himself exists in another world and loses there—we are saying that Nixon has a counterpart in some other world who loses. A counterpart is an individual in another world who resembles the actual individual sufficiently closely in the relevant respects. What counts as "relevant respects" is context-sensitive: in a modal context about political careers, political similarity matters; in a context about physical constitution, physical similarity matters. Counterpart theory has the advantage of keeping objects metaphysically tidy (each exists only once, in one world) at the cost of treating modal claims as covertly relational—what is possible for you depends on the facts about your counterparts elsewhere.

The choice between direct identity and counterpart theory has downstream effects on how you analyze de re modal claims—claims about what a specific individual could or must be. "Aristotle could have been a carpenter" means different things on the two theories: for direct identity, Aristotle-himself exists in some world as a carpenter; for counterpart theory, some sufficiently similar individual is a carpenter in some world. The theories also differ on essential properties: if direct identity is right, the essential properties of an object are those it has in every world where it exists. Counterpart theory redefines essence in terms of what all counterparts share. This matters for debates about whether material constitution or origin is essential to an object—the question of whether you could have had different parents, or been made of different matter, gets different traction depending on which framework you use.