Questions: Cross-World Identity and Counterpart Theory

Question 1

On Lewis's counterpart theory, when we say 'Aristotle could have been a carpenter,' what are we actually saying?

• A. Aristotle himself exists in some possible world where he chose to become a carpenter instead of a philosopher
• B. There is a possible world containing an individual sufficiently similar to Aristotle who is a carpenter
• C. In all possible worlds, Aristotle has the potential to have been a carpenter
• D. The actual Aristotle has the hidden dispositional property of being a possible carpenter

Answer: (B)

On Lewis's counterpart theory, all objects are world-bound — no individual exists in more than one world. When we say Aristotle could have been a carpenter, we are not saying Aristotle himself exists elsewhere as a carpenter. Instead, we are saying some other-world individual who resembles Aristotle sufficiently closely (in the relevant respects) is a carpenter. The 'could have been' is not about Aristotle-in-another-world but about Aristotle's counterpart in another world. This is a substantive metaphysical difference: what is possible for Aristotle depends on the facts about how similar other-world individuals are to him.

Question 2

Direct identity theory faces a challenge from Leibniz's Law. What is that challenge?

• A. If Nixon is identical across worlds, he must share all properties in all worlds — but he has 'winning in the actual world' and 'losing in some other world,' which seem to conflict
• B. Leibniz's Law implies that any two possible worlds containing 'Nixon' must contain numerically identical objects, making counterpart theory impossible
• C. Two objects can only be identical if they exist at the same spatiotemporal location, so trans-world identity is geometrically impossible
• D. Leibniz's Law implies all identical objects are indiscernible, but possible worlds clearly differ from each other, so nothing can be shared

Answer: (A)

Leibniz's Law states that if A = B, then A and B share all properties. If Nixon is the same individual across worlds, he seems to have both 'winning the 1968 election' (true at the actual world) and 'losing the 1968 election' (true at some other world) — which look contradictory. The standard response is to relativize properties to worlds: Nixon has 'winning at α' and 'losing at w,' which don't conflict. But counterpart theorists see this relativization as problematic, and prefer to simply deny that Nixon exists at multiple worlds at all.

Question 3

On Lewis's counterpart theory, the same individual object can exist in multiple possible worlds simultaneously.

• T. True
• F. False

Answer: False

Counterpart theory holds precisely the opposite: all objects are world-bound, existing in exactly one possible world. This is a defining feature that distinguishes counterpart theory from direct identity theory. When we make modal claims about an individual, counterpart theory analyzes them in terms of other-world individuals who resemble the actual individual sufficiently closely. No individual 'travels' between worlds — only counterpart relations hold between world-bound individuals.

Question 4

The choice between direct identity and counterpart theory has substantive consequences for what essential properties an object has.

• T. True
• F. False

Answer: True

On direct identity theory, an object's essential properties are those it has in every world where it exists. On counterpart theory, essence is defined in terms of what all counterparts share. These analyses can diverge: whether you could have had different parents, or been made of different matter, may receive different verdicts depending on which framework is used, because the counterpart relation is context-sensitive and can be defined in terms of different respects of similarity. The theories are not merely terminological variants.

Question 5

Why does counterpart theory make modal claims 'covertly relational,' and what does this mean for the objectivity of claims like 'I could have been taller'?

Model answer: On counterpart theory, 'I could have been taller' means there exists a world containing an individual sufficiently similar to me who is taller. What counts as 'sufficiently similar' depends on context — which respects of similarity are salient. In a context emphasizing physical constitution, physical similarity dominates; in one emphasizing psychological continuity, mental properties dominate. The modal claim is therefore relational: true relative to one contextually specified counterpart relation, potentially false relative to another. This makes de re modal claims partly context-dependent rather than objective facts about the individual simpliciter.

This is one of the main costs of counterpart theory that critics press. Direct identity theory makes 'I could have been taller' simply a claim about whether I myself exist at some world where I am taller — a fact about me and the worlds. Counterpart theory replaces this with a claim about other-world individuals and a context-sensitive similarity relation. Whether a given modal claim is true can shift with conversational context, which some find implausible. Lewis accepted this consequence; he argued that the context-sensitivity is a feature of our modal talk, not a defect of the theory.