David Lewis famously proposed that counterpart theory can substitute quantified modal logic. He argued that instead of formalising modal discourse using modal operators we can stick with first-order predicate logic with identity so long as we introduce talk of counterparts existing in possible worlds. To say that I could have been a plumber is to say that I have a counterpart in a possible world that is a plumber. This counterpart of mine is in his own world and I am in this world. No individual exists in more than one world.

Lewis first proposed counterpart¬†theory in ‘Counterpart Theory and Quantified Modal Logic’ (Journal of Philosophy, 1968). Fred Feldman, a few years later, published ‘Counterparts’ (Journal of Philosophy, 1971) wherein he argues that counterpart theory has serious difficulties with such¬†sentences as:

(1) I could have been quite unlike what I in fact am.
(2) I could have been more like what you in fact are than like what I in fact am, and at the same time, you could have been more like what I in fact am than like what you in fact are.

The difficulties that Feldman identifies turn on Lewis accepting the following theses:

(A) If you have a counterpart in another world, then it is the entity in that world which resembles you most closely.
(B) If an entity in another world is “quite unlike” you, then it is not your counterpart.

The final criticism that Feldman raises is that counterpart theory entails the substantive doctrine that there are no essential attributes, whereas it should be neutral on such an issue.

In this letter, written after Feldman published ‘Counterparts’, Lewis replies to all three objections. (¬© Estate of David K. Lewis.)