Counterpart Theory - Counterpart Theory and The Necessity of Identity

Counterpart Theory and The Necessity of Identity

Kripke's three lectures on proper names and identity, (1980), raised the issues of how we should interpret statements about identity. Take the statement that the Evening Star is identical to the Morning Star. Both are the planet Venus. This seems to be an a posteriori identity statement. We discover that the names designate the same thing. The traditional view, since Kant, has been that statements or propositions that are necessarily true are a priori. But in the end of the sixties Saul Kripke and Ruth Barcan Marcus offered proof for the necessary truth of identity statements. Here is the Kripkes version (Kripke 1971):

(1) ∀x (x = x)

(2) ∀x∀y

(3) ∀x∀y

(4) ∀x∀y

If the proof is correct the distinction between the a priori/a posteriori and necessary/contingent becomes less clear. The same applies if identity statements are necessarily true anyway. (For some interesting comments on the proof, see Lowe 2002.) The statement that for instance “Water is identical to H₂O” is (then) a statement that is necessarily true but a posteriori. If CT is the correct account of modal properties we still can keep the intuition that identity statements are contingent and a priori because counterpart theory understands the modal operator in a different way than standard modal logic.

The relationship between CT and essentialism is of interest. (Essentialism, the necessity of identity, and rigid designators form an important troika of mutual interdependence.) According to David Lewis, claims about an object's essential properties can be true or false depending on context (in Chapter 4.5 in 1986 he calls against constancy, because an absolute conception of essences is constant over the logical space of possibilities). He writes:

But if I ask how things would be if Saul Kripke had come from no sperm and egg but had been brought by a stork, that makes equally good sense. I create a context that makes my question make sense, and to do so it has to be a context that makes origins not be essential. (Lewis 1986:252.)