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.)
Read more about this topic: Counterpart Theory
Famous quotes containing the words counterpart, theory, necessity and/or identity:
“The rushing Pequod, freighted with savages, laden with fire, and burning a corpse, and plunging into that blackness of darkness, seemed the material counterpart of her monomaniac commander’s soul.”
—Herman Melville (1819–1891)
“No theory is good unless it permits, not rest, but the greatest work. No theory is good except on condition that one use it to go on beyond.”
—André Gide (1869–1951)
“With my desire to write he seemed in full sympathy, and in urging our early marriage he argued that my first necessity was leisure in which to develop and to master my craft. It appeared to me that with such a man as teacher and guide I could not fail, and it was in a queer mixture of young love and vaulting ambition that I became a wife.”
—Rheta Childe Dorr (1866–1948)
“Adultery is the vice of equivocation.
It is not marriage but a mockery of it, a merging that mixes love and dread together like jackstraws. There is no understanding of contentment in adultery.... You belong to each other in what together you’ve made of a third identity that almost immediately cancels your own. There is a law in art that proves it. Two colors are proven complimentary only when forming that most desolate of all colors—neutral gray.”
—Alexander Theroux (b. 1940)