Ehhhh…..as Kripke says, guy writes a book on something, another guy writes a book on how wrong the first guy was. Been that way since Day One. You and I, operating under the auspices of basic logical laws, reject the accordance of contingency with identity, but if somebody comes along and tweaks this definition, or fiddles with that perspective, he can obfuscate the established laws accordingly, and posit something nobody’s ever thought of before.
If you and I are going to get along with the pure analyticalists, we have to concede that when Kripke says, “ for any two objects x and y, if x is identical to y….”, it is more the case x is congruent to y rather than x being identical to y. Pretty simple, really; x is x and therefore not-y. Two objects having common properties is not the same as two objects being identical.
As for the category mistake, here’s my agreement with it:
“For every property F…..” F can be any property, such that if F belongs to x, and if x is identical to y then it is necessary that F belong to y. If F is the property of being round, and if x is round and y is identical to x, then y is round. That’s fine, in that x is,
e.g., a round cue ball and y is,
e.g., an identically round baseball. Which is also fine, insofar as the conditional is “for any two objects”, satisfied by one cue ball and one baseball.
It remains that a cue ball is not a baseball. But if x is to stand as identical to y, one of every property F is obviously not sufficient to cause x to be identical to y because of F. So keep adding F’s to x, maybe hundreds of F’s, such that when those properties also belong to y, they become closer and closer to both x and y being either a cue ball or a baseball. Still satisfies “for any two objects”, as well as for any property F which belongs to x also belongs to y.
The kicker: “For every property F….”, in order for the cue ball x and the baseball y to be identical, every property F must belong to both equally. It follows that in order for x to be identical to y, a space F belonging to x is the same space F belonging to y, and x and y simultaneously be commonly imbued with every other possible F equally. But two objects sharing the same space F is a contradiction, which negates the case. It must be, then, that they occupy different space F’s but still be commonly imbued with every other F equally. How does that happen, you ask….surely with bated breath. Well…..the space of x in one world, and the space of y in another world. What else?????
Hence contingent identity, contingent on the possibility of other worlds. Under the assumption of another merely possible world, however, such world can only have possible space, from which follows only a possible y can have the property of possible space, or, more correctly, only a possible y can occupy a possible space possibly, which reduces to a real x being identical to a possible y, which is not the original argument. In effect, then, in order to assume x = y identity necessarily, mandates a veritable maze of contingent possibilities.
And that’s a category mistake. Dunno if it’s yours or not, but it works, doesn’t it? The article goes on to circumvent these mistakes, re: “let us use necessity weakly”, or actually, to deny them altogether, re: “I will not go into this particular form of subtlety** here because it isn’t relevant”, in order to justify the notions contained further on in it.
But still, if a theory starts out illogically, and if the circumventions are not all that valid, wouldn’t it jeopardize the whole? Kripke is just saying, if it was this way, we could say this about it. But if it couldn’t be this way, why still talk as if it could? He goes on to talk about it in a different way, that’s all.
(** existence as a predicate, reflecting on existence in possible worlds)