Each and every property of a particular must be understood as essential to that particular, that's what makes a particular a unique individual, distinct from every other particular. This is what the law of identity recognizes. — Metaphysician Undercover
So now we're back to
@Isaac's teapot and the missing screw. In that discussion, the question was only about successfully referring to a particular that (might or) might not possess a property you believe (or don't believe) it does. I think it's plain that you can; for some cases, I'm leaning on the causal theory of names, and for others on how demonstratives work: you can clearly demand someone get "that" off your kitchen table even when you know very little about what "that" is. Exactly how that works may be unclear; that it works, I believe, is not. (We may come back to the double-bind theory of reference eventually.)
Here, we might start with the question of whether "being on my kitchen table" is a property of the object in question. It can be expressed as a predicate, as I've just done, but we could just as well express the situation as my kitchen table having the property of "having that on it," assuming again that "that" will manage to refer to the object. Or we could define a two-place predicate "on" such that "on" is true of an ordered pair <that, my kitchen table>. For either of the one-place predicates (of that, or of the table), I would be asking you to make something that is true of one of them false; for the two-place predicate, I would be asking you to make something that is true of the two of them false.
There are a couple ways to take that: I described "on" as a relation not just of two objects but of two objects in a particular order, so that on(table, thing) was already false, but on(thing, table) was true and I want it to be false. on(table, thing) and on(thing, table) describe different states of the world; in this case, the demand to make whichever is true false needn't concern itself with the order, because context will take care of that. But if I asked you to
put that thing on the table, my demand would not be satisfied by you putting the table on that thing. So if we want on/2 to carry the same meaning across different uses, we can't rely on context in that way, and have to build in the required order. How do we do that?
Do we say that "on" takes three objects, the two from before and a third that specifies the order? If so, the third would look something like this: "1 = thing, 2 = table". Such a list can be presented in any order, so we don't have a regress, only a rule about each natural number up to the arity of the predicate being used, so this is a genuine option. But our new on/3 takes two concrete objects and a third which, whatever it is, is not like that. I say "whatever it is," because the semantics of the ordering list are unclear at this point: are those objects in the list, or expressions referring to objects? I guess either would do, but we're still building in a lot of other stuff, some of which looks suspiciously abstract, so we could just give in and have "on" take a single abstract object which is the ordered pair <thing, table>.
If we do that, my asking you to get that thing off my kitchen table would be asking you to make "on" false of the ordered pair <thing, table>. No properties of the concrete objects will change when you do so. We've added a step, so that "on" is not true of the concrete objects themselves, but of an ordered pair of the objects, which is a bit of a surprise. I'm not sure how much that should count against the scheme.
Can we do something similar with other cases? For instance, if my bike tire is flat, is it a different object once it's inflated, or is it just a different arrangement of tire and air, the tire itself never changing? (In this case, we may or may not have any specific batch of air in mind.) But then what would we say about the shape of the tire, that surely changes when it's inflated? If anything is a property of an object, surely its shape is. But I make different shapes when I sit and when I stand — does that make me a different person? What all of these examples have in common is that there are at least two different times considered: the tire is never flat and inflated at the same time, I am never sitting and standing at the same time, and so on. So a first attempt at distinguishing what is essential to an object from what is accidental is, naturally, distinguishing what is constant or invariant about it, what does not change from one time to another, and what does or can change from one time to another. Essential is what is time-
less, and accidental is what is time-dependent. The same dog barks at one time and not at another.
But Isaac's screw-missing teapot raises a batch of familiar problems: evidently material constitution is not a great candidate for the timeless identity of an object. If we replace the missing screw with another of the same size, we have the Teapot of Theseus: is it the same teapot after as before the installation of the new screw? (It's considerations like this, if memory serves, that drove Peter van Inwagen to conclude that inanimate objects lack identity altogether, and thus do not, strictly speaking, exist.) One solution offered, in a sort of conventionalist spirit, is that this is all a collective fiction: there are no things with identities that we come along afterward and refer to; rather, our various acts of reference, intended and accepted by us as such, and our deeming these acts successful, is all there really is here. Thus, the slight oddity of Russell's account of definite descriptions — that they involves implicit existence claims — is vindicated, because indeed we are asking others to accept , at least for the duration of this exchange, what amounts to a
stipulation that there is a dog when we say "the dog is barking."
The conventionalist account doesn't automatically undermine a distinction between essential and accidental properties, of course; you could take it as simply falsifying all claims of essence, or you could conversely take essence as whatever we tacitly agree it is. We generally count me as being the same person sitting or standing, and since that's all there is, that's enough.
But there's an odd wrinkle to all this. If I, like Isaac's teapot, do have an identity, then a proper semantics of me would require everyone to speak of me as if I do, and we would expect the corpus of attempted references to me to roughly, and only roughly, follow this requirement. That means the conventionalist will argue that our broad agreement in how to talk is just that, and nothing more; while the identitarian will argue that our broad agreement is a consequence of there being objects with identities. The conventionalist would seem to have parsimony on their side, and can allow or disallow the hypothesis of concrete self-identical objects as their mood dictates; but the base position is that it is more perspicuous to venture only that we say what we say. The object-identitarian offers a theory that explains why we talk the way we do, and the conventionalist can just say he doesn't need one.
That means there are two overlapping arguments here: on the one hand, the conventionalist can keep poking holes in whatever theory of object identity the other side comes up, because he needs no such theory anyway, and may even think no such theory is possible; on the other hand, the object-identitarian has to come up with a theory that works and show that it is needed, which means he also has to find some flaw in the conventionalist account of our referential speech acts — not for the sake of his theory but to show that
some theory is even needed. What's not clear in any of this is how the evidence is to be handled: I'll venture that most people's pre-theoretical intuition is that we talk the way we do because things are the way they are, and that our talking the way we do is in fact evidence that things are the way we say they are.
But we have those pesky scientific refutations of how we talk: sunrise, solidity, and so on. That doesn't show that how we talk is
never evidence of how things are, but it does show that it isn't
always such evidence. On the other hand, the conventionalist can shift from the claim that how we talk is only evidence of how we talk, and nothing more only for methodological reasons, to a claim that how we talk is only we how talk — now meaning our agreement is precisely evidence that there is nothing more.
If that were true, it would not only deny the object-identitarian what was counted pre-theoretically as evidence but change the character of what's to be explained by any such theory. If the mean girls call you a loser, that's just a thing they say: the truth-value of their statement matters to you, but not to them; what matters to them is producing some effect, of hurting your feelings. That's the sense in which it is "just something they say." But not only can you not conclude from someone saying something that it must
not have a truth-value, in this case the effect is only produced if you assume that it does, and they assume that you will assume that it does. If they know you will discount what they say as being just mean-girl noise, or just noise period, there's no reason for them to say it. The conventionalist can retreat again and say that the hurt feelings are known inductively to follow utterances of "loser," and that's all the mean girls need. That might actually be true! But you have to show that such an account really will extend to cover all language use. This situation is so simple that I think what we're really seeing is not exactly language at all but something more like dominance signaling that happens to use language because, well, there it is; we tend to use words even when what we're doing is really nothing more than growling articulately.