First: What is it for a property to be intrinsic? Here is a loose gloss that I think will be sufficient for our purposes: F is intrinsic iff whether an object is F depends solely on that object itself, independent of anything else.
Confession: I don't think the argument from accidental (or temporary) intrinsics really has anything special to do with intrinsicness. It seems the problem, insofar as there is one, is a problem that can be run using any accidental (temporary) properties. By property I mean a feature of a single thing--the sort of feature that is expressed by a one-place predicate.
This is because the argument, as I understand it, trades on certain sorts of inferences. So, for example, forget whether being a person is intrinsic. But note that whether someone is a person does not have anything to do with whether they are in (e.g.) Winnipeg. So consider the following:
(a) Adam is a person in Winnipeg.
(a) is logically equivalent to (b):
(b) Adam is a person and Adam is in Winnipeg.
Both (a) and (b) imply (c):
(c) Adam is a person.
This sort of logical relationship shows that is a person is not a relation to being in Winnipeg. Let's call these sorts of inferences 'Term-eliminating inferences' (TEI) (the inference eliminates the term 'Winnipeg'). The TEI from (a) to (c) is valid. But TEI is not valid when we try it out on real relations. So consider (d):
(d) Adam is three feet from Dan.
(d) does not imply (e):
(e) Adam is three feet from.
This shows that being three feet from is a real relation and is not a one-place property.
Now what I think is that it is (partly) the licensing of TEIs that is really important to Lewis's argument. I think his reasons for choosing intrinsic properties are two-fold: first they seem to license TEIs. Second, if they are intrinsic, they are not really relations between independent things. But notice that one could run the argument(s) with any property that has these features. Intrinsic properties just happen to combine them handily.
Now let's consider one way of running the argument from temporary intrinsics. Suppose that at t Adam is bent and at t* Adam is straight. We can represent these claims semi-formally as follows:
Given that 'B' and 'S' represent intrinsic properties (and not relations), we can validly infer (h) via a TEI on both and conjunction:
(h) Ba & Sa
Given that (f) and (g) are true, and they validly imply (h), it follows that (h) is true. But (h) cannot be true; nothing (not even Adam) can be both bent and straight. (Note that my earlier example 'Adam is a person in Winnipeg' was carefully chosen: the "in Winnipeg" part is superfluous. In an exactly analogous way, according to the objection, the "at t/t*" part is superfluous given that the relevant properties are intrinsic. This is why the TEI is licensed here.)
Now for the parallel argument from accidental intrinsics. Adam has 5 digits on his left hand but he could have had 6. Let's represent these claims as follows:
By TEI and conjunction, we infer:
(k) 5a & 6a
On the assumption that (i) and (j) are true, and the inference is valid, (k) must be true as well. But (k) cannot be true; nothing (not even Adam) can be both 5- and 6- digited on his left hand.
Note that nothing was assumed about the nature of w or w*. All that is required is that (i) and (j) are true. This, presumably, just requires of 'w' and 'w*' that they refer. It does not matter what they refer to.
A worry: The argument from temporary intrinsics does not work on presentists. Since actualism is the modal analogue of presentism, doesn't the argument from accidental intrinsics fail against the actualist for exactly the same reasons?
Reply: I don't think all presentists automatically escape the argument from temporary intrinsics. And those that don't automatically escape are the ones that are the real temporal analogues of actualist realism. Let me explain. The most straightforward way out for the presentist is to deny that (at least) one of (f) or (g) is true. If 't' or 't*' does not refer to the present time, then, on this view, it does not refer. So at least one of (f) or (g) is false. Thus the argument for (h) is unsound. But here's another view that deserves the name 'presentism':
Non-present times exist, but they exist presently. They are abstract objects that represent things as being different than they (now) are. Only one of these ways the world was, is, or will be is instantiated, and all of the others are uninstantiated.
This view, I think, does not automatically avoid the objection from temporary intrinsics. And it is the real analogue of abstract realism about modality.
Another worry: Consider the following bit of literature, L:
Once upon a time, Adam has straight hair. The end.
It certainly does not follow from Adam's having straight hair in L and having curly hair in reality (R) that Adam has straight hair and Adam has curly hair. But an actualist realist thinks that ways things could be but aren't is relevantly analogous to ways things are according to certain stories, like L. So actualist realists are automatically invulnerable to the argument from accidental intrinsics.
Reply: Bottom line: worldly actualist realism is not relevantly analogous to the view sketched above. The imagined objector is right that we should not regiment the claim that according to L, Adam has straight hair and according to R, Adam has curly hair as follows:
Rather, we should think of "according to L" as a sentential operator that is not reducible to a quantifier over "stories" (indulge me in thinking of Reality as one of the "stories", but an ontologically special one). So (l) and (m) should be regimented as follows:
On this view, (n) and (o) do not entail (l) and (m). Furthermore, (n) does not entail (p) but (o) does entail (q):
So one cannot validly infer (p) and (q) even if the relevant properties are intrinsic.
Note that this "irreducible operator view" is exactly analogous to the view of presentists who immediately avoid the argument from temporary intrinsics. They hold that "WAS", "WILL", "NOW" operators are not reducible to quantification over times. So they hold that the logical form of 'Adam was bent' and 'Adam is straight' are (r) and (s), respectively:
And just like on the "stories" operator view, (r) does not entail (t) but (s) does entail (u):
So one cannot validly infer the conjunction of (t) and (u) from the truth of (r) and (s) on this view.
Now, on the modal analogue of this view, the logical form of 'Adam could have had 6 digits on his left hand' and 'Adam has 5 digits on his left hand' are, respectively:
where the operators 'POSSIBLY' and 'ACTUALLY' are not reducible to quantifiers over worlds. On this view, (v) does not entail (x) but (w) does entail (y):
Thus, as on the other views, one cannot, on this view, validly infer the conjunction of (x) and (y) from the true (v) and (w). But it is absolutely crucial to this response that the operators are not reducible to quantifiers over worlds. If they were, then (v) and (w) would imply (i) and (j):
and we would be right back where we started.
So what's wrong with this sort of actualist realism? Perhaps nothing. (Barring the obvious point that any philosophical view whatsoever has some sort of problem.) I'm even inclined to think that it is correct (though not because of the argument from accidental intrinsics). But note that this view is not a version of what Divers calls worldly actualist realism. That is, the view cannot accept claims like (P) and (N):
(P) <>P iff there is a world at which P
(N) P iff at all worlds, P
(More carefully, this sort of actualist realist cannot accept a reduction of modal operators to quantification over worlds.)
Thus, I conclude, worldly actualist realists do not "automatically" escape the argument from accidental intrinsics the way some presentists do. So I also conclude that the problem, insofar as it is a problem, is not only a problem for the concrete realist.
(To be clear: I am not trying to suggest that the argument is fatal to any view. I've only tried to show how one does not automatically escape it by being some sort of abstract realist.)