Like the endurantist, the perdurantist has to accept that continuants have their temporary intrinsics only relative to times. If I am a worm, I am not bent simpliciter. I am now, but since I was standing a few minutes ago, I was not then. Nonetheless, unlike the endurantist, the perdurantist can maintain that being bent is still an intrinsic property of something, even if that thing (a momentary slice) is not a persisting object. It just can't be a temporary intrinsic, since the things that are bent simpliciter do not persist, and so have their intrinsics for the whole (very short!) duration of their existence.
Lewis also suggests the following. When, at a time, we talk about what is true, we restrict our domain of discourse to "ignore everything located elsewhere in [that] time". If I utter "Look, there's no beer left!", the domain of discourse is restricted in numerous ways including to that which exists only at the time of utterance (as I'm not talking about beer that was or will be there) and at the location of utterance. Similarly, if I utter "Look, I'm bent!", the domain is restricted to what exists at the time of my utterance, and as that is a momentary stage, my utterance is true, even if I-the-worm am not bent simpliciter.
The rejoinder is this. Say that all having of properties is relational, even for the perdurantist. Whenever it seems that something has a property P simpliciter, really it stands in the bearing having to relation to P, so that the having of all properties is relational. Or to put it a bit differently, even when one of my stages seems be bent simpliciter, really it stands in the having/instantiation relation to being bent. If that's so, why is adding one more temporal relatum to the having relation any worse? Why is x has-at-t P any worse than x has P?
While Lewis accepts the existence of these relations, he thinks they are not fundamental and hence not what explains having simpliciter. He appeals here to Bradley's regress which should be quite obvious given what Lewis says on p. 6. Suppose it is true that I am bent at t. So there is a three-place having relation that holds between me, t, and being bent. In virtue of what do I stand in this relation? Well there must be a having relation that holds between me, t, and the having relation holding between me, t and being bent. In virtue of what does this relation hold? Well there must be a having relation that holds between... Hence having simpliciter cannot be explained in terms of a relational having.
Lewis thinks that properties are the sets of their instances, i.e. all the things that have the property. So the property redness is the set of things that are red. (We can extend this to relations by saying that a relation is the set of sequences of individuals that stand in the relation. Hence if Sam loves Pam, then the ordered sequence [Sam, Pam] is a member of loves.) But then it looks like a thing has a property iff it is a member of it, and membership is a relation, so having simpliciter turns out to be a relation for Lewis. Lewis responds by denying the existence of the membership relation! He gives a few reasons. One is that it would have to be a proper class having proper classes as members, which is impossible (by definition of 'proper class') or else it would have to include the Russell-set, which is again impossible. The second is that he is a set-theoretic structuralist. That means that while he believes there are things that play the set role and something that plays the membership role, there is no one thing that is the membership relation. Compare this with mathematical structuralism according to which there are no numbers, just things that play the number role (and addition, subtraction, etc. roles).
As we read last week, Haslanger defends an endurantism according to which to say that one is bent at t is to say that the proposition that one is bent is true at t, and that being bent remains an intrinsic property. One way of making sense of this is to say that the proposition has the property as a constituent. Equivalently, Lewis say that the proposition, whose truth is time-dependent, behaves just like a property of times. The proposition that you are bent at t just is the property of being a time such that you are bent at that time. In that case, the property is a structural one having being bent as a constituent. Suppose it has you and bent and the time as a constituent. With you being a constituent of the property, what intrinsic properties do you have? And so we seem to be back at the original problem of explaining how you could be both bent and straight relative to different times.
The stage view, like the worm view, holds that things perdure, i.e. persist in virtue of (standing in some relation to) temporal parts. The difference between them is that the worm view holds that continuants are sums of temporal parts united by some "genidentity" relation--i.e. a relation of identity over time, whereas the stage view holds that continuants just are the stages which persist in virtue of standing in the genidentity relation to other stages. Right now, I am a momentary stage that will exist at the next moment in virtue of standing in the genidentity relation to another stage, even though I am not literally identical to that stage. Note that no two stages are literally identical so that genidentity for persons, for example, is the relation of being the same person as, which may be different from strict identity.
Some will claim that on the stage view, there are no continuants. If I am literally a momentary stage, then I have all my intrinsics at every time at which I exist, and so I have no temporary intrinsics. So the stage theoretic solution to the problem is to deny temporary intrinsics! In other words, it is to deny change! Sider responds by saying that momentary stages do change in the relevant sense since they have intrinsic properties that they will fail to have or failed to have in the past. Clearly the stage view is playing a lot on the fact that there are two senses of identity in question. I am literally not spread out in time since I am a momentary stage. But the same person is spread out in time since I am the same person as--but not identical to!--other stages that exist at other times.
Another variation on this objection parallels the so-called Humphrey objection to modal realism. In saying that I have a temporal property like being bent in the future in virtue of standing in some relation to something wholly distinct from me, we have attributed the temporal property not to me but to that other thing. That is of course strictly false: I have the property of standing in relation to that thing, so I have the temporal property. It is also true that the other thing has a different temporal property in virtue of standing in that very same relation. But that does not take away from my having the tensed property. If there is an objection here that Sider does not consider, it is that if certain temporal properties exhibiting change are intrinsic, then they wrongly turn out extrinsic on the stage view. E.g. if my having a certain mass tomorrow is an intrinsic property of me, then stage theory wrongly classifies it as an extrinsic, relational property of me and the future stage to which I'm I-related. The problem is that it does not seem that temporal properties like this are intrinsic. If there are such intrinsic properties, then the burden is on the opponent to give some examples.