Persistence is a theoretically-neutral notion: a thing persists just in case it exists at various times. A thing endures just in case it exists wholly at various times. A thing perdures just in case it exists at various times in virtue of having temporal parts that wholly exist at those times. Endurantism is the view that things persist by enduring, and perdurantism is the view that things persist by perduring.
I can make sense of temporal parts but if you notice, Lewis addresses those who claim not to be able to make sense of the idea (and such denier exist in print!) Our commonsense view of time is not one according to which things have temporal parts. Such a view comes from the concept of time according to contemporary physics, so anyone holding strong to a commonsense conception might deny the coherence of temporal parts.
The modal analog of perdurantism is counterpart theory, the view that a thing has a modal property, say possibly having had pancakes for breakfast, just in case it has a counterpart--something sufficiently resembling it--that has pancakes for breakfast. One's counterparts represent them as being certain ways. The difference between counterpart theory and perdurantism is that Lewis does not think things are sums of their counterparts. Next week we look briefly at the true modal analog of perdurantism, called stage theory (defended by Sider).
He thinks that it cannot cope with the problem of temporary intrinsics. He considers two endurantist solutions to the problem and claims they both fail. The problem is in how to account for change in intrinsic properties over time. How can I be such that I was straight-shaped ten minutes ago (because I was standing) and bent-shaped now (because I'm standing) while remaining the same individual from then to now? (By Leibniz's Law, two things having different properties are distinct.) The endurantist has two solutions. The first is to deny that shape is intrinsic, and to say that it's a relation to a time and a thing. Lewis claims that to be incredible. The second is to claim that the only intrinsic properties a thing has are those it has at present. Lewis claims that on this view, a version of presentism, persistence is denied altogether.
It is to say that things can change their intrinsic properties in virtue of their parts changing spatiotemporal relations to each other. I can be straight-shaped at one time because my constituents are arranged a certain way at that time and bent-shaped at another time because my constituents are arranged differently at that time. How is this a solution? We still have that one and the same thing has different properties at different times. That's true, but it is in virtue of unchanging fundamental parts standing in different relations to each other at different times, and that is no poses no problem for temporary intrinsic properties since relational properties are not intrinsic. In a follow-up paper, Lewis has something to say about this sort of solution, as we'll see.
First part of Lewis's objection. First, it may be true that fundamental particles never change their intrinsic properties, but it may also be false. If science proves otherwise, Lowe's solution fails. So the solution is hostage to "scientific surprises". Second, it is contingent (let us suppose) that fundamentals never change their intrinsic properties. What do we say concerning persistence in a world where fundamentals change their intrinsic properties?
Second part of Lewis's objection. Even if the problem of temporary intrinsic properties goes away, we have a problem of temporary intrinsic relations. Take two particles a and b at a distance x from each other at time t. Suppose they are at a different distance y from each other at another time u. It's still puzzling that one thing x can be one distance from y and yet another distance from y. Or to put it differently, consider the mereological sum of a and b. It has the intrinsic property of its parts being a certain distance from each other at one time and a different distance at another. Aha! We have the same old problem of temporary intrinsic properties again. (We needn't even assume that there are sums of particles, which some philosophers reject; all we need is that things have them as constituents.)
Third part of Lewis's objection. If things and their constituents-at-a-time are distinct, as most anyone holds, then Lowe has not addressed the problem of how complex objects (i.e. things composed of unchanging fundamental particles) persist. He has only given us a solution to how fundamental particles persist (or more generally, how intrinsically unchanging things persist, if there be more than just the fundmeantal particles.)
Her solution is the "adverbial" option, which is to say that objects have properties at times and that times modify the having, not the subjects or the properties. She then notes two semantical options compatible with the adverbial option. Say that Lewis is bent at t, just in case either (i) the proposition that Lewis is bent is true at t, or (ii) the proposition that Lewis is bent at t is true. On the first we have temporalism according to which propositions are true relative to times and they may change their truth value (whether I am bent is true now but not thirty minutes ago), and on the second we have eternalism (about propositions) according to which the truth value of a proposition never changes (whether I am bent at t is true at every time or false at every time).