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3.3.1 The Persistence Problem

According to perdurance theory, an object persists through some times by having tem- poral parts at those times (the locus classicus here is ((Lewis, 1986), p204). To get a grip on the notion of temporal part, a helpful analogy is space: just as objects are spatially extended, and are so by having different spatial parts at different locations, so they are temporally extended, and are so by having different temporal parts at different times. Granting this, we can say that an object persists from time t to time t+n provided at each time it has a temporal part existing then, and we can follow Sider in defining a temporal part as so:

x is a temporal part of y at t iff "(i) x exists at, but only at, t; (ii) x is part of y at t; (iii) x overlaps at t everything that is part of y at t." (Sider, 2001,p60)

There are a battery of reasons familiar to the literature for adopting this theory of persis- tence. I don’t intend to go through them all, mainly because I have nothing interesting to add to the debate, and it won’t be necessary for what comes later in the thesis2_.

That said, it will be helpful to review some of the arguments offered in its favour, as doing so will help get the view on the table. So let’s consider perhaps the most famous argument for perdurantism in this section (in the next, we’ll consider another): its account of problems of coincidence.

1_{Here, in particular, are some important issues I will not be discussing. Firstly, whether or not the}

debate is genuine or merely verbal. For an expression of the latter position see e.g. (Miller, 2005). Secondly, which further views one is, or is not, committed to by virtue of being a perdurantist (endurantist): for recent discussion of this matter, see Magidor, 2015. Thirdly, and somewhat relatedly, the metaphysics of time each view requires. A couple of references are: (Markosian, 1994), (Zimmerman, 1996). Fourthly, and still relatedly, I won’t consider four dimensional views which do without temporal parts such as (Parsons, 2000): in my usage, four dimensionalism will be just the claim that there are temporal parts, and it is intended to be neutral between stage and worm theory.

2_{Some references: Lewis has a rather complicated argument in (Lewis, 1983); it is discussed in (Wasser-}

man, Hawthorne, and Scala, 2004). Sider presents an argument from vagueness in the book already cited; discussion is, for example, (Koslicki, 2003). Sider provide a nice compendium and assessment of extant arguments in chapter four of his book.

There are a variety of forms which such problems, which concern what appear to be two material things which occupy the same space for part of their career, can take. The most famous example is from (Gibbard, 1975) . Consider a lump of matter, Lumpl, which exists for a while, before being formed into a statue, Goliath, which itself exists for a while, before being squashed. Goliath and Lumpl have different properties: Go- liath has existed for less time than Lumpl, for example. Or Lumpl could have survived squashing, while Goliath couldn’t. Or, to consider an example that doesn’t involve potentially problematic temporal or modal issues, Goliath is Rubenesque but Lumpl isn’t (Fine, 2003). Given that they appear to have different properties, it appears they are different objects. But clearly they occupy exactly the same space. How can two different material objects occupy exactly the same space?

For the four dimensionalist, the argument goes, this is no problem. An analogy helps: two roads can overlap. For example Interstate 70 merges with Interstate 76 on the Pennslyvania turnpike. The same stretch of road is then in fact two roads: I70 and I76. Although they are different roads, as evidenced by the fact that they begin and end in different places, they physically overlap for a while, i.e. they share some spatial parts.

For the four dimensionalist, we have the same sort of thing, only temporally. The statue and the lump have sometemporalparts in common: in particular, they have the parts from when the statue was formed to when it was destroyed in common. Despite this, they’re not the same, just as the I70 and I76 aren’t the same, because, for example, the lump is longer lasting than the statue.

There’s plenty of controversial things about this argument. For one, we can note that things get troublesome when we consider cases of permanent coincidence (Gib- bard, 1975): imagine a statue and a lump coming into being, and going out of being, at exactly the same time. We can’t uphold the idea that we have two objects here by pointing out that they don’t entirely overlap, because they do. But, one might think, if we have two objects in the original Lumpl and Goliath case, we have two here.

Some, such as Lewis, have appealed to counterpart theory here, saying that indeed the statue and the lump are one and the same, but the invocation of different coun- terpart relations can make sense of why a sentence such as ’the statue could not have survived squashing’ is true while ’the lump could not have survived squashing’ is false. The problem with this is that it can’t easily extend to cases like Fine’s Rubenesque: ’the statue is Rubenesque’ doesn’t appear to use any vocabulary that would invoke coun- terpart relations. Here an answer has been to just bite the bullet and say that the lump is indeed Rubenesque, albeit it’s a misleading way of speaking in most cases (Frances, 2006).

For another issue with this argument, we can note that the endurance theorist has proposed alternative theories of what’s going on which don’t appeal to temporal parts. For example, Thompson (Thomson, 1998), among several others, defends the view that the statue and the lump are indeed different, so that there are two objects before one once the statue has been formed. And she appeals to the notion of constitution to make sense of this, and to allay any worries one may have about the two being unduly squashed together. The statue is constitued by the lump (but not vice versa), and this enables them to occupy the same space, but nevertheless constitution is a bona fide relation, so there are two things.

Here is not the place to evaluate all this. One might well be uncomfortable with the idea that therearetwo objects occupying the same space, as opposed to one shared part. On the other hand, one can note that this constitution idea works straightforwardly in the cases of permanent coincidence the perduranist struggles with. In all, perhaps one

should say it’s a dialectical tie. Let’s move on and consider another reason for believing in perdurence theory. Doing so will enable us to present the perdurantists’ answer to the property problem.

3.3.2 The Property Problem

Lewis famously argues that problem of change itself supports four dimensionalism: that is, he thinks that the perdurance theorists’ answer to the property question is a good reason to believe in it. Let’s see what that answer is.

The key idea behind the perdurantist’s response to the property problem is that it’s parts of objects that bear temporary intrinsics. For example, just as I have a spatial part where my heart is, and also another, larger one where my thorax is, so, for the perdurantist, I have a temporal part spanning from my first birthday to my second, and another larger one spanning from my birth to the day I got my tonsils out when I was eight.

Now consider a sometimes bent, sometimes straight stick. Assume it came in to being on Sunday and was bent all day, and then at the stroke of midnight became straight, and remained so til Tuesday. Then the stick has a temporal part spanning from its coming to being to Sunday night, and another from then til Tuesday. The first part bears the property of being bent simpliciter, while the second bears the property of being straight simpliciter. Thus–by having parts which possess them–can the stick itself, the whole thing with all its temporal parts, possess the seemingly incompatible properties of being bent and being straight simpliciter,andit can do so without making the assumption, beyond the pale for Lewis (as we will see), that properties are time relative.

This isn’t hugely dialectically satisfying. As we will see, Lewis rests a lot of weight on the intuition that intrinsic properties just aren’t relational. But here’s another in- tuition, one might think: it’s everyday objects like you or me that possess properties. So it’s such everyday objects, if any, that possess intrinsic properties. But that’s not so for him: everyday objects are those persisting things which have temporal parts–the mereological fusion of all of them. Such things are not plain straight, nor are they are plain bent. Rather, the things which are plain straight or bent are parts of such objects. But it seems we’ve gone considerably past intuition in saying this (that a lot here seems just to turn on a clash of intuitions is noted by Sider, loc. cit. p96).

However, if it’s not pretheoretically compelling, it doesn’t mean that it’s a bad pic- ture overall. Indeed, it seems coherent, and even if it’s not intuitive, arguably that doesn’t matter: why should metaphysics be intuitive? Although Lewis seems to care a lot about intuition, that’s no reason for us to do so. Let’s now see how endurance theory can do.