Metaphysics

Let me start with the idea that there are temporal parts. Pre-theoretically, objects seem to persist through time: I existed yesterday, and I exist now. Now we noted that Buddhism tends to disagree with this (I'm not so much concerned, here, as to why this is so, but see e.g. Siderits (Reference Siderits and Zalta2015) and references therein), but even so, the idea surely has something going for it, and we should seek an explanation for it (or perhaps for why we are attracted to the idea). What is going on when an object persists (or seems to persist) through time?

This is a question which has been the subject of a lot of recent and sophisticated work in analytic metaphysics. The discussion normally starts with the following classical formulation of the problem, and the space of solutions, from David Lewis:

It will be helpful, before considering the two views, to follow Lewis and introduce an analogy which lies at the heart of the debate: the analogy between being temporally extended and being spatially extended.

It's uncontroversial that things are extended in space. My feet are there, my legs there, my head here. Consider the portion of space surrounding my feet. I occupy it, although I don't exactly occupy it, because I occupy other portions of space as well. What is it for me to occupy the space around my feet? Here's a plausible answer: I occupy it because parts of me exactly occupy it. My occupying it is derivative of having parts, my feet, that exactly occupy it. I also occupy the space surrounding my head, my torso, and so on, in the same way.

Not all occupation, arguably, is like that. Consider universals: blueness, for example. We might want to say that there's a decent sense in which blueness occupies a location: it occupies the location where the shirt I'm currently wearing is, perhaps. It also occupies the location on my desk where my bottle is. But it doesn't do so, we might think, by having parts at these places: rather, it exists entirely at each location. It is, we might say, multiply located in space. Again, it's not so much the truth of these views that is important, as the fact that they are metaphysically coherent ways of describing the world. And that they surely are.

Now return to the question of persistence through time. I exist now, I existed yesterday, and I existed at each time in between. That is, there's a series of times t₁, t₂, . . ., t_n such that I exist at them. What's going on? Well, here's a way to describe what's going on: just as I occupy different spatial locations, so I occupy different temporal locations. This requires treating different times as ontologically on a par with different spaces, which is of course a vexed and important metaphysical question. It is to be taken as a premise in all that follows (some discussion in Markosian (Reference Markosian1994) and Zimmerman (Reference Zimmerman1996)).

Once we've redescribed our question like that, we can recognize two different accounts of persistence: we can say that an object occupies a series of times like I occupy space: by having different parts existing at the different times of the series. But these won't be spatial parts, these will be temporal parts. Alternatively, we can say that an object occupies a series of times in the same way a universal occupies space, by being multiply located at each of the times in the series.

These are the two main metaphysical positions, called perdurantism and endurantism respectively. For the perdurantist, an object exists through a series of times by having temporal parts which exist at that time; for the endurantist, it does by so completely existing at those times.Footnote ¹

How are we to decide between these views? My aim here is certainly not to try to do so. Rather, my aim is to show how one of them, when combined with a view in semantics, can make good sense of the Buddhist position sketched above. However, it will be useful to consider, if briefly, the sort of considerations typically brought forth in favour of these views, if only to help the reader get a greater sense of them, and what's at stake between them.

So let's consider perhaps the most famous dispute between the endurantist and the perdurantist, that concerning overlapping objects (Gibbard (Reference Gibbard1975)). Lumpl is a lump of clay, which existed from t₀ to t₁₀. At t₃, it was formed into a statue, Goliath. At t₆, the statue was flattened, and the clay persisted lumpily until it went out of existence at t₁₀. Are Goliath and Lumpl the same? It seems not. After all, we don't tend to think of two objects as the same if they have different properties. But Lumpl and Goliath have different properties: Goliath is Rubenesque (Fine (Reference Fine2003)) and couldn't survive squashing, for example, while Lumpl is not and could. So are there then two objects before us at t₄?

Here the endurantist and the perdurantist differ. The endurantist will say yes, and that two objects can be located at exactly the same place in space. Although there's only one bit of space before us, the two objects nevertheless both manage to occupy it. The perdurantist, however, will say there's only one object before us: a temporal part shared by both Goliath and Lumpl.

To explain this, the spatial analogy is again helpful. We are familiar with the idea that two things can spatially overlap. Thus, to use the stock example, two roads can merge into one for a while, before again diverging. At the time they've merged, there are two roads, but only one stretch of concrete. For the perdurantist, the same thing happens here: Lumpl and Goliath temporally overlap – they share a temporal part – from t₃ to t₆, and this is how there can be two things before us even if there's only one bit of matter.

Who is right here? The perdurantist argues that the endurantist's claim that there are two objects before us at t₄ departs from common sense. She can say: no, what we have before us is one temporal part shared by two perduring entities. Because the perdurantist works, in essence, with two different notions of object – the parts, and the wholes composed of those parts – she can account for both the sense that Lumpl and Goliath are different, but also the sense that there's just one object before us.

It might seem that the perdurantist comes out on top of this debate. But the endurantist has moves to make. He can note that the response just offered is of no use in cases of permanent coincidence. Imagine Lumpl and Goliath came into, and went out of, existence at exactly the same time. Then they share all their temporal parts. So, for the perdurantist, that means that they are one and the same. (Again, consider the roads: we can't make a lot of the sense of two roads beginning in the same place, following the same path, and ending in the same place. Two roads sharing all their spatial parts aren't, in fact, two roads after all.) But that seems wrong: after all, as before, Goliath is Rubenesque but Lumpl isn't.

Here is just one other central bone of contention, the problem of temporary intrinsics. Consider the notion of a property, and in particular an intrinsic property. An intrinsic property, very roughly, is something possession of which turns on features only of the possessor, and not any other object. A stick's being bent, for example, is intrinsic to it, whereas its being owned by me is not intrinsic to it.

Now consider a stick that was bent in the morning, and straight in the afternoon. This might seem like a problem for the endurantist theory. After all, for the endurantist, it exists completely both in the morning and in the afternoon. So in the morning, it possesses the property of being bent. And in the afternoon, it possesses the property of being straight. So it seems like it possesses the property of being bent and of not being bent, which is impossible (at least on standard assumptions).

The reader is liable to be nonplussed: to think that something crucial has been left out here, namely time. Property possession should be indexed to time: what's going on is that the stick is straight in the morning, and bent in the afternoon, and these are not incompatible properties.

Lewis, famously, thinks this reply is no good. He thinks it amounts to saying that being bent is a relation: it relates an object to a time provided the object is bent at that time. And that, he thinks is ‘simply incredible . . . If we know what shape is, we know that it is a property, not a relation’ (Lewis (Reference Lewis1986), 204).

By contrast, he thinks the perdurantist is well-placed to account for our stick: he says that bentness is indeed a property, but one possessed by temporal parts, and not the whole temporally extended entity. The stick is straight in the morning by virtue of having a part existing in the morning which possesses the property of straightness, and bent in the afternoon by having a part which possesses the property of bentness.

There are moves and countermoves available here: it's a large and lively debate, of which we have only here scratched the surface.Footnote ² The relevant point for our purposes is that I think that the Buddhist views surveyed above can help us here. In particular, we saw the claim made that none of an object's parts are that object, and neither is the sum of its parts. Treating temporal parts on a par, we could then say that none of its temporal parts are the object, and nor again is the sum of them. That is, the Buddhist would deny the perdurantist position, which says that an object is the mereological sum of its parts. But nor would the Buddhist be particularly attracted to the endurantist position, which recognizes one and the same object existing at more than one time, contra the claim of impermanence. So then what should we say? Well, the passage quoted from The Questions of King Milinda recognizes the existence of the parts, and that there's some sense to be made of the idea that all the parts taken together just are the object, at least in the weak sense that we can correctly speak of the object, and in so doing we speak of the congeries of parts. In the next section, I want to show how we can make sense of this idea in terms of contemporary semantic theory.

Semantics

Names seem to stand for objects: ‘Milinda’ seems to stand for Milinda, ‘Paris’ for Paris, and so on. As with persistence, the Buddhist thinks that this is in some sense to be qualified. But again, it's intuitive and at least the fact that it seems like names behave thus is something that should be explained, even if it's not an ultimate truth about the world.

For a long time, semanticists thought they had an explanation. Saul Kripke's pioneering work (Kripke (Reference Kripke1980)) suggested that names are Millian expressions. The important idea here is that a name stands for a particular object in the world, and doing so exhausts its semantic function. A relatively neat way to think of this, for those familiar, is that names are like constants in first-order logic, as opposed, say, to variables or predicates or quantifiers.Footnote ³

Recent years, however, have seen that explanation called into question. There is a range of both English and cross-linguistic data which suggests that names might be more like predicates than constants. To be more linguistically precise, there's data to suggest they might be like common count nouns. Here are some sentences with count nouns as subject:

1. (1) No parrots are dull.

2. (2) Some book is interesting.

3. (3) All politicians are corrupt.

The reason to think that names are count nouns is simply that they sometimes behave as such:

1. (4) No Alberts are young.

2. (5) An Alfred joined the club today.

3. (6) All Delias are good at philosophy.

In light of this, predicativists (such as Burge (Reference Burge1973), Elbourne (Reference Elbourne2005), Matushansky (Reference Matushansky2008), Fara (Reference Fara2015)), have argued that we should take sentences like (4)–(6) seriously, and say that names are predicates. In particular, ‘Alfred’ is a predicate which has as its extension all the people named ‘Alfred’.

Of course, it's notable that the similarity between names and count nouns has its limits. There are environments where names occur where predicates cannot, as, for example, and importantly (where * indicates ill-formedness):

1. (7) Carrie swam.

2. (8) * Politician joined the club.

But even here there are things to say. We can note that in some languages other than English one gets names occurring as the nominal in a definite determiner phrase and occurring in argument position:

1. (9) La Maria dorme.

   the Maria sleeps.

   Maria sleeps.

In light of this, to account for (7), the standard move is to posit a covert, unpronounced definite determiner, giving a syntactic logical form like so, where ‘Ø’ preceding a word indicates it is unpronounced:

1. (10) [_s [_dp [_d Ø THE] [_np Carrie]] [_vp swam]]

This move is not without its perils (for which, see, for example, Schoubye (Reference Schoubyeforthcoming)). But if we accept it, then we can account for both the syntax and the semantics of (7). It's simply a definite description with a covert definite syntactically, and an incomplete domain semantically.Footnote ⁴

Again, it's not my goal to argue for predicativism. I hope that this brief discussion, however, has shown that it has something to say for itself: the English and cross-linguistic data, at least, are worth talking seriously.

Now let's turn to Buddhism. The Buddhist doubts, as we have seen, that there is some unified object over and above what we call the parts of an object: there is just Milinda's skhandas and the different types of matter composing his body. I suggested we could understand that, taking our lead from the debate about persistence, as saying that all there was to Milinda was his temporal parts. Now if names were constants, which stood for just one thing, it would be unclear how what the relation between ‘Milinda’ and the world was. But if names are predicates, which stand for multiple things, then there is something to say: we can say that a predicate like ‘Milinda’ has as its extension all Milinda's temporal parts. Predicativism lets us make sense of our referential practices even if there is no object out there for our terms to refer to, as the Buddhist says. This is, I take it, a welcome result, especially given the empirical plausibility of predicativism.

Although I noted that it's not my aim here to consider how the central idea of impermanence has been treated in the many schools of Buddhist philosophy, it's worth pointing out one interesting parallel in the debate concerning universals and particulars found in Dharmakīrti (my source here is Dunne (Reference Dunne2004), 91ff.). Dharmakīrti is keenly aware of the tension between the impermanence of the world and the ability of language to function. In his terms, what exists must be momentary, but what is thought or spoken about must exist without changing. That is, what exists are particulars, while what is thought or spoken about are universals (indeed, for him, universals don't really exist, but we needn't get into that). This seems notably close to the predicativist thought which I'm appealing to that the contents of our referential devices are general and not particular.Footnote ⁵

So that's my view. To repeat: names are predicates which have stages in their extension. In particular, a name like ‘Milinda’ stands for all of Milinda's stages. There is no object over and above these (no mereological fusion, as the perdurantist would say), just as the Buddhist claims. But nevertheless we can talk about Milinda using a name because names are general terms which stand for all the parts of an object.

Refinements and Discussion

That's the basic view. Now let me put more flesh on the bones by sketching, albeit briefly, the semantics, and indicating some interesting and distinctive features of the view.

First, then, let's say a bit more about the semantics. Names are predicates which have stages in their extension. Let's consider what to say about the compositional semantics – how the truth value of the sentence is determined on the basis of its parts – of a simple sentence like this:

1. (11) Milinda laughed.

Here is what we want: we want it to be true if there are some stages of Milinda such that together they laughed. For example, if Milinda laughed from 3.00 p.m. to 3.01 p.m., all his stages from that period, taken together, would make true the sentence. But also, of course, if he laughed from 3.01 p.m. to 3.02 p.m., then those stages taken together would also make the sentence true: provided there are some stages that are laughing stages, our sentence is true. So we want existentially quantificational truth conditions. But more than that, we want it to have plurally quantificational truth conditions: there are some stages which, taken together, laugh. But that's no problem: we can appeal to plural logic to help us (for plural logic see e.g. Boolos (Reference Boolos1984), Oliver & Smiley (Reference Oliver and Timothy2013)). We can note that English, in addition to having singular quantification, also appears to have genuine plural quantification. Just as we have:

1. (12) Some woman laughed.

So we have:

1. (13) Some women surrounded the castle.

Plural logic is well understood logically and on solid grounds philosophically (the above references show this). So we can use it here, and say that the quantifier is in fact a plural one. Following the literature in using ’xx’ to stand for plural variables ranging over stages, we would have the following truth conditions:

∃xx. Milinda(xx) and Laughed(xx).

Not only that, but we can note that this isn't even all that implausible as a matter of natural language semantics. There are a range of well-understood and empirically sophisticated theories that make use of covert existential quantification, either as part of the syntactic logical form or as part of the interpretative procedure (for the former, I have in mind, a little roughly, Pietroski (Reference Pietroski2005), while for the latter Hans Kamp's DRT (Kamp & Reyle (Reference Kamp and Uwe1993)).

For example, Pietroski develops a conjunctivist semantic framework, according to which all expressions uniformly contribute predicates of, and free variables standing for, events to logical form, which variable is bound by an obligatory text-level existential quantifier. Without going too much into the details, such a view is familiarly helpful when it comes to making sense of certain inferences which seem good in virtue of form, such as the following:

1. (14) John buttered the toast slowly, so John buttered the toast.

If we hold that the underlying logical form of our inference is:

1. (15) ∃e. Agent(John, e) & Action(buttered, e) & Patient(the toast, e) & Manner(slowly, e) so ∃e. Agent(John, e) & Action(buttered, e) & Patient(the toast, e)

We can explain why the inference is good: it's just an instance of the valid in virtue of form argument going from ∃x. F(x) and G(x) to ∃x. F(x).

I suggest that we follow Pietroski's conjunctivist lead, except we say that the variable is not a singular event variable, but a plural stage variable. In other work, I show how to develop such a theory in detail, extending it to cover natural language quantification and variable binding (McKeever (Reference McKeever2016)). I omit those technicalities here.

Second, it's interesting to note that my view adds new spins both to predicativism and to perdurantist theory. On the standard predicativist view, names are general terms standing for each of the name's bearers: ‘Milinda’ stands for all things called ‘Milinda’, ‘Paris’ for all the things called ‘Paris’. This is not so for me: for each bearer, there is a different predicate. Names are ambiguous in the way that, for example, ‘bank’ is ambiguous as between a river bank and a financial institution.Footnote ⁶ We could notate the disambiguations with subscripts, so there is ‘Milinda₁’, which stands for one Milinda, ‘Milinda₂’ which stands for a different Milinda, and so on. This view has advantages and disadvantages. For a disadvantage, it can't capture, out of the box, central predicative uses like:

1. (16) An Alfred joined the club today.

The truth conditions of this are that some person named ‘Alfred’ joined the club, but I can't get this. For me, each disambiguation stands for a different Alfred. It seems that my theory would predict (if anything) that, relative to some disambiguation ‘Alfred_n’ of Alfred, (16) is true provided some stage of one of the Alfred_n joined the club, which isn't what we're looking for.

This doesn't worry me overmuch, however. I need to resort to some sort of ambiguity view: I'll say that names have different uses. On one, ‘Milinda’ is ambiguous, and has different disambiguations for each Milinda. On the other, ‘Milinda’ stands for all the Milindas, which is to say that its extension contains the set containing all Milinda₁’s parts, the set containing all Milinda₂’s parts, and so on. It's this latter use we appeal to for paradigm predicativist sentences like (16).

One might think that the fact that I am forced to resort to an ambiguity view puts me at a marked disadvantage. But I don't think it actually does, because the standard predicativist seems to require an ambiguity view too. It's been noted that the predicativist can't account for all predicativist-like uses. In particular, consider something like:

1. (17) She's a real Einstein.

2. (18) He's no Jack Kennedy.

The predicativist can't account for the truth of these sentences in terms of their theory. The second sentence here, for example, is saying something like the man in question doesn't exemplify the qualities of one particular person called ‘Jack Kennedy’, namely JFK. But it would seem that the standard predicativist would predict that it's true provided there's no person called ‘Jack Kennedy’ such that the man in question is him. That's the wrong prediction.

So even the standard predicativist can't account for all predicative uses of names. Accordingly, I don't think this feature of my view is a problem, and indeed it shows something that I think is well borne in mind: that predicativism should be considered primarily a syntactic view, that names belong to the same category as count nouns, and not a semantic view.

I think the view is also an interesting twist on standard perdurance theory. In order to see that, let me note briefly the typical perdurance theory of predication. According to it, an object possesses a property by virtue of having a (possibly, indeed normally, non-instantaneous) temporal part which possesses it. I was young by virtue of having a part – say the part of me extending from 1 to 13 – that possesses the property of youth. Note that these are existential truth conditions: that I was young is true provided there is a part of me that possesses the property of youth.

My view somewhat mimics this. The only difference is that instead of requiring that there be a part, I require that there be some parts, plural. What this means is that I don't require that there be a lot of mereological fusions. Indeed, it seems that my view is an instance of a recognizably perdurantist theory that nevertheless need not appeal to the principle of unrestricted composition which says that for any objects, there's an object which is their fusion. This should be of interest to those working in the debate, because it's been noted that perdurantism often comes bundled up with certain other views which it is nevertheless distinct from, and one of those is unrestricted composition (Magidor (Reference Magidor2015)). This view provides an independently attractive example of how one can be a perdurantist without accepting unrestricted composition.