Temporal Predicates and the Passage of Time

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Temporal Predicates and the Passage of Time

M. Joshua Mozersky

Introduction

Traditionally, advocates of the tenseless, B-theory of time deny the reality of temporal passage (e.g. Smart 1963, 1980; Mellor 1981, 1998; Horwich

1987; Price 1996). I argue that this is a mistake. B-theorists should accept that time passes not only because there is overwhelming evidence that it does, but also because the B-theory provides the best resources for making sense of the passage of time. I defend this view via a consideration of the puzzle of change: how is it possible to make sense of a single object having incom-patible properties at different times? I present and defend a solution to this puzzle that needn’t worry B-theorists and allows for a coherent and satisfying theory of change, persistence, and temporal passage.

The logical form of temporal predicates

Consider the temporal predicates “x is past,” “x is present,” and “x is future,” which I shall refer to as “A-predicates.” Assume that the variables take individuated entities, such as events or times, as values. Let us begin with a simple question about these predicates: are they one-place (monadic) or are they many-place (relational)? If the former, then their logical form is as follows:

(A) F(x), G(x), and H(x);

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110 DEBATES IN THE METAPHYSICS OF TIME

if the latter, then their logical form is:

(B) F(x, y), G(x, y), and H(x, y),1

which I shall refer to as “B-relations.”2 How might we decide between these two options? A useful place to start is with a consideration of the nature of change. The concept of change can certainly appear puzzling. On the one hand, change requires difference: if x changes from F to ~F, then x is no longer exactly the same before and after the change. On the other hand, change requires identity: if x changes from F to ~F, then it must be x that is both F and ~F; if distinct entities are F and ~F respectively, then nothing has changed. Yet identity and difference appear to conflict with each other. If x = y, then x and y cannot differ in any way (Leibniz’s Law); but, if x changes from F to ~F, then it seems that whatever it is that is F cannot be identical to whatever it is that is ~F. Hence, change appears to be impossible (see Hinchliff 1996). We can generate a similar puzzle with A-predicates. The reason for this is that if these predicates are to model time, then if anything satisfies a given A-predicate, it must also satisfy the others (let us ignore the complication of a first or last moment of time, as this will not impact the arguments here). If some event is, say, present, it does not remain present for eternity; it is eventually past and something else is present, and so on. But then one and the same entity must be both F (present) and ~F (past), and the conflict between identity and difference arises for anything that satisfies A-predicates. I propose that the solution to the puzzle of change and the decision between (A) and (B) are the same. So, let us start with change. Suppose some object, x, goes through a change, say from being (entirely) blue to being (entirely) green. If we let “F(x)” = “x is blue” and “G(x)” = “x is green,” and assume that F(x) entails ~G(x) (and vice versa), then the formal description of this change appears to be the logically impossible:

(1) F(x) &G(x).

In other words, when ordinary predicates are understood monadically, attribu-tions of change are outright contradictions. One can, however, reconcile identity and difference while avoiding contra-dictions in one fell swoop. The trick is to assume that ordinary predicates, such as “x is blue” and “x is green,” are two-place relations that hold between objects and times. In that case, the logical form of the predicate “x is blue” is:

(2) F(x, t)

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TEMPORAL PREDICATES AND THE PASSAgE OF TIME 111

and the logical from of the predicate “x is green” is:

(3) G(x, t).

Given this, the proposition that some object has changed from blue to green is:

(4) ( x)(F(x, t1) &G(x, t2)).

Notice that in (4) it is one entity, x, that satisfies both relational predicates, so identity through change is preserved in this description. Furthermore, in (4) x is blue at one time, green at another, so difference is represented. Finally, note that (4) is consistent since two otherwise incompatible relations can be combined without contradiction if they relate an entity to two different times. So, the problem of how to coherently describe change has been resolved. Returning to A-predicates, we can engage in a similar line of reasoning. Suppose that some event, e, is present, then past. How are we to represent this? If A-predicates are monadic, our choice would seem to be (1) again, which is a contradiction because F(x) entails ~G(x) and G(x) entails ~F(x). Let us, then, try an analogous solution: “e is past” will be understood as a relation between an entity and a time:

(5) F(e, t).

Similarly, “e is present” will be:

(6) G(e, t).

Now the change an event undergoes from being present to being past can be expressed as follows:

(7) ( x)F(e, t1) &G(e, t2).

This proposition is logically consistent and reconciles identity and difference. Accordingly, (B) is to be preferred over (A) and we may conclude that A-predicates are relations. It appears that the simple question with which we began has been answered. This argument may look familiar. It is, with one important difference, very much like McTaggart’s argument against the coherence of the A-series (McTaggart 1908, 1927). The important difference is that McTaggart thought that propositions such as (7) preserve identity and logical consistency at the cost of difference; in other words, he believed that neither (4) nor (7)

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represent change. Hence he took the argument against (A) to be an argument against the existence of time on the grounds that time entails change. But why follow McTaggart here? I turn next to three lines of reasoning intended to indict (4) and (7) as unsatisfactory accounts of change.

Objections to the relational theory

McTaggart

The first objection, which is noted above, is due to McTaggart who argued that propositions such as (7) and (4) are not truly representations of change because their truth-values are unchanging:

The fact that [a poker] is hot at one point in a series and cold at other points cannot give change, if neither of these facts change … It follows from what we have said that there can be no change unless some propositions are sometimes true and sometimes false. (McTaggart 1927: 15)

B-relations have temporally stable extensions. If x is blue at t, then x is blue at t in a temporally insensitive way: it will not one day become false that x is blue at t because events in time are not variable in that way. So McTaggart is right that a proposition of the form of (7) is, if true, a tenseless truth. Must we, however, follow McTaggart in concluding that (7) cannot represent change? I don’t see why we should. Even if a representation does not itself change, it does not follow that it is not a representation of change. Heather Dyke has very importantly drawn attention to what she calls the “representational fallacy” (Dyke 2008), which is, roughly, the attempt to read off features of non-linguistic reality from features of our linguistic represen-tations.3 I think she is right to be suspicious of such reasoning. There are many instances in which features of our representations—for example, the presence of words—fail to be features of what we represent. In general, therefore, a property of a representation isn’t necessarily a property of that which is represented. McTaggart’s suspicion of (7) appears to rest, however, on the even more dubious inverse of the representational fallacy. One would only follow McTaggart’s argument that (7) does not accurately represent change if one were to suppose that a property of what is represented must be a property of the representation. In this particular case, McTaggart assumes that the world can exhibit change in properties only if propositions about that world change their properties, in particular their semantic properties. This is, however,

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simply not credible for, if generalized, it would entail that any representation of a red item must itself be red, or any story about evil must itself be evil, or that a picture of a living person must itself be alive, and so on. There is no reason to suppose that there is anything like a one-to-one correspondence here. What we may conclude is that McTaggart had good reason to insist that the only coherent conception of A-predicates is relational, but wrong to assume that this meant the unreality of change.

Lewis

It has been argued that the relational account is incompatible with the idea of intrinsic change. David Lewis gives forceful expression to this concern:

Persisting things change their intrinsic properties. For instance shape: when I sit, I have a bent shape; when I stand, I have a straightened shape. Both shapes are temporary intrinsic properties; I have them only some of the time. How is such change possible? I know of only three solutions … First solution: contrary to what we might think, shapes are not genuine intrinsic properties. They are disguised relations, which an enduring thing may bear to times. One and the same enduring thing may bear the bent-shape relation to some times, and the straight-shape relation to others. In itself, considered apart from its relations to other things, it [i.e., a changing object] has no shape at all. And likewise for all other seeming temporary intrinsics; all of them must be reinterpreted as relations that something with an absolutely unchanging intrinsic nature bears to different times. The solution to the problem of temporary intrinsics is that there aren’t any … This is simply incredible … If we know what shape is, we know that it is a property not a relation. (Lewis 1986: 203–4)

One can identify three complaints in this passage: first, that the relational solution reduces objects to loci of unchanging intrinsic natures; second, and relatedly, that the relational view entails that nothing is temporarily intrinsic to an object; and third, that it is simply unbelievable that, for example, an object’s shape could be a relation between it and a time. I address each of these in turn. Concerning the first objection, it is hard to see why expressing ordinary change by way of propositions of the form of (4) above reduces x to something that has an unchanging intrinsic nature. Perhaps the thought is that if, for example, shape is a relation between x and t, then x in fact lacks a shape. But just because it is only meaningful to predicate some shape of x if

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there is some time or other at which x has that shape, it doesn’t follow that x itself is somehow shapeless. One has to keep in mind that we are concerned here with relations between material objects and times, and if there is no time at which x is shaped, well, then x has no shape. For a material object to have a shape is for it to be shaped at some time or other, and this does not entail that the object lacks shape. It simply entails that shape predications only make sense in reference to a time at which the shape is exemplified.4 So, in other words, it is truly x that has a shape in the relational view; it is just that the having of its shape is not something that can be rendered sensible without reference to some time or another. Hence, I think that the relational view does not render objects featureless. If this is right, then the reply to Lewis’s second objection is as follows. It is true that ascriptions of shape, size, color, mass, and so on, are neces-sarily relative to times. This, however, is compatible with shape, size, color, mass, and so on, being intrinsic to objects because according to (4) above it is precisely the object, x, and not something else that has shape, size, color, mass, and so on, at a time. In particular, it is not the object–time pair that is, say, round, or large, or blue, and so on. Suppose, for comparison, that John is inside a house. This is a relation between John and a house, and the relation requires the existence of both, so in that sense one might want to say that the pair instantiates the “is inside of” relation. Nevertheless, in this pair it is John who is inside; the John–house pair isn’t inside of anything. Now, of course, this isn’t an intrinsic property of John, so the comparison is misleading in that respect. However, the point I am trying to emphasize is this: the fact that x stands in relation R to y doesn’t entail that there is no asymmetry, with respect to R, between x and the pair <x, y>. So, even though x’s being blue entails that there is a t at which x is blue, and in this sense can be said to entail that the pair <x, t> instantiates the “is blue at” relation, this is all compatible with it being x that is blue rather than the pair <x,t> (how could such a thing be blue anyway?).5 I think we can see that this is sufficiently “intrinsic” if we examine this concept in a bit more detail. Lewis writes that “A thing has its intrinsic properties in virtue of the way that thing itself, and nothing else, is” (Lewis 1983: 197). It is important to note that, according to the relational theory defended above, although x is red at t in virtue of standing in the “is red at” relation to t, x’s being red doesn’t depend on the way that t is. It depends, rather, on there being a t at which x is red. Lewis in fact defends an analogous position, for in his view (Lewis 1986) for x to be F is for x to be F in some world or other. Lewis does not, nor should he, conclude on that basis that for any F, x’s being F depends in part on the “way x’s world is” and so isn’t intrinsic. To be F is to be F in some world, for Lewis, even if F is intrinsic. Analogously, in the relational view, for any material object to be F is for it to be F at some time, even if F is intrinsic.

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Here is more from Lewis:

The intrinsic properties of something depend only on that thing; whereas the extrinsic properties of something may depend, wholly or partly, on something else. If something has an intrinsic property, then so does any perfect duplicate of that thing; whereas duplicates situated in different surroundings will differ in their extrinsic properties. (Lewis 1983: 197)

I think, however, that the first sentence is wrong. Since to be a material object is to occupy space and time, all properties of material bodies depend on space and time for their instantiation; material bodies would not exist without space and time. Nonetheless, there is still a difference between those properties that are properties of the object (its being round) and those that are not, or not wholly, of the object (e.g., its being to the left of something). It should be added, moreover, that in the relational view of predication, a perfect duplicate of a material object would not differ intrinsically from the original object. What follows from the relational view is that for an object and its duplicate, any specification that the object or duplicate is F must make reference to time, that is, to when the object is F. This is in fact a strength of the relational view, for we don’t want to commit to an account of material objects that does not tie their descriptions to spatial and temporal locations. An object is material only if it instantiates its predicates at some time (place) or another and this will be true of both an object and its duplicate. So, the relational view appears to be compatible with the distinction between those predications that describe an object itself and those that do not. The distinction depends on whether one needs to specify a time/place in describing the object or whether one needs also to specify other objects. If one insists that even in the former case, the concept of something being intrinsic to an object has been destroyed, then my reply is “Let us lay this concept to rest in peace,” for it has become impossible to suppose that any predication ever captures anything intrinsic about a material object without denying that material objects are necessarily related to at least one time (and place); that is, without denying something that is essential to materiality. The relational account has an alternative understanding of “intrinsic” close at hand. As for Lewis’s third objection, I think that the sting is taken out of it by the foregoing considerations: the relational theory of temporal predication seems less bizarre once we realize that it doesn’t render objects featureless or lacking intrinsic characterizations. What’s more, it captures something we want any theory of objects to capture, namely that it makes no sense to predicate anything of a material object without entailing that there is some time at which that predicate is instantiated. I conclude that Lewis’s concerns are not telling against the relational theory.

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Mellor

D. H. Mellor argues that the relational account of predication fails because:

… relations generally do not require the entities they link to share locations in space and time. My being taller than Napoleon, for example, is quite consistent with his dying before I was conceived; while my conception’s being later than his death positively requires it. (Mellor 1998: 93–4)

So, argues Mellor, “x is blue at t” cannot be a relation between x and t because if x is blue at t then x must exist at t but R(x, t) does not entail that x coexists with t. As a result, Mellor argues that predicates such as “x is blue” are monadic but that temporal predications must include a temporal operator, for example:

(8) At t: Fx.

If x changes from F to ~F, then:

(9) At t’: ~Fx.

For Mellor, the operator indicates the location of a fact (that x is F and ~F respectively). In this way, consistent descriptions of change are possible. As Mellor himself observes (Mellor 1998: 94), some relations do entail sameness of temporal location; his example is “x is simultaneous with y.” But, we should note, there are very many relations that entail temporal (and, in many cases, spatial) coincidence or overlap. Here are just a few examples: “x is in (physical) contact with y,” “x is above y,” “x is beside y,” “x is talking to y,” “x is at y,” and so on. So in some cases the fact that x stands in R to y entails that x and y overlap temporally; in other cases it does not. It is, therefore, hard to see why Mellor’s words in the quotation above count, in any decisive way, against the relational view of predication. What appears to be the case is that some relations are spatial- or temporal-overlap entailing and some are not, but that this difference is not the result of logical form. Mellor presents a response to this sort of challenge:

But it is no answer to say that changeable properties too are relations which entail this [i.e., sameness of temporal location]. For what makes [“a is F at t”] entail that a is located at t, if not the fact that, as I argued in §3, F’s being a non-relational property requires a to be located wherever and whenever a is F. (Mellor 1998: 94)

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This is an interesting suggestion, but ultimately fails as an argument against the relational view. The reason for this is that the argument in §3 to which Mellor alludes is that the gain or loss of any of x’s real properties must have its first effects on, in or at least near x:

The birth of another child to my parents is not a change in me, because its first effects are neither on nor near me … In short, real changes of properties need effects, and for them to be changes in the things to which we ascribe those properties, that is where their first effects must be. (Mellor 1998: 87–8)

Notice, however, that “e’s first effects are at/on x” (where e indicates an event that is a change in x) is a relational predicate, and if it can entail that e and x are co-located, then so can “x is blue at t,” or “x is green at t” entail that x and t are co-located. Perhaps Mellor has in mind that there is something about causation that does the essential work here, that is, that it is only because e is the effect of the gain or loss of a property of x that e and x are co-located. This does not strike me as plausible because causally disconnected events or objects can coincide or overlap. However, even if we accept this line of reasoning, nothing prevents the advocate of the relational account of temporal predication from helping herself to a similar story. That is to say, the relationalist can argue that it is because becoming blue has its first effects, say at t, on x that “x is blue at t” entails that x and t are co-located; this is fine and doesn’t change the fact that “x is blue at t” is a relational predicate.6

Mellor also makes the following, further point:

The causal test for properties is related to another one, namely that a thing’s properties should be detectable just by inspecting that thing. (Mellor 1998: 88)

However, as my argument above entails, there is no way to inspect something without inspecting it at some time or other. Hence, there is no way to detect anything about some object, x, independent of time. The fact that everything manifested by some object is manifested relative to a time in no way excludes the possibility of that object’s properties being detectable by inspection of that object alone. It is simply a mistake to treat relations to times as akin to relations to other objects in this respect. It makes perfect sense to suppose that a material object, x, is red independent of its relations to any other objects in the universe, that is, that it would still be red even if they did not exist; this may turn out to be physically impossible,7 but it is a coherent supposition.

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What is not coherent, however, is to suppose that x is red independent of its relations to time, for that would entail that x could be red even if there were never a time at which it is red (or that we could inspect it for color but not at a particular time), which is absurd.8

We can extend these observations to temporal operator accounts of predication in general. In indicating a temporal location, the operator “At t” in “At t: Fx” sets up a relation, in particular the relation of temporal co-location, between t and x, or between t and that fact that x is F.9 “At t,” in other words, indicates the time at which x is F. Since there will, in general, be some times at which x is F and some times at which it is not, the formula:

(8) At t: Fx.

will be satisfied by ordered pairs, <x, t>, of objects and times, which is another way of saying that (8) expresses a relation.10 There is simply no getting around it: temporary predicates, including A-predicates, are relational in form.11

The passage of time

I have argued that the relational account of temporal predication leads to a coherent and satisfactory account of change. If I am right, then change is compatible with a tenseless, or B-theoretic, world-view. It seems to me to follow from this that the passage of time is itself compatible with a tenseless, B-theoretic world-view. I propose the following: time passes if and only if first one thing (or a set of things) happens, then another. Temporal passage is, in other words, the ordering of events by the B-relation, “x is earlier than y.” People age and die, species arise and fall, fruit ripens and rots, and planets orbit stars. All of this is describable in the tenseless, relational view of temporal predication. Most authors who defend a tenseless, B-theoretic account of time, however, deny that time passes; for example:

It is clear, then, that we cannot talk about time as a river, about the flow of time, of our advance through time, or of the irreversibility of time without being in great danger of falling into absurdity. (Smart 1949: 485)

There is no real passage of time. What we refer to by “the passage of time” is an illusory feature of conscious experience. (Prosser 2007: 81)

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My present thesis would resolve the antinomy by rejecting the extra idea of passage as spurious altogether. (Williams 1951: 462)

There are many other examples one could mention (e.g. Smart 1963, 1980; Mellor 1981, 1998; Price 1996). I think that this is a mistake. We all have overwhelming evidence that time passes: I am now typing on a computer but earlier today I was not; I used to carry my daughter on my forearm but she is now too big for that; 25 years ago nobody had a smart phone while today they are ubiquitous; and so on. Accordingly, the denial of temporal passage lends unneeded credibility to the opponents of the tenseless, relational view of time. So the question I want to address next is: “Why do B-theorists reject the passage of time?”12

I think there are two reasons. The first is that many B-theorists accept McTaggart’s view that only the A-series can explain passage. Mellor, for example, writes:

One author, however, I will acknowledge: J. E. McTaggart, who proved the unreality of tense and of the flow of time. (Mellor 1981: 3)

What is wrong with McTaggart is not his attack on time’s flow but his view that change requires it. (Mellor 1998: 72)

Here we see a move from the tenseless view of the world (i.e., the denial of the tensed view) to the unreality of the flow of time. But such a transition can now be seen to be unnecessary and unmotivated. If the passage of time required monadic A-predicates, then there would indeed be no passage of time. But what authors such as Mellor overlook is the possibility of a tenseless, B-theoretic temporal passage to be equated, I argue, with the temporal ordering of events. The tenseless, B-theoretic world-view is one in which the sum total of events, objects, and processes is unchanging (which is why the extensions of temporal predicates are not temporally variable). This, however, is compatible with change:

… change is always variation in one thing with respect to another, the totality of absolute facts about those functional relations remaining forever constant. (Horwich 1987: 25)

Horwich is right: the existence of genuine change does not require the totality of facts to change with respect to time. Therefore, the passage of time does not require such change either. Michael Dummett disagrees:

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Now if time were real, then … there would be no such thing as the complete description of reality. There would be one, as it were, maximal description of reality in which the statement “The event M is happening” figured, others which contained the statement “The event M happened”, and yet others which contain “The event M is going to happen”. (Dummett 1978: 356)

The problem is that this argument presupposes that real change or passage requires absolute (i.e., non-relational) A-predicates to apply to events. Without this assumption, then what “M is happening” or “M is now” expresses is a temporally invariant relation between M and a particular time, and this relation is expressible at other times. As I have argued above, the non-relational account of A-predicates is untenable and I see no reason to cling to its ghostly apparition, that is, to the idea that without it nothing really changes. The second reason that B-theorists deny temporal passage is that they think of it as a kind of motion, a motion whose rate is indefinable. Here, for example, is Smart:

Contrast the pseudo-question “how fast am I advancing through time?” or “How fast did time flow yesterday?.” We do not know how we ought to set about answering it. What sort of measurement ought we to make? We do not even know the sort of units in which our answer should be expressed. “I am advancing through time at how many seconds per—?” we might begin, and then we should have to stop. What could possibly fill the blank? Not “seconds” surely. In that case the most we could hope for would be the not very illuminating remark that there is just one second in every second. (Smart 1949: 485)

A more recent variation is due to Huw Price:

Indeed, perhaps the strongest reason for denying the objectivity of the present is that it is so difficult to make sense of the notion of an objective flow or passage of time. Why? Well, the stock objection is that if it made sense to say that time flows then it would make sense to ask how fast it flows … Some people reply that time flows at one second per second, but even if we could live with the lack of other possibilities, this answer misses the more basic aspect of the objection. A rate of seconds per second is not a rate at all in physical terms. It is a dimensionless quantity, rather than a rate of any sort. (Price 1996: 13)

There is, however, nothing in the relational account of change that entails that temporal passage must be thought of as a kind of motion. Our

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language is perhaps a bit misleading here. We speak of the passage of time as though some single, individuated entity, Time Itself, is changing or moving, when in fact what is really going on is that changes occur within or with respect to time. So, “the passage of time” strikes me as a summary concept that refers to the ongoing processes of change that constantly occur, in order, with respect to time.13 The only thing all these processes have in common is that they involve events related by “is earlier than”; it is this relation and not the concept of motion that captures the essence of temporal passage. Suppose that a person begins the day with nervous energy, becomes stressed as the day progresses, and then feels a late afternoon bout of sadness before feeling happy and relieved in the evening. What could the rate of this change possibly be: so many moods per hour? Even if there is no answer to this question (perhaps moods are not divisible in the requisite way), it is obvious that this person has undergone various emotional changes over the course of the day. So, it is not essential that there be a well-defined rate of change in order for change to occur (and we certainly don’t need to know that there is such a rate in order to correctly conclude that change has occurred).14

In sum, passage needn’t be a kind of motion nor explained in terms of monadic A-predicates in order to be real. There is, therefore, no conflict between the tenseless, B-theoretic world-view and the reality of temporal passage.

On two rival views: Temporal parts theory and presentism

The relational view of temporal predication, change, and passage that I defend above differs in important respects from two popular philosophical theses: presentism and perdurantism. First, the relational view ontologically commits to more than one time (e.g. (4) above) which conflicts with the presentist proposition that, necessarily, all and only that which is present exists. Second, in the relational view, when an object changes it is numeri-cally the same object before and after the change—for example x in (4) above takes the same object as its value in both places—and this conflicts with the perdurance view that objects persist in virtue of having distinct temporal parts that are located at different times. Let me make a few brief remarks on presentism and perdurantism in turn. Arthur Prior sets up one of his many defenses of presentism by noting the need to make room for a concept of temporal passage:

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I believe that what we see as a progress of events is a progress of events, a coming to pass of one thing after another, and not just a timeless tapestry with everything stuck there for good and all. (Prior 1996: 47)

I have argued, however, that the relational view is perfectly consistent with genuine and objective change as well as temporal passage. So there is no need to appeal to the coming into (and passing out of) being of events to make sense of the passage of time. This is a good thing, for I consider such a process to be deeply mysterious. I also prefer a view that allows past and future times, objects and events to serve as the referents and truthmakers of propositions about the past and future, since this strikes me as the most straightforward way of making sense of thought and talk about the past and future (I discuss this issue in Mozersky 2011). The relational theory allows for all this. Others defend presentism on other grounds. For example, Craig (1998) argues that presentism is the only way to solve the apparent contradiction entailed by A-predication.15 The arguments above suggest otherwise. Others suggest that presentism is the common-sense view (Markosian 2004; Zimmerman 2008). Note, however, that the relational account defended above is based on the proposition that objects persist through change, then uses rather straightforward logical considerations to draw conclusions, including that the passage of time is real; I submit that there is little to offend common sense here. In short, by committing to the reality of change and passage, avoiding McTaggart’s contradiction and cohering with common sense, the relational view allows one to resist many of the arguments used to push one toward the presentist ontology. As I mention above, I take this to be a consideration in favor of the relational view. According to perdurance theory, on the other hand:

… change over time is the possession of different properties by different temporal parts of an object. (Hawley 2001: 12)

It is worth noting that in this kind of view the primary bearers of predicates are temporal parts of objects, not objects; x is F at t in virtue of having a temporal part, p, located at, and only at, t such that p is F. I find perdurance theories to be less extravagant than presentism—no mysterious coming into existence from nothing—but the former still incur the disadvantage of committing to entities, namely temporal parts, that are unfamiliar. Is the commitment to such entities necessary? Sider argues that one reason for believing in temporal parts is that it solves the puzzle of change:

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The temporal parts account of change is that incompatible properties are had by different objects, different temporal parts of the whole. Change is therefore no more remarkable than the variation of a road with some bumpy stretches and some smooth stretches. (Sider 2001: 93)

This is by no means the only or even the central argument Sider provides for a temporal parts ontology, but the relational view does remove a motivation for the view by providing an alternate account that has what I believe to be the distinct advantage that objects retain their strict, numerical identity as they change. Sider adopts “stage theory” according to which later temporal parts of an object, though numerically distinct from earlier ones, are the object at later times (they are temporal counterparts). So, he does not take perdurantism to be the denial that objects persist. However, as the quotation above makes clear, his view is still the denial that there is a single material object involved when, say, an apple changes color. Hence, his view does, I think, retain a curious consequence that the relational theory avoids. Again, I see this as an advantage of the relational view, which does not move us to reinterpret our ordinary way of thinking about persistence in terms of numerical identity; a way of thinking that is, I think, reinforced regularly by our interactions with the world. I take it that the foregoing considerations suggest that the relational view retains a comparative advantage over presentism and perdurantism as a result of its relatively minimal metaphysical and revisionary commitments. It is, in short, an economical, plausible, and satisfactory account of change, persistence, and passage that lacks the drawbacks of its competitors and ought, therefore, to be preferred to them.

Conclusion

A seemingly simple question about the nature of temporal predicates, answered through a consideration of the puzzle of change, has led to a number of interesting conclusions. First, that any predicate of a material object that indicates a changeable feature of that object expresses a relation between the object and a time. Second, that the logical form of predications of time, tense, and change is tenseless. Third, that the passage of time is real and also tenseless, describable by relations whose extensions are temporally invariant. In sum, in so far as one believes in genuine change and temporal passage, one should accept the tenseless, B-theoretic world-view.16

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Notes

1 For simplicity I shall let two-place predicates stand for relational predicates in general; the difference between two-place and higher-order relational predicates is of no relevance here.

2 Following McTaggart, I will assume here that A-predicates order a set of events as an A-series; B-relations order a set of events as a B-series.

3 Savitt (2002) also points out the need to distinguish properties of a representation from properties of that which is represented.

4 What about abstract objects, such as geometric squares? Wouldn’t they have shape but not at any time? I think that the right thing to say is that geometric squares don’t have shape but, rather, are shapes. If, however, one were to insist that they have shapes, such shapes are essential to their objects and so cannot be temporary intrinsics and hence cannot be implicated in the puzzle of change.

5 Thanks to Donald Baxter for raising this issue.

6 Temporal parts theories (more on these below) explain how an object, x, is, say, red at t, by positing the existence of a red temporal part, p, that is located at t. Such accounts are, therefore, committed to the idea that some relations are existence entailing and are not, accordingly, in a position of relative advantage over the relational view with respect to the issue of explaining what it is for an object to exist/be located at a time.

7 It is possible, for example, that physics will discover that being red involves molecules on the surface of an object entering into quantum entanglement with particles on the far side of the galaxy.

8 It might be argued that the phenomenal form of temporal predicates such as “x is red” is monadic, expressing a non-relational property of the apple. Perhaps, but I have doubts. First, I am convinced by the foregoing that for an apple to be red is for it to stand in relation to time; so, when we notice an apple, we notice something that is related to time. Second, for an observer to notice the color of an apple is for her to stand in relation to time, so the experience itself is best understood as a relation between an observer and a time. I doubt, therefore, that there is a monadic phenomenal predicate or property available. Suppose, however, that there is. Then what follows, I think, is that this predicate constitutes an incorrect representation of the apple (rather than, say, of the experience of the apple). If our experience of the apple convinces us that “x is red” is non-relational, then our experience is, I believe, misleading. I am willing to accept that experience is misleading in this way, but I don’t think it gives us any reason to doubt the relational account of temporal predication anymore than the fact that experience convinces us that the sun rises gives us reason to doubt the heliocentric model of the solar system. Thanks to Nathan Oaklander for suggesting I clarify this point.

9 Indeed, it is hard to think of a more paradigmatically relational term than the preposition “at.”

10 If times are substantive entities whose existence is independent of that of any events, then B-relations relate substantive entities in general. If times

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are simultaneity classes of events, then B-relations will typically relate classes, though in some cases they will relate substantive entities such as objects to such classes. Either way, the logical analysis above goes through since the logical form of the relations is permissive with respect to the kinds of entities that satisfy them. Thanks to Nathan Oaklander for suggesting I clarify this.

11 Could temporal operators be functions from propositions to truth-values? Perhaps, but in that case propositions lack truth-values when considered independently of time. In other words, it would be impossible to express something determinately true or false about a material object’s properties without reference to time, in which case the essential features of the relational account will transfer.

12 Notable exceptions include Beer (1988) and Oaklander (1984, 2004). What follows is in broad agreement with these works; indeed, it is very much indebted to them.

13 In this respect, it is like the term “natural selection,” which is a general phrase that refers to the processes by which inherited traits result in differential rates of survival and reproduction in a given environment; there needn’t be any single process that occurs in all cases.

14 My principal goal in the foregoing is to defend the notion of temporal passage without appeal to monadic A-predicates or the concept of motion. Accordingly, I identify the passage of time with the existence of B-relations between times and events. Since B-relations share a logical form with other tenseless relations, such as “x is red at t,” it might be thought that my account is incomplete for it lacks an explanation as to what differentiates B-relations from other logically similar relations such that the former but not the latter determine that time has passed. At least part of what is required here is an account of the direction of time. One of the ways in which B-relations differ from, say, color relations is that the former are directed. Now, this is not the place to outline an account of the direction of time, but I think the view defended above has the strength of being compatible with various accounts of direction: however one fills in the theory of temporal asymmetry, the logical form of temporal relations will remain as outlined above (the pairs related by B-relations are ordered pairs, after all). Indeed, I think the account here is compatible with all manner of ontological views on the nature of B-relations, from nominalism—that is, the view that relations are identified with sets of ordered pairs—to more robust views in which the B-relation has ontological standing in addition to the relata. If, say, nominalism is correct, then it is an ontologically basic fact that some entities are ordered by the asymmetric “x is earlier than y” relation and others are not; nothing will be added by positing the existence of a relation in addition to the ordered pairs. Indeed, perhaps the asymmetry of the relation is primitive as well. If, on the other hand, an ontology that recognizes relations in addition to the relata turns out to be the best account of the temporal asymmetry, then the logical structure of the account defended above will not be overturned. So, I think that whichever way these debates turn out, the essence of the relational account can be preserved. Thanks to Nathan Oaklander for bringing these issues to my attention.

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15 To be precise, Craig defends the claim that only presentism can solve McTaggart’s paradox within the context of a tensed theory of time. He rejects a relational solution in part because it leads to a tenseless theory. I think, however, that his approach puts the cart before the horse: let us first give the best account of change and persistence and only thereafter worry about whether the world is tensed or tenseless, rather than accepting or rejecting solutions to the puzzle of change on the basis of a position on the tensed–tenseless debate. I recommend this in part because metaphysical theses such as presentism are substantial: they ask us to believe that events come into existence from nothing and then pass back into nothingness; they ask us to believe that propositions about the past can be true even if nothing past is real; and so on. Better, I propose, to solve philosophical puzzles prior to taking on such commitments, if at all possible.

16 Some of the material from this chapter was presented at Queen’s University, the University of Connecticut (Storrs), and a meeting of the Pacific Division of the American Philosophical Association. I would like to thank audience members, my APA commentator, Michael Tooley, and L. Nathan Oaklander for their suggestions and comments.

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Temporal Predicates and the Passage of Time