The Argument from

Transtemporal Relations

A dissertation submitted to

the University of Manchester

for the degree of

Master of Research

in the faculty of Humanities

2012

Benjamin Scott Harrison

School of Social Sciences

2

Acknowledgements

I am very grateful to Chris Daly for his supervision and comments on drafts of this paper.

3

Number of Words: 17, 651

Contents

Abstract

1. Transtemporal Relations 2. The Problem of Singular Propositions 3. The Truthmaker Objection 4. Mark Hinchliff’s Unrestricted Presentism 5. Span Tense Operators and Berit Brogaard’s Irreducibly Tensed Relations 6. Craig Bourne’s Future for Presentism 7. Roderick Chisholm’s “Overlapper” Solution 8. John Bigelow’s Relational Properties Solution 9. Theodore Sider’s Quasi Truth

10. Conclusion

Appendixes

A. Declaration B. Intellectual Property Statement

4

In this paper, I examine the argument from transtemporal relations. The argument has been discussed frequently in recent literature and the solutions available to presentists are great in number. I survey the majority of these solutions in an attempt to identify the strongest on offer. I conclude that unified solutions to the problem come at a high price. However, careful consideration of each type of transtemporal relation permits stronger partial solutions.

5

I begin this paper by examining the argument from transtemporal relations in some detail . I dis-tinguish the argument from two similar objections to presentism, namely the argument from singu-lar propositions and the truthmaker objection – . The majority of the paper examines current solutions to the problem – . In light of the various types of transtemporal relations, I conclude that unified solutions come at a high price. However, careful consideration of each type of tran-stemporal relation permits stronger partial solutions.

Transtemporal Relations Presentism is the thesis that everything is present. More formally, it is the thesis that

(x)(x is present) Some philosophers claim that the universal quantifier here is unrestricted such that, for every x, x exists at the present time (e.g. Crisp , ). However, this view is unneces-sarily strong. If the universal quantifier is left wide open, it follows that, if abstracta exist, abstracta exist at the present time. Later on in this paper we will see that some presentists might want to deny that abstracta exist in time. For this reason, we should restrict the quantifier to temporal objects. We should understand presentism as the thesis that, for any x that exists in time, x exists at the present time.

This is in contrast to eternalism, the view that all things past, present and future share the same metaphysical status, such that all things that once were, and all things that will eventually be, are as real as the things that exist right now. According to eternalism, dinosaurs, ancient philosophers and human colonies on Mars (should there ever be any), all exist in the same way that we do.

Not only is presentism supported by our intuitions regarding the nature of time, it also provides a simple solution to the problem of temporary intrinsics, which arises be-cause past property instantiations are often incompatible with present property instantia-tions. Suppose a chameleon changes its colour from green to pink such that it instantiates the properties being green all over and being pink all over. As nothing can be both green all over and pink all over, we appear to have a contradiction. In response to the problem, the presentist simply denies that past property instantiations are real. The chameleon pres-ently instantiates being pink all over and no longer instantiates being green all over. The chameleon has just one of the two contradictory properties and the contradiction disap-pears. (See Hinchliff ( , ); Merricks ( , ); Zimmerman ( , ) for dis-cussions of presentism in light of the problem of temporal intrinsics).

In this paper, I defend presentism against the argument from transtemporal rela-tions. To understand why transtemporal relations pose a problem for presentism better, we must first introduce the following principle to govern all relations:

(RP) Necessarily, for any relation R, if R is an n-placed relation that holds between

x , x , …, xn then x , x , …, xn must exist. (RP) says that the relata of any given relation must exist and, as such, is thought to be true (see Bigelow , ; Crisp , ; Davidson , ). Furthermore, I will call a rela-tion transtemporal when its relata exist at different times such that, if an entity x bears the

6

relation R to another entity y at a time t, R is a transtemporal relation if and only if y does not exist at t.

The problem for presentism is as follows. If all entities in time presently exist, then it follows from (RP) that all relations in time hold between presently existing entities. In other words, there are no transtemporal relations. But, as we shall see, there are various types of transtemporal relations and so presentism is false. (See Adams ( , – ); Bigelow ( , – ); Bourne ( , ff.); Crisp ( , – ); De Clercq ( , ); Sider ( a, – ) for discussions of this argument in recent literature.)

For instance, transtemporal intentional relations occur when people think about past entities in a certain way. Suppose that the aspiring philosopher Ned is thinking about the deceased Aristotle as a great philosopher. We might express this with the following Moorean proposition:

( . ) Ned admires Aristotle.

A Moorean proposition is a proposition whose truth we cannot deny. If Ned is genuinely full of admiration for Aristotle, we know that ( . ) is true with the utmost certainty. What is more, the most natural reading of ( . ) predicates a relation of admiration to both Ned and Aristotle, such that

( . *) Ned bears the admires relation to Aristotle The admires relation in ( . *) is transtemporal because its relata, namely Ned and Aris-totle, do not co-exist. Ned exists in the present while Aristotle, if he exists, exists in the past. Like admiration, other intentional relations of fear, love, jealousy, and so on are also transtemporal when people direct their thoughts towards something that exists in either the past or the future. However, the conjunction of (RP) and ( . *) entails that both Ned and Aristotle exist, that is, because a relation obtains between them and the relata of any relation must exist. But if Aristotle exists then presentism is false since presentism denies the existence of all past entities, including Aristotle.

– . He points out that either ( . ) is synonymous with ( . *) or it is not. If not, the presentist can accept ( . ) without accepting the troublesome ( . *). If it is, ( . ) is not Moorean as ( . *) entails the proposition that Aristotle exists. Since we cannot be sure that Aristotle exists, ( . *) is not Moorean and so neither is ( . ).

This does not seem like a good argument to me. It is the conjunction of ( . *) and (RP) that entails the proposition that Aristotle exists, not ( . *) alone. Even so, philoso-phical analyses of Moorean propositions, if informative, will provide propositions of a different epistemic status. Without further argument, we have no reason to think that ( . ) is Moorean if and only if ( . *) is Moorean.

In addition to transtemporal intentional relations, there are also transtemporal com-parative relations, causal relations and semantic relations for the presentist to contend with:

( . ) Elizabeth II has fewer fingers than Anne Boleyn. ( . ) Today’s flood was caused by yesterday’s downpour. ( . ) The proper name “Socrates” refers to the man Socrates.

7

Taking a natural reading of ( . ), the comparative relation having fewer fingers than occurs in ( . ) and obtains between Elizabeth II and Anne Boleyn. (RP) tells us that Anne Bo-leyn must therefore exist but since she is a past entity, presentism is false. Similarly, if ( . ) and ( . ) are true then the past event [yesterday’s downpour] and the past entity Socrates must exist; that is, if the present event [today’s flood] and the present linguistic token “Socrates” are to bear the is caused by and refers to relations to them, respectively. There are, of course, other transtemporal relations than those mentioned here—we shall consider a fifth later—but ( . ) through ( . ) are sufficiently varied for us to work with.

The Problem of Singular Propositions Before we begin to consider any responses to the argument from transtemporal relations, I think it is important to distinguish the argument from two similar problems for presen-tism. In this section, I consider the problem of singular propositions. In the next, the truthmaker objection.

Consider the following singular proposition (singular because it is about Socrates in particular):

( . ) Socrates was wise.

If we accept the Russellian view that singular propositions depend for their existence on the entities they are about, this raises the question of what, along with the property being wise, constitutes this proposition; that is, assuming presentism is correct and Socrates does not exist. (See David ( ) for a recent discussion of Russellianism about singular propo-sitions.)

Theodore Sider suggests the following paraphrase of ( . ):

( . *) P(x)(x is called “Socrates” & x is wise) where P is a past tense operator that reads, “it was the case that” ( , ; see also Bourne , ; Markosian , – ). Whereas ( . ) has Socrates as a constituent, ( . *) is a general proposition that only contains the qualitative properties, being called Socrates and being wise. Moreover, as the particular quantifier falls within the scope of the past tense operator, the particular quantifier is not “existentially committing” (Sider ,

; see also Prior , – ). This is important since the presentist does not want to say that the x called “Socrates” exists.

Some of this should feel familiar because it is similar to Bertrand Russell’s solution to the classic problem of reference to the nonexistent (see Russell , ). Russell held the view that proper names like “Batman” are actually disguised definite descriptions like “the crime fighting superhero from Gotham City” (his descriptivist theory of names). Moreover, Russell thought that the logical form of a sentence containing a definite de-scription is the conjunction of an existence claim, a uniqueness claim and a universal claim (his theory of descriptions). If we combine both theories, the true logical form of the proposition <Batman is fearless> is

8

( . ) (x)(Fx & (y)(Fy x = y) & Gx) where F is the property being a crime fighting superhero from Gotham City and G is the property being fearless. More colloquially, ( . ) is the proposition <there is at least one entity called ‘Batman’, there is at most one entity called ‘Batman’ and that entity is fear-less>.

Nevertheless, the problem of transtemporal relations is still a problem for the Rus-sellian presentist (pace Bourne , – ). The Russellian presentist can attempt to paraphrase ( . ) as

( . ) (x)(y)(Qx & (z)(Qz z = x) & Wy & (w)(Ww w = y) & Rxy &

x y)

where Q is the property being the present Queen of England, W the property being the second wife of Henry VIII, and R the relation having fewer fingers than. ( . ) does not make any direct claims about past and therefore nonexistent entities. However, ( . ) still entails the propositions that there exists a y that is the second wife of Henry VIII and, as we know, there is no such present thing.

What is more, the past tense operator that allowed the Russellian presentist to avoid this problem when dealing with singular propositions cannot offer any reprieve here. She might use the operator in two ways and neither are acceptable (following Sider a,

). One option is to embed the entire proposition within the scope of the operator:

( . ) P(x)(y)(Qx & (z)(Qz z = x) & Wy & (w)(Ww w = y) & Rxy &

x y) But what is being said in ( . ) is that there is a past time at which both Elizabeth II and Anne Boleyn exist—and the Queen is certainly not that old. Alternatively, she might embed just one of the particular quantifiers within the scope of the operator:

( . ) (x)((Qx & (z)(Qz z = x)) & P(y)(Wy & (w)(Ww w = y) & Rxy &

x y)) This solves the problem of existence as Elizabeth II is now only said to exist in the pre-sent, but the transtemporal relation itself, Rxy, still falls within the scope of the tense operator and this does not seem quite right. ( . ) expresses a present truth whereas ( . ) expresses a past truth. It states that Elizabeth II had fewer fingers than Anne Boleyn at some past time (Sider a, ). Note that the Russellian presentist cannot place the relation outside of the tense operator either because the second relatum, namely y, would become an unbound variable since the particular quantifier binding y lies within and not outside the scope of the operator. In my view, this is a serious problem because, although it was true that Elizabeth II had one fewer finger than Anne Boleyn yesterday, several days ago and indeed any time at which Elizabeth II existed, it is fewer clear to my mind that ( . ) was true before Elizabeth II existed, that is, including all times at which Anne Boleyn existed. This is so for as long as we hold an indeterministic view about the future. In which case, at all times before Elizabeth II existed, it was indeterminate whether

9

<Elizabeth II has ten fingers> was true and thus indeterminate whether ( . ) was true. ( . ) is therefore an unacceptable paraphrase of ( . ) as well.

Despite this, Russellian presentists are well placed to address the problem of tran-stemporal relations. This will become more apparent in later sections. Suffice it here to say, all presentists must explain why ( . ) through ( . ), in addition to being inconsistent with (RP), appear to be propositions that are constituted, in part, by past entities. To make this clearer, consider an alternative solution to the problem of singular propositions, that singular propositions about past entities contain blanks (see Markosian , – ). The general idea is that whereas propositions about present entities contain those entities as constituents, propositions about past entities are “unfilled” (Braun , ). The trouble with this solution is that the sentence “Socrates was wise” now expresses the same proposition as, for example, “Gandalf was wise”, namely the proposition < ––– was wise>. This does not seem right. Socrates really was wise; Gandalf is fictional. For the same reason, we do not want to say “Ned admires Aristotle” expresses the same proposi-tion as “Ned admires Gandalf”. (Markosian does not hold the view that propositions about past entities are unfilled but suggests it following the work of, among others, Adams and Stecker ( ), Braun ( ) and Salmon ( ) on the problem of empty names.)

Suppose we do not want to be Russellians about propositions. Will this help the presentist solve the problem of transtemporal relations? Crisp considers this possibility. He suggests the idea that propositions might outlive their constituents ( , ; following Plantinga ). With this approach, ( . ) is true just in case Socrates once existed and was wise. This does not require Socrates to exist in the present. But, as Crisp notes, this will not help to avoid the argument from transtemporal relations. Even if propositions about Russell exist in his absence, ( . ) is such that a relation is currently being held to Russell and (RP) says that if something stands in a relation to Russell then Russell must exist. For the remainder of this paper I will assume that Russellianism about propositions is true.

There are other problems for Russellian presentists, however, and it worth consid-ering them before we move on. The first is Saul Kripke’s rigidity argument (see Sider

, ; Bourne , ). Kripke objects to the descriptivist theory of names because of its behaviour in modal contexts ( ). Consider that

( . ) Necessarily, Socrates is Socrates.

is a tautologically true, whereas

( . ) Necessarily, Socrates is the Greek philosopher that drank hemlock.

is false. ( . ) is false because, in another possible world, Socrates did not commit suicide by drinking hemlock. This is problematic because, intentional contexts aside, the truth value of a proposition should always remain the same when one synonym is replaced by another (Quine , ). Craig Bourne points out that the same consequences occur in temporal contexts as well ( , ). For instance, if the tallest person in the world is called “Billy”, then it is true that

( . ) Billy was two feet tall.

but false that

10

( . ) P(x)(x is the tallest person in the world & x is two feet tall) ( . ) is false because there is no past time at which the tallest man in the world measured up at just two feet tall, where “the tallest man in the world” is read de dicto (of the word) and not de re (of the thing), such that “the tallest person is the world” picks out whoever happens to be the tallest person in the world at that time, that is, rather than Billy, who is the tallest person in the world at the present time. Thus, in both modal and temporal contexts, proper names do not appear to function as definite descriptions.

The obvious response is to deny de dicto readings of definite descriptions in modal and temporal contexts and opt for de re readings instead (Bourne , – ; De Clercq , ). In this way, definite descriptions are rigid. They denote the same entity x in all possible worlds in which x exists (in all x-worlds) and at all times at which x exists. They can then be substituted salva veritate with proper names. Consider that the de dicto reading of “the British Prime Minister is a conservative” says that the British Prime Minister, whoever he happens to be, is a conservative. Whether or not this ex-presses a true proposition will depend on the time and place of its utterance. The de re reading, however, says of the current British Prime Minister, namely David Cameron, that he is a conservative. Read de re, the sentence expresses the proposition <David Cam-eron is a conservative>. Thus, read de re, “the Greek philosopher that drank hemlock” and “the tallest man in the world” can be substituted salva veritate with “Socrates” and “Billy” respectively:

( . *) Necessarily, Socrates is the Greek philosopher that drank hemlock in the ac-

tual world.

( . *) P(x)(x is the tallest man in the world in & x is two feet tall)

So much for Kripke’s rigidity argument. However, to my mind, there is a second problem facing Russellian presentists. To begin with, I want to follow a famous example from Keith Donnellan ( ). Suppose I ask, “Who is the man in the corner that is drink-ing ale?” Further suppose that the man is actually drinking wine. Since the man that I intended to denote fails to satisfy my universal claim—the claim that the man in the corner is drinking ale—no one should rightly know what I am asking about. I am here waiving concerns about the uniqueness condition. There are indeed legitimate concerns regarding the uniqueness condition because it is so often false (see Strawson , –

). In this case, the claim <there is at most one man in the corner> might have been false had another man been stood in the same corner. However, as nothing in my argu-ment turns on the uniqueness claim, we need not pursue this any further. In any case, my question seems legitimate so how do we explain this? Donnellan thinks that, despite my inaccuracy, I have successfully referred to the man drinking wine; I have used the definite description referentially, that is, not to denote the man that satisfies the definite descrip-tion, the attributive use, but to refer to the man that I intended (and failed) to denote.

Still unaware of my mistake, the next day I ask, “Who was the man in the corner drinking ale last night?” Once again, I have failed to denote the right man. He was drink-ing wine. Much to my regret, however, he drank too much wine and died from alcohol poisoning. It seems to me that the Russellian presentist is now in trouble. She cannot fall back on the referential use because the man drinking wine does not presently exist—he

11

does not exist at all and thus cannot be referred to. As Kent Bach notes, “one cannot successfully use a definite description referentially to refer to [a] nonexistent entity”. He continues, “One could try to use ‘the man in the moon’ referentially… but one could succeed only if there were a man in the moon” ( , ; emphasis in original). Yet it would seem that my intention was to refer; in particular, to that man, whether he satisfied my description or not. It was not to ask about the man that just so happened to be drink-ing ale last night, which is how we must understand the attributive use.

In this section, I have shown that the problem of singular propositions is distinct from the problem of transtemporal relations. Presentists can be Russellians about singu-lar propositions but even Russellian presentists struggle to explain transtemporal rela-tions. I have also shown that Russellian presentists are at odds with definite descriptions used referentially to refer to past entities. In the next section, I distinguish the arguments from transtemporal relations and singular propositions from the truthmaker objection.

The Truthmaker Objection

Truthmaker theorists claim that presentists cannot ground true propositions that refer to past entities. This, the so-called truthmaker objection assumes the following principle:

(TM) For any true proposition <p>, there exists some entity e such that <p> is true in virtue of e.

which says, for every truth, there is something in reality that makes it so. It is not clear what best qualifies as a truthmaker. Some favourites include particularised properties, states of affairs and entities that instantiate properties. Suppose they are particularised properties. Following (TM), truthmaker theorists will say that the particularised prop-erty Socrates’ wisdom is a truthmaker for ( . ) as ( . ) is true in virtue of Socrates’ wisdom. However, Socrates’ wisdom does not exist according to the presentist; neither do states of affairs involving Socrates nor Socrates himself for that matter. Lacking a truthmaker, ( . ) must therefore be false. But since ( . ) is true, presentism must be rejected. (Both Arm-strong ( , ff.) and Sider ( a, – ) advance this argument. For various presen-tist responses, see Sanson and Caplan ( ; ).)

Whereas the problem of singular propositions turns on what constitutes past propositions, the truthmaker objection turns on what makes past propositions true. Note that these need not be the same thing. Although Socrates is a truthmaker for

( . ) The Greek philosopher that drank hemlock was wise

he does not figure as a constituent because ( . ) is a general proposition. Consequently, presentists that paraphrase singular propositions as general propositions must still offer an account of what makes them true. Even though Socrates is not a constituent of ( . ), it seems that he must still exist as its truthmaker.

Truthmaking has received its fair share of criticism over recent years for being too stringent. How could negative truths like <there are no penguins in the room> be true in virtue of something rather than the absence of something? (See Liggins ( ; forthcom-ing) and Schneider ( ) for this and other problems.) Nevertheless, (TM) gets some-thing right in so far as it attempts to ground truth in reality and it is this that causes

12

problems for presentism. To make this clearer, note that presentism is also inconsistent with the alternative thesis that truth supervenes on reality (Liggins , – ). Briefly, if truth supervenes on reality then, for any true proposition <p> and any two possible worlds, if <p> is true in one world and not the other then something exists in one world and not the other. Now consider two possible worlds with different histories that con-verge on the present. Suppose that a proposition about the past is true in one but not the other. If presentism is true, both worlds share the same ontology and thus nothing exists in one world that does not exist in the other. From this, we can conclude that truth does not supervene on reality if presentism is true.

A popular means of avoiding the truthmaker argument is to ‘enrich the present’ in-ter alia with past-tensed states of affairs like [Socrates was wise] (see Sanson and Caplan

, ). Armed with past-tensed states of affairs, the presentist is well equipped to provide truthmakers for past truths like ( . ). Even so, it should be immediately clear that an enriched present would not remove the problem of transtemporal relations in so far as transtemporal relations obtain between relata that exist at times other than the present. Nevertheless, an enriched present does open up some options for the presentist. For instance, some presentists enrich the present with the haecceities of past individuals (e.g. Adams ). These uninstantiated haecceities are the constituents of propositions about past entities. What is more, they are able to stand in relations to present entities. I will consider this in more detail later.

. Mark Hinchliff’s Unrestricted Presentism Perhaps the most obvious response to the problem of transtemporal relations is to reject (RP). If relations are not existence entailing, the presentist should have no trouble dealing with transtemporal relations.

Property presentism =df necessarily, for any entity x: (a) if x exists in time, x exists at the present time and (b) if x instantiates a property or stands in a relation at the present time, x exists at the present time.

Unrestricted presentism =df necessarily, for any entity x: (a) if x exists in time, x exists

at the present time but (b) for at least one entity x, x instantiates properties or stands in relations at a time t and x does not exist at t.

Presentists wanting to deny (RP) must deny property presentism. Those that do are known as unrestricted (or less favourably) frivolous or non-serious presentists.

The unrestricted presentist thinks that entities can stand in relations at times at which they do not exist, that is, at times other than the present. Mark Hinchliff, some-times cited as the only unrestricted presentist, writes, “For every property an individual had in the past, there is a corresponding complex property, which that individual has in the present” ( , ; see also Hinchliff , fn. ). For example, if something once instantiated the property being blue then it now instantiates the property having been blue. In a similar vein, Nathan Salmon states that “Socrates does not exist in my present cir-cumstance, yet he has numerous properties here—for example, being mentioned and discussed by me” ( , ).

13

Some philosophers note that unrestricted presentism yields counterintuitive results (e.g. Crisp , ; Markosian , ). It seems very strange to say that Ned admires Aristotle if there is also nothing that Ned admires. And it is no less strange to compare Elizabeth II with Anne Boleyn if there is nothing to which she is being compared; or to say that yesterday’s downpour caused today’s flood if there is nothing that caused today’s flood.

Hinchliff explains that this as a consequence of our firm belief that “predication is connected to quantification… [and] what is in the domain of quantification exists” ( ,

). He calls this the triangle argument for property presentism, which we can express as follows (following Inman , ):

( ) If <Fx> is true, then there is something that is F. ( ) If there is something that is F, then there exists something that is F. ( ) Therefore, if <Fx> is true, then there exists something that is F.

In order to reject ( ) and therefore property presentism, the unrestricted presentist must reject either ( ) or ( ). “To deny property presentism and keep the other connections in place produces incoherence,” says Hinchliff ( , ). This has led philosophers to believe that unrestricted presentism entails Meinongianism, as the Meinongian infa-mously rejects ( ) (see e.g. Crisp , ; Keller , ). The Meinongian thinks that it is possible to quantify over something without taking it to exist; that is, when an object subsists but does not exist. The Meinongian presentist accepts that ( ) is true. She accepts that there is something, the subsisting Aristotle, that Ned admires, but she denies that the subsisting Aristotle exists. There are some things that do not exist.

Meinongianism, however, is a theory long out of favour. It faces universal rejection, in no small part, because of Russell’s criticisms. Russell thought that nonexistent entities infringe the laws of non-contradiction and excluded middle both ( , – ). The round square, if it subsists, is both round and square, and thus round and not round, which is a contradiction. And, by the law of excluded middle, either <the present King of France is bald> or <the present King of France is not bald> is true, but if the present King of France is nonexistent then surely he is neither. Russell also felt that his theory of descriptions offered a far superior solution to the puzzle of reference to nonexistents. (See Smith ( , ff.) for a detailed discussion of Russell’s objections to Meinongian. Quine also thought that Meinongianism ruins our sense of reality because it is “a breeding ground for disorderly elements” ( , ).)

Whether these objections are a problem for Meinongian presentism in addition to straight Meinongianism remains to be seen. In my view, the Meinongian presentist need only include a subset of nonexistent entities in her ontology, namely the set of entities that once existed. The Meinongian presentist has no reason to countenance the troublesome round square or the present King of France.

Simon Keller suggests that Meinongian presentism in particular is untenable ( , – ). As he sees things, Meinongian presentism is indistinguishable from eternalism

because, on the former view, existence is a mere label. Just like eternalists, Meinongian presentists claim that past entities instantiate properties. Unlike eternalists, Meinongian presentists claim that those past entities do not exist; they subsist—“but so what?” Keller

.

14

Keller seems to think that the Meinongian is not entitled to the distinction between existence and subsistence. However, Keller also appears to be working under the assump-tion that objects subsist in the past. Subsisting objects might be atemporal instead. Thus, the difference between existence and subsistence would be more than just a label. For one, it would concern the nature of entities as existing in time.

Alternatively, the unrestricted presentist might deny that her rejection of ( ) com-mits her to Meinongianism after all, with neo-Meinongianism (or noneism) being the alter-native. Graham Priest, a recent champion of noneism, argues that

the particular quantifier (being the dual of the universal quantifier) should not be read as ‘there exists’—or even ‘there is’, there being no difference between being and exis-tence; it should be read as some leaving it open whether the some in question exist or not

( , ; emphasis in original). On this view, if something is (in any sense of the word) then it exists. Thus, the neo-Meinongian presentist does not think there are (in any sense of the word) past entities. Nevertheless, this is no barrier to their instantiating properties and standing in relations in the present. Similarly, Richard Routley argues that there are two kinds of quantification ( , – ). There is existentially loaded quantification, which should be understood as saying “there exists”, and neutral quantification to be understood as being equivalent to Priest’s “some”.

If one is willing to accept neo-Meinongian quantification, then unrestricted presen-tism offers a novel solution to the problem of transtemporal relations. But, whether justified or not, I imagine most philosophers will follow William Lycan in holding the view that “it is literally gibberish or mere noise” such is its distance from the norm ( ,

; emphasis in original).

. Span Tense Operators and Berit Brogaard’s Irreducibly Tensed Relations

Earlier we saw that the Russellian presentist was unable to make effective use of the past-tense operator in her paraphrases. Recall that that in ( . ) the relation between Elizabeth II and Anne Boleyn fell within the scope of the tense operator, such that it obtained at a time when Anne Boleyn existed. The Russellian presentist might object to our reading of the tense operator in ( . ). She might insist that <Pp> should not be read as “<p> is the case at one instant of past time”, that is, as a slice operator, but rather as “<p> is the case at some interval of past time”, as a span operator (see Lewis , ; Sider a, – ). Where sPan is our past-tense span operator (from Bourne ( )), ( . ) would then be paraphrased as:

( . ’) (x)(x is called “Elizabeth II” & sPan(y)(y is called “Anne Boleyn”, & x has fewer fingers than y))

In ( . ’), the has fewer fingers than relation does not necessarily obtain at some particular instant at which Anne Boleyn existed. The relation occurs in the past but it is left open just how far. Before we consider some objections to the use of span tense operators, I

15

think it is worth noting that even ( . *) does not say that Elizabeth II presently has fewer fingers than Anne Boleyn; so presentists looking for an accurate paraphrase of ( . ) may well be disappointed.

David Lewis argues, twofold, that span tense operators “create ambiguities even when prefixed to a sentence that is not itself ambiguous” and make truths of contradic-tions on certain disambiguations ( , – ).

( . ) sPan(x)(y)(x is called “Socrates” & y is called “Kant”) ( . ) sPan(it is raining and it is not raining)

( . ) is ambiguous between “Socrates existed at some instant of past time, and Kant ex-isted at another instant of past time” and “Socrates and Kant existed at the same instant of past time”. The former expresses a true proposition whereas the latter expresses a false proposition. On the other hand, ( . ) contains the contradiction <it is raining and it is

as, “it was raining at one instant of past time and it was not raining at another instant of past time”.

These problems should not faze the presentist. She can disambiguate both sen-tences by reemploying slice operators in addition to her new span operators (see Bourne

, ; Brogaard , ).

( . ’) sPan(x)(y)(x is called “Socrates” & y is called “Kant”) & ~P(x)(y)(x is called “Socrates” & y is called “Kant”)

( . ’) is the proposition that Socrates and Kant existed at some interval of past time, and Socrates and Kant never existed at the same instant of past time. If ( . ’) was not the desired meaning of ( . ), and the desired meaning was indeed that Socrates and Kant coexisted, then the presentist should simply replace the span operator in ( . ) with a slice operator. Similarly, if ( . ) is supposed to be a contradiction, replacing the span operator with a slice operator will achieve this.

A second objection comes from Sider, who argues that presentism is simply incom-patible with propositions that involve span tense operators as they constitute past excep-tions to presentism ( a, ). We can understand a past exception to presentism as the claim that

( . ) P(x)(x exists in time & x is not present)

that is, as the claim that, for some x, x exists in time and x is not present. But presentism is thought to be a necessary thesis, such that, necessarily, for any entity x that existed in time, x existed in what was, then, the present time. Therefore, the presentist cannot make use of span tense operators.

It is not clear to me that this argument succeeds. Sider rightly points out that ( . )

is true because its component (x)(y)(x is called “Socrates” & y is called “Kant”) “is true of many spans of time in the past”. He continues, “since there is no one instant at which Kant and Socrates exist, this component… constitutes a violation of the presentist doc-trine that there cannot exist non-present things” ( a, ). This is a non sequitur in my view. Sider appears to make the error of thinking that if something is true of an interval of

16

past time then it is true at an instant of past time within that interval (see Brogaard ,

). In order for (x)(y)(x is called “Socrates” & y is called “Kant”) to entail ( . ), it must have been true at some particular slice of past time. Naturally, the presentist denies that there is any such truth. She only accepts its being true of a region of past time, that is, she only accepts the truth of ( . ). ( . ), however, does not entail ( . ). It only entails the weaker claim that

( . ) P~(x)(x is called “Socrates” & P(x)(x is called “Socrates”)

at some instant of past time, Socrates did not exist and (at that time) it was the case that Socrates had existed. ( . ) is perfectly compatible with presentism—just as, for example, its being true that Socrates existed and is not (now) present is compatible with presentism. The lesson here is that an entity’s not being pre-sent within an interval of past time is not a problem so long as it was present at the time of its existence. Therefore, I argue that ( . ) does not constitute a past exception to presen-tism.

Span tense operators can also be used to paraphrase transtemporal causal and se-mantic relations too. The schema for any transtemporal relation is as follows, where x is any present entity and y is any past entity:

( . ) (x)(sPan(y)(Rxy))

I mentioned earlier that ( . ) would only offer past-tensed paraphrases of transtemporal relations, and it would be a strange thing for presentists to deny that ( . ) through ( . ) are presently true, but there is a more serious problem lurking here. We previously consid-ered the truthmaker objection to presentism. I take it that a successful solution to the problem of transtemporal relations must not fall easy prey to the truthmaker objection and, in the discussion that follows, I demonstrate that instances of the schema ( . ), in virtue of its having Rxy as a constituent, cannot be grounded as easily as tensed singular propositions. This is troubling for advocates of span tense operators because there is a growing consensus that tense operators cannot be primitive and that tensed propositions must be explained in terms of tenseless propositions (see Bourne , – ; Merricks

, ; Sider a, – ; Sanson and Caplan , – ; Sanson forthcoming, –; Tooley , ).

Nevertheless, some presentists do take their tense operators to be primitive. They think tense is a fundamental part of reality—whether as tensed states of affairs like [Soc-rates was wise] or tensed properties like having been wise or even being a world in which Socrates was wise, which cannot be analysed in terms of tenseless states of affairs and prop-erties (see Bigelow , – ; Brogaard , – ; Kierland and Monton ,

– ). These tensed states of affairs and properties then ground past-tensed proposi-tions. However, presentists that invoke tensed states of affairs and tensed properties are thought to be ontological ‘cheats’. Sider argues that if tensed properties are irreducible then they must also be categorical, where categorical properties are properties that “involve what objects are actually like”. They must not be hypothetical properties that “point be-yond” themselves ( a, ). For example, being fragile is hypothetical because an entity’s being fragile is determined by its atomic structure and the laws of nature. It is not deter-mined by an entity’s intrinsic nature alone. Having the atomic structure S, on the other hand, is categorical. An entity instantiates this property in virtue of its intrinsic nature.

17

Being blue is also hypothetical. It can be reduced to a categorical property having the sur-face reflectance property R and certain characteristics of the human eye etc. Now suppose that an entity has tensed properties in virtue of how it was rather than how it is. As tensed properties say nothing about the current intrinsic nature of their bearers, they should be reduced to categorical properties or stricken from our ontology. (See also Sanson and Caplan ( , – ; , ), who appeal to truthmakers as proper explanations for the truths they ground. They say hypothetical properties have their explanatory power in virtue of the categorical properties to which they should be reduced.)

It would be useful here to draw a parallel between tense operators and modal opera-tors. In modal logic, <◊p>, that is, possibly <p>, is true just in case <p> is true or could have been true. As mere possibilities are not actual, modal truths often point beyond themselves; that is, just as <Pp> points into the nonexistent past. Consider the following modal proposition:

( . ) She could have baked a tastier cake.

How should ( . ) be grounded in reality when the cake she could have baked, but did not bake, does not exist? Modal realists and ersatz modal realists (the latter are sometimes called modal actualists) say that ( . ) is true if and only if there is a tastier cake that she baked in at least one possible world. According to modal realists, possible worlds share the same metaphysical status as the actual world (see Lewis ). According to ersatz modal realists, possible worlds are maximally coherent sets of propositions that could obtain (e.g. Adams ) or conjunctions of uninstantiated properties that could be instan-tiated (e.g. Forrest ; Stalnaker ). Note that the ersatz modal realist uses the modal notion “could” in her definition of a possible world, which makes her analysis of modal discourse circular and therefore non-reductive. In contrast, the modal realist does not use modal notions, for hers is the only reductive analysis.

In a sense, eternalists are the modal realists of time. They say that <Pp> is true if and only if <p> is true at some past time, where past times share the same metaphysical status as the actual time. Presentists can therefore look to ersatz modal realism for inspi-ration. This is Bourne’s approach ( , ch. , § ). As an ersatz presentist, Bourne ex-

presses times as ordered pairs of the form < , n>, where is a maximally coherent set of present-tense propositions, n represents the date at which these propositions are true and n belongs to the set of real numbers ( , ). The present time is the set of propositions that is true simpliciter; that is to say, true right now. All other times (ersatz times) are the sets of propositions that were or will be true (hence, this analysis is non-reductive) that are E-related to the present. Moreover, Bourne states that the E-relation is not the genuine earlier than relation because it relates abstracta and not spatiotemporal objects ( , –

). For instance, the time ⟨ , n⟩ is E-related to another time ⟨, m⟩ if and only if n bears the being less than relation to m.

Thus, it follows that: <Pp> is true simplicter iff <p> is a member of a set of present-tense propositions that

is the first element of an ordered pair ⟨ , n⟩ that is E-related to the ordered pair ⟨, m⟩,

where is the set of present-tense propositions that is true simpliciter, and n is less than m.

18

<sPanp> is true simplicter iff <p> is a member of the first element of any time among those times E-related to the ordered pair ⟨ , n⟩, where is the set of present-tense

propositions that is true simpliciter, that comprise the interval , where is a set of E-related times.

(Bourne , ; , ). In other words, the tensed propositions <Pp> and <sPanp> are grounded in the tenseless proposition <p> and its belonging to a set of propositions that is appropriately related to the present time.

I think there must be some concern here about why ersatz times come ordered as they do, that is, as a series that is a sufficient substitute for a series of concrete times. Why suppose that maximally coherent sets of propositions are the first elements of ordered pairs, where the second element represents the date at which they were or will be true? Sanson and Caplan suggest that the ersatz series has its order in virtue of the order of concrete times ( , – ; see also Oaklander , ). The tenseless proposition <p> belongs to the set of propositions that is the first element of the ordered pair ⟨ , n⟩

that is E-related to the present time ⟨, m⟩, where n is less than m, because there is a concrete time that is earlier than the present time at which <p> is true. Suppose that <p> is <Bucephalus is the horse of Alexander the Great>. Then there is an ersatz time earlier than the present at which <Bucephalus is the horse of Alexander the Great> is true. Sanson and Caplan think that this ersatz time is earlier than the present because there is a concrete time at which Bucephalus still is the horse of Alexander the Great.

Crisp, another ersatz presentist, argues that explanation must end somewhere. For him, the E-relation is fundamental and so there is no further explanation to be had about the order of the ersatz series ( , ). For Sanson and Caplan, the E-relation is not fundamental; it must be grounded in the genuine earlier than and later than relations that obtain between concrete times. They say that “it becomes less reasonable to suppose that explanation bottoms out in the contingent fact that certain times are earlier than others when those times are abstract [rather than concrete]” ( , ) . This issue must be resolved elsewhere.

The problem of temporary intrinsics is also a concern for the ersatz presentist. I said that presentism is thought to avoid this problem because it denies that past property instantiations are real, but ersatz times reintroduce the problem in a new form. For any proposition in the ersatz series <p>, <p> is true simpliciter when it belongs the present time and false simpliciter when it belongs to an ersatz time. Both property instantiations are real and it is a contradiction for <p> to be true simplicter and false simplicter. (Nathan Oaklander advances this argument against Crisp’s ersatz presentism and I think it applies equally well against Bourne’s ( , ).) It will not do to say that propositions are true simplicter and false simplicter at a different times either. To be true simplicter is not to be true at-a-time. Surely, all propositions in the ersatz series are true at-a-time, but only some are true simplicter. Suppose that the ersatz presentist does qualify truth simplicter temporally. Perhaps <p> is true simplicter at t and false simplicter at t . The trouble here is that <p> is always true simplicter at t and is always false simplicter at t . What is more, the very same is true of all other propositions in the ersatz series. Thus, all semblance of temporal becoming has been lost. Although time is static in this way for many eternalists, presentists are committed to a dynamic view of time because the present carries a special metaphysical status and is always changing.

The trouble with transtemporal relations, however, is that they resist Bourne’s analysis anyway. If any instance of ( . ) is true simpliciter, then its component Rxy must

19

be a member of the first element of any time among those times E-related to the ordered pair ⟨ , n⟩, where is the set of present-tense propositions that is true simpliciter. How-ever, Rxy contains two unbound variables and, as Bourne notes, “any attempt to bind them results in the false claim that these two distinct objects existed at the same time” ( , ).

For example, take

( . ) (x)(x is called “Ned” & sPan(y)(y is called “Aristotle”, & x admires y)) as an instance of ( . ). In the following analysis of ( . ), its component <x admires y> contains two unbound variables:

(x)(x is called “Ned” & sPan(y)(y is called “Russell”, & x admires y)) is true sim-

plicter iff (x)(x is called “Ned”) is a member of the first element of the ordered pair ⟨ ,

n⟩, where is the set of present-tense propositions that is true simpliciter, and (y)(y is called Russell) is a is a member of the first element of any time among those times E-

related to ⟨ , n⟩ that comprise the interval , and <x admires y> is a member of… Span tense operators are not therefore a solution to the problem of transtemporal rela-tions. They only conceal the problem. This is the kind of ontological cheating that Sider intends to prevent with his hypotheticality argument.

But the presentist need not admit defeat here. She might object that the hypotheti-cality argument proves too much. Very few philosophers endorse modal realism, the only reductive theory of modality, over the non-reductive ersatz modal realism. Moreover, it has been argued that even modal realism cannot reduce all modal discourse to non-modal discourse (see Lycan ; Salmon , – ; Shalkowski , ). The general idea is that modal realists are committed to the claim that there are possible worlds for every way that a world could have been; that is, in order to rule out impossible worlds, where “could” and “impossible” are modal notions. So if modality is irreducible and hypothetical, why not tense too? (Both Brogaard ( , ) and Keller ( , ) make this observation. Sider himself is hopeful that a reductive analysis of modal discourse can be achieved with-out embracing modal realism ( b, – )).

For now, the presentist might argue that there is nothing wrong with primitive span operators. Alternatively, she might want to follow Berit Brogaard in distinguishing be-tween tenseless relations and irreducibly tensed relations. Brogaard also amends (RP) such that

(RP*) Necessarily, for any tenseless relation R, if R is an n-placed relation that holds

between x , x , …, xn then x , x , …, xn must exist. ( , ). Once this amendment is made, the reason for making the distinction between tenseless and irreducibly tensed relations is clear. As only tenseless relations are existence entailing, the presentist should claim that all transtemporal relations are tensed.

The propositions ( . ) and ( . ) express a tenseless relation and a tensed relation, respectively, where the tensed verbs are italicised:

( . ) Kittens are not as scary as dinosaurs.

20

( . ) Kittens are not as scary as dinosaurs were.

Whereas a proposition like <Dinosaurs were scary> is tensed in one place, ( . ) is tensed in two places. It points towards the present in its first position and points towards the past in its second position, and so the are not as scary as … were relation is existence entail-ing on the left-hand side only. In other words, the relation obtains in virtue of how kit-tens presently are and how dinosaurs were in the past. In contrast, the tenseless ( . ) points neither here nor there in the time series and so, as neither of the relata are said to exist in the past, its truth entails the existence of both kittens and dinosaurs. Further-more, as Brogaard takes tensed relations to be irreducible, the problem of how to express transtemporal relations in tensed logic dissipates.

What, then, should a presentist say about ( . ) through ( . ), which appear to in-volve tenseless relations? Brogaard thinks that the presentist must deny their truth and offer similar truths in their place; truths that involve tensed relations:

( . a) Ned admires what Aristotle did. ( . a) Elizabeth II has fewer fingers than Anne Boleyn had.

As before, the admires what … did and has fewer fingers than … had relations are only existence entailing on the left, which means that ( . a) and ( . a) are consistent with pre-sentism.

Brogaard does not think that tensed relations offer a complete solution to the prob-lem of transtemporal relations, however. Without offering any argument, she claims that causal relations are necessarily tenseless ( , ). I am not so sure. In fact, I think substitutes for both ( . ) and ( . ) can be given using the tensed relations is caused by an event that … was and refers to that which … was.

More troubling is Giuliano Torrengo’s objection that irreducibly tensed relations are inconsistent with the order of time ( , – ). Any adequate theory of time must ensure that the instantiations of past-tensed properties and relations in the present depend on the past instantiations of present-tensed properties and relations, respectively. For example, if Alexander the Great instantiates the past-tensed property having had a horse called “Bucephalus” then, necessarily, Alexander instantiated the present-tense prop-erty has a horse called “Bucephalus”. Thus, truth conditions for the past-tensed proposition <Pp> can be given through truth ascriptions to the present-tense kernel <p> in the meta-language:

<Pp> is true iff it was the case that <p> is true

( , ). In contrast, truth conditions for tensed relations cannot “be derived from the general behaviour of tenses” as they do not have present-tense kernels underlying their structure ( , – ). In fact, they have no structure at all because they are primitive. And as we have already seen, transtemporal relations cannot be expressed in tensed logic anyway.

The presentist might put forward principles to govern each transtemporal tensed relation individually. For instance, the following principle (P ) ensures that ( . a) coheres with the order of time:

21

(P ) It is true that the admires what … did relation is instantiated by x and y (in that order) iff it was true that the will admire what … is doing relation is in-stantiated by x and y (in that order).

However, for every other tensed relation including ( . a), a new principle is required. The presentist therefore faces an explosion of ad hoc principles for tensed relations ( , –

; see also Torrengo , – ). A second worry is that (P ) and its kind only hold if the future is predetermined. If

we maintain an indeterministic view of the future, then ( . a) does not entail that it was true that <Ned will admire what Aristotle is doing>. This proposition points to the future in its first position and so, whether or not ( . a) is true, its truth value was indeter-minate. To be sure, in another possible world, Ned never studied philosophy nor came to know Aristotle. The same objections can be levelled at primitive span tense operators too. Instances of the schema ( . ) do not cohere with the order of time unless the presentist postulates unique principles for that purpose and buys into a deterministic view of the future. Thus, the cost of primitive span tense operators and irreducibly tensed relations is the same and too great.

. Craig Bourne’s Future for Presentism In his A Future for Presentism, Craig Bourne offers solutions for comparative and causal relations ( , ff.). His treatment of comparative relations is the simplest and the best place to start.

For Bourne, ( . ) is a logical consequence of the truth of two other propositions, namely <Elizabeth II has ten fingers> and <Anne Boleyn had eleven fingers>. It is a logical consequence, he thinks, simply because ten is less than eleven. Thus, any talk of a transtemporal relation has been “shifted” to an atemporal relation between numbers (i.e. ten bears the being less than relation to eleven) ( , – ; see also De Clercq ,

– ). Moreover, Bourne’s ersatz presentism is well equipped to deal with the past truth about Anne Boleyn: <Anne Boleyn had eleven fingers> is true if and only if <Anne Boleyn has eleven fingers> belongs to the set of propositions that is appropriately related to the set that is true simplicter. Concerns about the constituency of such propositions can be avoided by being a Russellian, as we have already seen.

Comparative relations are not always quantitative in this way, however. Some com-parative relations like ( . ), for example, are qualitative in nature and, as such, cannot be reduced to relation between numbers. In these cases, Bourne suggests that transtemporal relations supervene on facts about each relata that are represented by propositions in the ersatz series. This means that they can be disposed of, ontologically speaking. There are various kinds of supervenience (see Kim ( ) for a survey). Suffice it here to say, A supervenes on B if and only if there cannot be an A-difference without a B-difference. Thus, ( . ) supervenes on facts about kittens and dinosaurs if and only if ( . ) cannot be false without there being a difference in the facts about kittens or dinosaurs, that is, with-out kittens or dinosaurs differing in some qualitative respect. Bourne has therefore of-fered the presentist two very promising solutions for transtemporal comparative relations.

Bourne’s treatment of causal relations, on the other hand, is to deny that causation is a genuine relation ( , ; see also Brogaard , ). This view of causation is not

22

uncommon. For instance, Lewis analyses causation in terms of counterfactual dependence

between propositions ( , – ). Let O(x) be the proposition “x occurs” and □ a rule of truth such that

X □ Z is true iff either (a) there are no possible X-worlds (in which case it is vacu-ously true) or (b) some X-world in which Z holds is closer to the actual world than any X-world in which Z does not hold.

Then <a caused b> is true if and only if:

( . ) O(a) □ O(b)

( . ) ~O(a) □ ~O(b)

On this account of causation, if both events occurred, ( . ) is automatically true be-cause the actual world is the closest possible a-world and b occurs in the actual world. Thus the truth of <a caused b> depends on ( . ), such that <a caused b> is true if and only if, in the closest possible world in which a does not occur, b does not occur either. In other words, had a not occurred, b would not have occurred either. The presentist can therefore state that ( . ) is true if and only if

( . ) P(~O(yesterday’s downpour)) □ ~O(today’s flood) which says that if [yesterday’s downpour] had not occurred, then [today’s flood] would not have occurred either. There is no longer any need to posit transtemporal relation between both events.

Alternatively presentists might reduce causation to explanation using the sentential connective “because” such that x caused y if and only if because PO(x), O(y) (see Mellor

– ; see also Sider , ). The idea is that we say, “because of x, y” when x raises the chances of y occurring after it. Better still, presentists that are unwilling to deny that causation is a genuine relation might instead deny that causation is transtemporal (see e.g. Markosian , ). On this view, if a caused c then a and c are contemporaneous or else there is some third event b that is contemporaneous with both a and c and is such that a caused b, and b caused c. As I see things, this approach falls under the overlapper solu-tion, which I consider later.

Bourne thinks that other transtemporal relations can be reduced to causation and subsumed under his solution as well ( , ). For instance, he thinks that

( . ) Harry is the father of Herbert

is true just in case

( . ) Harry caused Herbert to exist

23

However, it is also true that Herbert’s grandfather caused Herbert to exist, and yet Her-bert does not have two biological fathers.1 The presentist might want to point out that Harry is a more direct cause of Herbert than Herbert’s grandfather is. We can character-ise the directness of a cause as follows:

P is a more direct cause of R than Q =df Q caused P, and P caused R.

(following Schneider , ). So while Herbert’s grandfather caused Herbert to exist, it is only in virtue of his causing Harry to exist that this is so. Harry is the father because he is the more direct cause of Herbert. Furthermore, mothers and fathers, both of which are equal direct causes of their children (or at least— to discount particular biological happen-ings from being parents —the most direct human causes) can be disguised according to facts about gender. Fathers are the most direct causes that are also male, whereas mothers are the most direct causes that are female.

Similarly, Bourne thinks that if we adopt Kripke’s causal theory of reference then transtemporal semantic relations are not a problem either. The general idea behind the causal theory is that proper names are passed from person to person along a causal chain. The chain begins with an initial naming ceremony, figuratively speaking, at which an entity is given its name. Names are then passed from person to person, creating a chain of reference preserving links in so far as each person in the chain intends to use the name in the same way as the person from which it was learned (Kripke , – ; see also Evans and Altham , ). There are no transtemporal relations. Instead, there are causal chains of facts that link present linguistic tokens to their past referents. These facts must be represented in some way by the presentist, but, for Bourne, this is just a matter of pointing to the right tenseless propositions in the ersatz series.

Less convincing is Bourne’s solution for intentional relations. Bourne argues that the presentist’s troubles with ( . ) stem from her inability to talk about the past entity Aristotle; and any focus on the admires relation is a “red herring”, says Bourne ( , ). But this is not right. As we have seen, Russellian presentists cannot paraphrase transtem-poral relations despite being able to talk about past entities. The causal theory cannot help here either. It does not matter how we succeed in talking about Aristotle, (RP) requires that Aristotle exists in virtue of standing in some relation nonetheless.

Perhaps I am being too quick here, but it does not seem that Bourne can reduce in-tentional relations to causation either. Suppose that ( . ) is true just in case Aristotle caused Ned to admire him. Following the Lewisian account of causation again, the truth of ( . ) would turn on the truth of

( . ) ~P((x)(x is called “Aristotle”) □ ~((y)(y is called “Ned”, & y admires x)) But while ( . ) is surely true—as Ned would not admire Aristotle had Aristotle never existed—it does nothing to eliminate the transtemporal relation which, predictably, con-tains an unbound variable. Presentists might want to say that Aristotle caused Ned’s admiration, and that ( . ) supervenes on the counterfactual dependence between Aristotle

1 Thanks to Chris Daly for this objection.

24

and Ned’s admiration. However, this approach is not very promising since it cannot tell us what Ned admires.

We must therefore look elsewhere to solve the problem of transtemporal inten-tional relations. Nevertheless, Bourne has demonstrated that presentism is consistent with transtemporal comparative relations because they are atemporal relations between abstracta in disguise or they supervene on facts represented in the ersatz series. Bourne’s decision to deny that causation is a genuine relation is also an attractive option for presen-tists.

. Roderick Chisholm’s “Overlapper” Solution Roderick Chisholm suggests that transtemporal relations might be reduced via temporal overlapping ( a, – ; see also b, ). Chisholm focuses on transtemporal semantic relations or, as he puts it, the problem of “how it is that we refer to things that no longer exist—even though there are no such things for us to refer to” ( a, ). But the overlapper solution has been extended to cover other kinds of transtemporal relations too.

The crux of Chisholm’s proposal is as follows: If there once was a philosopher who drank the hemlock and who no longer exists, then there always will be something—for example, the property blue—which once was such that there is a philosopher who is drinking the hemlock.

( a, ). Thus, we refer to some past entity because we stand in some relation to another entity, the property being blue; the overlapper, that once stood in some relation to

that past entity. And so ( . ), which appears to have the logical form (x)(y)(Rxy), has the hidden logical form

( . ) (x)(y)(R’xy & P(z)(R’’yz)) where y is the overlapper, being blue in this case, and neither R’ nor R’’ are transtemporal relations. However, as Matthew Davidson rightly objects, the fact that “Socrates” stands in some relation to the property being blue, which once stood in some relation to Socrates, is not sufficient for the refers to relation to hold between “Socrates” and Socrates ( ,

). After all, it is true for any linguistic token x and any abstracta y that x stands in some relation to y and y once stood in some relation to Socrates. But clearly not all linguistic tokens refer to Socrates.

Philosophers have since improved Chisholm’s initial proposal to prevent it from generating unwanted transtemporal relations, that is, by restricting what qualifies as an overlapper for any given transtemporal relation. Discussing transtemporal semantic relations, Rafael De Clercq suggests that “the abstract entity [the overlapper] in question is a type-name which is supposed to have a present token and to have referred to some entity in the past” ( , ). De Clercq does not strictly identify his solution with Chisholm’s but it is clear his type-names function as overlappers, that is, by standing in the is a type of relation to present linguistic tokens and having stood in the refers to relation to past entities. Neither of these relations are transtemporal, and using type-names as

25

overlappers does not over generate transtemporal relations because, for example, “Aris-totle” is not a token of the type-name that referred to Socrates.

Davidson asserts that transtemporal relations between present and past entities must be the relation that holds between them and the overlapper ( , ). This re-quirement is too strong for semantic relations but it gets something right when it comes to some comparative relations. For instance, he suggests that

( . ) Davidson is of the same political party as Franklin D. Roosevelt.

is true just in case Davidson is of the same political party as his fellow democrat, Frank, who coexisted with FDR and was of the same political party as FDR.

Even so, Davidson does not think that this explanation is sufficient for ( . ). Sup-pose that FDR’s presidency had been disastrous. Then Davidson might have been the only active democrat. Under these circumstances, nobody that belonged to the Democ-ratic Party at the same time as FDR would now belong to the same party as Davidson, and yet we would still want to say that Davidson is of the same political party as FDR. Davidson rightly concludes that Frank has nothing to do with his bearing the is of the same political party as relation to FDR ( , ). And I agree that Frank is not a suitable overlapper, but it does not follow that the overlapper solution is a nonstarter when it comes to comparative relations. To help us along here, we can draw from Bourne’s solu-tion. Accordingly, the relation is of the same political party as supervenes on facts about both relata, namely, the fact that FDR belonged to the Democratic Party and the fact that Davidson belongs to the Democratic Party. As I see things, Bourne’s solution turns on the Democratic Party’s being a common constituent of both facts. Thus, it is the Democ-ratic Party, not Frank, that is the overlapper in ( . ).

Intentional relations are more difficult, however. Our best bet for an overlapper in cases like ( . ) are abstracta, such as Aristotle’s ideas or characteristics. Presentists might say that Ned admires intelligence, which is something that Aristotle once had, or better yet, that Ned admires a summation of certain properties that Aristotle once instantiated (see e.g. Markosian , – ; Oreste Fiocco , ). This claim is not strong enough, though, since there are many people that Ned would admire that he nevertheless does not admire, that is, because Ned is unaware of them and thus unaware that they instantiate these properties—in the same way that, without further supplementing the view, ( . ) would be true even if Ned had never heard of Aristotle. This would be a highly controversial view to accept. It is therefore necessary for Ned to recognise the fact that Aristotle has these properties (see Markosian , – ). ( . ) is therefore true just in case

( . ) Ned admires the properties P , P , …, Pn and Ned believes that there was an

x called “Aristotle” and that x instantiated P , P , …, Pn. Note that, not only is ( . ) true even though Aristotle does not presently exist, ( . )

would be true even if Aristotle had never existed. In this way, transtemporal intentional relations are very similar to intentional relations that obtain between people and fictional entities. After all, what we fear, love, and so on is limited only by our imagination and so, presentism aside, there appear to be many relations that are not existence entailing.

( . ) Kun fears the Abominable Snowman.

26

( . ) Children love Santa Clause. In ( . ), Kun fears something that has never existed and (presumably) never will and yet her fear is no less real. Similarly, ( . ) is true but Santa does not exist either. If we wish to maintain (RP), both of these propositions must have hidden logical forms too, and presentists would do well to push forward the same solution again, that people fear and love certain properties of fictional characters.

A more direct approach to solving transtemporal intentional relations might be sought via uninstantiated haecceities (sometimes referred to as thisnesses). The most nota-ble use of haecceities in a presentist context is Robert Adams’ solution to the problem of singular propositions. Before I demonstrate how to extend this solution to cover the problem of transtemporal relations as well, it is necessary to be clear on what haecceities are.

According to Adams, a haecceity is “the property of being identical with a certain particular individual—not the property that we all share, of being identical with some individual or other, but my property of being identical with me, your property of being identical with you” ( , ). The haecceity of Socrates is the property being identical with Socrates and the haecceity of Adams is the property being identical with Adams etc. To borrow some of Alvin Plantinga’s terminology, haecceities are individual essences:

E is an individual essence iff (a) an entity x has E essentially and (b) there is no possible world in which there exists an entity distinct from x that has E.

where x has E essentially if and only if x has P in every x-world (Plantinga , – ,

). This means that Socrates instantiates his haecceity, the property being identical with Socrates, in every possible world in which he exists and anything that is not Socrates can-not instantiate his haecceity. This is intuitive since, necessarily, everything is identical with itself and nothing else.

What is interesting about haecceities, for our purposes, is that they continue to exist after their bearers cease to exist and remain available as the constituents of singular propo-sitions about past entities (Adams , ). There is, however, some disagreement over how this solution works. Ned Markosian suggests that ( . ) is to be paraphrased as

( . ) P(x)(x is identical with Socrates & x is wise) which is very similar to the Russellian paraphrase that we considered earlier. However, whereas Russellian paraphrases turn singular propositions into general propositions, “this proposition somehow involves or directly refers to Socrates, in virtue of having Socraticity [the property being identical with Socrates] as a constituent” (Markosian , ). Keller suggests that haecceities instantiate properties themselves, and that these properties ‘mir-ror’ the properties that their bearers once instantiated ( , ). Thus, Socrates instan-tiates the property being wise if and only if Socrates’ haecceity instantiates the property being wise*. As for ensuring that Socrates’ haecceity presently represents the way that Socrates was, Keller suggests that haecceities instantiate their properties in relation to haecceities of times. For my part, I would prefer haecceities to constitute the propositions that belong to sets of propositions in the ersatz series.

In either case, haecceities are suitable overlappers for transtemporal intentional rela-tions. But rather than simply saying that Ned bears the admires relation to Aristotle’s

27

haecceity, a stronger proposal is to use Aristotle’s haecceity as an overlapper such that Ned admires Aristotle’s haecceity, which Aristotle once instantiated. This allows the presentist to satisfy more intimate transtemporal relations, that is to say, relations be-tween people themselves. This is useful because I think there is something less than satis-factory about ( . ) as a paraphrase of ( . ). What we want to say, and what ( . ) literally says, is that Ned admires Aristotle himself, not that Ned admires certain things about Aristotle. Although these claims are similar, presentists should be able to account for both. I am here assuming that individuals are something more than mere bundles of properties; that there is an underlying substance that instantiates these properties. If individuals are just bundles of properties, so much the better for the presentist that ac-cepts ( . ). (Bundle theorists include Campbell ( , ); Hume ( ); Schaffer ( ). See Chisholm ( , ff.); Kant ( , B – ); Van Cleve ( ) for objections to the bundle theory.)

In spite of this, we should be sceptical about the possibility of uninstantiated haec-ceities (Keller , ; Markosian , ). If there is a property, being identical with Aristotle, then it is a complex property that consists of the identity relation and Aristotle. This means that Aristotle’s haecceity cannot exist unless Aristotle exists and, conse-quently, is not presently available as a constituent in singular propositions nor as an over-lapper. One option is to reduce an individual’s haecceity to the summation of properties instantiated by that individual a la ( . ), but this undermines the appeal of haecceities as allowing for relations that are more intimate. Presentists that are also bundle theorists can take this option but I am not willing to pay that price. In the next section, I offer an alternative solution to the problem of transtemporal intentional relations that does not commit us to the bundle theory.

. John Bigelow’s Relational Properties Solution In the last section, we saw that there appear to be intentional relations that obtain be-tween people and fictional entities. In fact, there appear to be other types of relations that obtain between fictional entities too:

( . ) Arya is the younger sister of Sansa.

Those familiar with George Martin’s “A Song of Fire and Ice” will know that Arya truly is the younger sister of Sansa but would never believe that such characters really exist. Yet, despite this, (RP) says that if ( . ) is true then there exist two girls named “Arya” and “Sansa”.

John Bigelow suggests that when we say that Arya is the younger sister of Sansa, we do not mean that Arya bears the is the younger sister of relation to Sansa. What we really mean is that “A Song of Fire and Ice”, the series of novels, has the relational property being a series of novels such that, in those novels, the character named Arya is the younger sister of the character named Sansa ( , – ). Similarly, going back to ( . ), when Kun fears the Abominable Snowman, she does not stand in the fears relation to a nonexistent Yeti in the Himalayas, she instantiates the relational property being afraid of the Abominable Snow-man. So when it comes to transtemporal relations, Bigelow thinks there are only presently instantiated relational properties. Thus, Ned admires Aristotle just in case Ned instanti-

28

ates the relational property being an admirer of Aristotle. Since relational properties are monadic, that is, instantiated by a single entity, they are not governed by (RP). This is the relational properties solution.

Earlier, we saw that singular propositions about past entities were, on the face of things, inconsistent with presentism. For the same reason, relational properties appear to be inconsistent with presentism too. Being an admirer of Aristotle is a complex property that consists of the admires relation and Aristotle himself. Thus, if there any such rela-tional properties, Aristotle exists and presentism is false. Presentists might argue that uninstantiated haecceities constitute these relational properties (see Davidson , ). In other words, being an admirer of Aristotle consists of the admires relation and Aristotle’s haecceity. But this would be ill advised without further argumentation. As we have seen, haecceities are relational properties too. Being identical with Aristotle consists of an iden-tity relation and Aristotle and cannot exist unless Aristotle exists.

I think there is a better way to avoid this problem. Remember that singular propo-sitions about past entities can be paraphrased as general propositions. In this way, past entities do not figure as the constituents of singular propositions. Russellian presentists can take the same approach with relational properties. The relational property being an admirer of Aristotle can be paraphrased such that

( . ) Ned instantiates the relational property being an admirer of the Ancient Greek

philosopher that wrote the “Nicomachean Ethics”.

Aristotle is not a constituent of ( . ) and ( . ) seems to capture what we want to say about Ned. Ned is an admirer of the unique entity that was an Ancient Greek philoso-pher and that wrote the “Nicomachean Ethics”.

The trouble with the relational properties solution is that it cuts the logical ties be-tween relational properties and relations (Davidson , – ). Intuitively, ( . ) is true if and only if

( . ) Ned stands in the admires relation to the Ancient Greek philosopher that

wrote the “Nicomachean Ethics”. On the relational properties solution, this is not so. Ned is an admirer of that unique entity but he does not stand in any relation to it—he cannot; there is nothing that pres-ently satisfies the definite description “the Ancient Greek philosopher that wrote the ‘Nicomachean Ethics’”. This is quite strange.

It is not, however, a decisive objection in my view. It would be useful here to make the distinction between intrinsic and extrinsic properties. The nature of this distinction is a problem in its own right. (See Francescotti ( ) for a useful discussion.) I will be following the view of Lewis ( , ; , – ). According to Lewis, an intrinsic property, like having a certain chemical or microstructural constitution, belongs to an entity independent of its relations to the world. It belongs to the entity as the entity is in itself. In contrast, an extrinsic property, like being an uncle, belongs to an entity as it relates to the world. If an entity has an intrinsic property, then so does its duplicate. This is not so for extrinsic properties.

If relational properties are necessarily extrinsic, then ( . ) is true in virtue of Ned’s standing in some relation to the world; in particular, it would seem, to Aristotle. But relational properties are not necessarily extrinsic:

29

( . ) Jill is identical with herself.

In ( . ), Jill instantiates the relational property being identical with Jill but this relational property belongs to Jill independent of her relations to the world; it belongs to the Jill as she is in herself. Being identical with Jill is therefore an intrinsic relational property of Jill (see Francescotti , ). The question now is whether relational properties like being an admirer the Ancient Greek philosopher that wrote the “Nicomachean Ethics” are intrinsic too. If so, the presentist can block the move from ( . ) to ( . ).

To that end, we must consider the nature of mental content, that is, what inten-tional mental properties, such as beliefs, desires, hopes and fears are about; in particular, we must consider the debate between narrow and broad mental content. According to extreme internalism, all mental content is narrow. It is, according to Hilary Putnam, the view “that no psychological state [mental property], properly so called, presupposes the existence of any individual other than the subject to whom these states are ascribed” ( ,

). In contrast, extreme externalism is the view that all mental content is broad. It is the view that mental content is not in the head ( , ). Mental properties are not deter-mined solely by the thinker’s intrinsic properties but by the external world as well. If extreme externalism is right, ( . ) is true because Ned stands in certain relations to the external world. In other words, ( . ) is true if and only if ( . ) is true. This would be bad news for the relational properties solution. On the other hand, if extreme internalism is right; if the mental property being an admirer the Ancient Greek philosopher that wrote the “Nicomachean Ethics” has narrow mental content then the truth of ( . ) is determined by Ned’s intrinsic properties alone, making it wholly independent of Ned’s relation, if one there be, to Aristotle. ( . ) would be a truth about Ned alone, and the presentist can happily deny that its truth entails the troublesome ( . ).

Putnam’s argument for externalism is well known. Though created to prove exter-nalism about the meanings of sentences, it has since been extended to mental content (see Burge , fn. ). Suppose there is a planet, Twin-Earth, that is identical to Earth in every way except that what Twin-Earthlings refer to as “water”, the liquid that falls from the sky and covers most of Twin-Earth’s surface, is not the chemical substance H O but the chemical substance XYZ. Suppose also that Twin-Earthlings and regular Earthlings have the same intrinsic properties and that neither are aware of the chemical structure of water. Despite this, when each believes <water quenches thirst>, the mental content of their mental properties differ. Twin-Earthlings believe <XYZ quenches thirst> whereas Earthlings believe <H O quenches thirst>. Since Twin-Earthlings and Earthlings are identical, their relations to the world must determine their mental content. Extreme internalism is false (Putnam , – ; see also Burge , – ).

The literature that has followed Putnam’s paper is vast. Some philosophers have objected to the very possibility of Twin-Earth (e.g. Kuhn , ). By their lights, anything with the same basic properties as water is, necessarily, H O. Other philosophers accept the thought experiment but attempt to deny the externalist conclusion. This is the approach of John Searle, with whom I side.

Searle’s solution is simple. He argues that intentional mental properties are only possible if the thinker represents the intentional object to herself in some way ( , ). In order for us to believe that water quenches thirst, we must first represent the inten-tional object, water, to ourselves. Since neither Twin-Earthlings nor Earthlings are aware of the chemical structure of the liquid that quenches their thirst, their mental content is

30

the same. Both have beliefs about something with the properties being a transparent liquid, being wet, being such that it falls from the sky, and so on. To be sure, the world determines what satisfies these beliefs but this is not the mental content itself.

Searle also notes that this is consistent with there being no XYZ or H O at all ( , ). We can and often do represent nonexistent entities to ourselves. This has been presented as an argument against extreme externalism in itself (see Segal , ff.). If there are mental properties about Abominable Snowmen and other fictitious characters then the mental content in such cases cannot be external in so far as the world is devoid of such entities. We can express this point as follows:

( . ) Kun fears the Abominable Snowman

does not have the logical form , it has the logical form (where F is the property being the Yeti in the Himalayas):

( . ) (x)(Fx & (y)(Fy x = y) & Kun fears x)

( . ) Kun believes (x)(Fx & (y)(Fy x = y) x & Kun fears x)

by the sentence “there is a Yeti in the Himalayas and Kun fears it”. is expressed by the sentence “Kun believes there is a Yeti in the Himalayas and Kun fears it”. Whereas ( . ) is true if and only if the Abominable Snowman exists, ( . ) is true just in case Kun believes the Abominable Snowman exists and fears it. This is because the particular quantifier falls within the scope of the belief operator (Searle , ). Thus, so long as Ned believes that there was an Ancient Greek philosopher that wrote the “Ni-comachean Ethics”, the fact that Aristotle does not exist is no barrier to Ned’s instantiat-ing the relational property being an admirer of the Ancient Greek philosopher that wrote the “Nicomachean Ethics”. Ned cannot stand in the admires relation to Aristotle but, as Ned’s representation of Aristotle is fully internalised, this relation is not essential. The presen-tist is therefore free to accept ( . ) and deny ( . ).

To clarify, I am not suggesting that Aristotle’s existence is superfluous. I certainly do not want presentists to become sceptics about the external world. What I am denying is that there are any genuine relations between Ned and Aristotle. I think there are vari-ous causal explanations for Ned’s beliefs about Aristotle, that he was an Ancient Greek, that he wrote the “Nicomachean Ethics” etc., that is, explanations involving Aristotle himself. But we have already seen that causation is not a genuine relation. The presentist can happily explain how Ned came to have his beliefs about Aristotle without accepting the truth of ( . ).

It is worth noting, however, that the relational properties solution is less apt for dealing with other kinds of transtemporal relations. Suppose that Elizabeth II instanti-ates the relational property having fewer fingers than Anne Boleyn. Waiving concerns about constituency, we shall struggle to find the necessary independent motivation for denying that Elizabeth II bears the having fewer fingers than relation to Anne Boleyn. Intentional relational properties are special in so far as they obtain in virtue of how their bearers represent the world to themselves. Comparative, causal and semantic relational proper-ties, on the other hand, are instantiated in virtue of how the world really is; that is, in virtue of relations that obtain between worldly constituents—constituents that must exist

31

according to (RP) and that, in the case of past and future entities, cannot exist if presen-tism is true.

. Theodore Sider’s Quasi Truth A less conventional approach to the problem of transtemporal relations is to deny that propositions involving transtemporal relations are true. Sider suggests that they are quasi true instead ( , – ):

A proposition <p> is quasi true iff there is a true proposition <q> such that, were X true, <q> would have been true and would have entailed <p>

where X is a thesis of ontology, such as presentism, eternalism, platonism, and so on, which aims to answer the question of what does and does not exist. For our purposes, X stands for eternalism.

Let us consider a simple example of Sider’s proposal at work before moving onto propositions involving transtemporal relations. Consider Socrates and his having been wise once again. Accordingly, ( . ) is quasi true because the tensed proposition

( . *) P(x)(x is called “Socrates” & x is wise) which is consistent with presentism, is such that, were eternalism true, ( . *) would still have been true but would have entailed ( . ). ( . *) is a quasi supervenience base for ( . ). Were eternalism true, ( . ) could not be false so long as ( . *) is true. Although ( . ) is, strictly speaking, false, the presentist can “salvage something from what we commonly say” because it is quasi true ( , ; emphasis in original).

What is interesting to note is that Sider rejects the claim that ( . ) is synonymous with ( . *). Even though ( . *) is consistent with presentism, ( . ) is not because Socrates does not exist as its constituent. Similarly, Sider accepts that presentist friendly para-phrases might be available for ( . ) through ( . ) but denies they are synonymous with the originals. In many cases, the paraphrase is simply too complicated ( , ). Sider therefore takes propositions involving transtemporal relations at face value, that is, as

having the logical form (x)(y)(Rxy) rather than as having a hidden logical form. So even if the presentist can paraphrase ( . ) through ( . ), she must still deny that they are true.

As he does for singular propositions about past entities, Sider argues that presentist friendly paraphrases offer a quasi supervenience base for propositions about transtemporal relations. For instance, the proposition

( . ) (x)(x is called “Elizabeth II” & x has ten fingers & P(y)(y is called “Anne Boleyn” & y has eleven fingers)

is the quasi supervenience base for ( . ). ( . ) is true and, were eternalism true, ( . ) would still be true and would entail ( . ). As the presentist must still find suitable paraphrases

32

for propositions involving transtemporal relations, Sider’s quasi truth is, in essence, a challenge to presentism—one that Sider believes cannot be met. Sider’s own argument from transtemporal relations turns on a type of relation that we have not considered.

Before we consider Sider’s argument, we should consider Crisp’s argument that quasi truth has bizarre consequences when we substitute other theses of ontology for X. For suppose that there is a thesis known as goblinism, the thesis that, necessarily, there are goblins. There is also the proposition <all squares have four sides> such that, were gob-linism true, <all squares have four sides> would be true and would entail <goblins exist>. <Goblins exist> is therefore quasi true. Note that similar arguments can be constructed for a whole host of strange propositions. Let X be your favourite thesis of ontology that postulates the existence of some strange entity x, let <p> be the proposition <x exists> and let <q> be any necessary truth. Necessarily, were X true, <q> is true and entails <p>. So as it turns out, a proposition’s being quasi true is worth very little. It is of no consola-tion to the presentist that propositions about transtemporal relations share the same status as propositions about goblins and other strange entities.

Crisp does consider the possibility that X should only range over certain theses, whereby goblinism is not one of them. But, he argues, presentists should not discriminate between eternalism and goblinism because, if presentism is true, they are both falsehoods ( , – ). I am not convinced. As quasi truth aims to preserve ordinary discourse, I think there is still something to be said for restricting the range of X. Presentists may indeed hold that both eternalism and goblinism are falsehoods but they would surely think that, of the two, only eternalism coincides with ordinary discourse. If we often spoke of goblins sincerely, as we do of past entities, that is, as existing, then I would be more inclined to agree that <goblins exist> is quasi true. With that said, I think we can go one better.

There is something less than satisfactory about Crisp’s use of necessary truths in his argument. In order to block such a move, I propose the following account of quasi truth

A proposition <p> is quasi true iff there is a true proposition <q> such that, were X true, <q> would have been true and would explain <p>

On my account, ( . ) through ( . ) are still quasi true because, as we have seen, there are various true paraphrases on offer that would have been true had eternalism been true and would explain ( . ) through ( . ). Take ( . ) for example, the proposition that Elizabeth II has fewer fingers than Anne Boleyn. ( . ) is the quasi supervenience base for ( . ). It is expressed as, “there is something called ‘Elizabeth II’ that has ten fingers, and there was something called ‘Anne Boleyn’ that had eleven fingers”. Had eternalism been true, ( . ) would have been true. Moreover, ( . ) would explain ( . ). Elizabeth II would have fewer fingers than Anne Boleyn because there would have been something called ‘Elizabeth II’ that has ten fingers, and there would have been something called ‘Anne Boleyn’ that had eleven fingers. <Goblins exist>, however, is not quasi true on my account. For any neces-sary truth <q>, <q> would have been true had goblinism been true but <q> would not explain <goblins exist>. A square’s having four sides, for example, does not explain why there are goblins.

What kind of proposition would explain why goblins exist? Qualms over what gob-lins might be aside, the following seems sufficient:

( . ) (x)(x is a mischievous evil & x has pointy ears)

33

Were goblinism true, ( . ) would explain <goblins exist>. Goblins would exist because something exists that is a mischievous evil and has pointy ears. But ( . ) is not true. Nothing is a mischievous evil and has pointy ears. As a guide, Sider states that “a sentence is quasi true if the world is similar enough to the way it would have to be for the sentence to be genuinely true” ( , ). But what similarity is there between the world as it is and the world as it would have to be for <goblins exist> to be true? So far as I can tell, there is no such similarity. To be sure, there are various truths about goblins in fiction but these propositions would not explain why goblins exist. For example, <The Lord of the Rings is such that goblins are the smallest of the Orcs> would have been true had goblinism been true but would not explain why there are goblins in the world.

Sider’s argument against presentism is that propositions about transtemporal spatial relations do not have a quasi supervenience base. If Sider is right, no amount of paraphras-ing will help the presentist here. What is common to the paraphrasing strategies is that propositions about transtemporal relations are really propositions about various instanta-neous “snapshots” of reality. These snapshots are captured using past tense slice opera-tors. For instance, the overlapper solution says that propositions about transtemporal

relations have the hidden logical form (x)(y)(R’xy & P(z)(R’’yz)). This hidden logical

form can be reduced to a snapshot of the present, (x)(y)(R’xy), and a snapshot of the

past, P(y)(z)(R’’yz)). Sider argues that although “the presentist’s tensed language contains the resources to specify a series of ‘snapshots’ capturing what the world is like at various instants”, it does not have “the resources to specify how to spatially line up the snapshots; the presentist cannot, therefore, capture certain facts about the states of mo-tion of particles” ( a, ).

This would not be a problem if substantivalism about spacetime were true. Accord-ing to the substantivalist, space is an objective part of reality and consists of enduring places that entities move in and out of over time. From the presentist’s point of view, enduring places are useful because their location in space is the same at all times. To understand this point better, consider the following transtemporal spatial relation:

( . ) Ted occupies the very same place that Bob once occupied.

If there are enduring places, the presentist can offer the following paraphrase of ( . ) in the spirit of the overlapper solution:

( . ) There is a place p that Ted occupies & P(Bob occupies p) (Sider a, ). However, relationalism is an opposing theory of spacetime. According to the relationalist, our best scientific theories do not require space to consist of enduring places (see Sider a, ; Zimmerman , ).

What does this mean for presentism? We have seen that, if substantivalism is true, the presentist can seek to capture transtemporal spatial relations through snapshots of reality that consist of enduring places. However, if relationalism is true, the presentist is in trouble. She cannot rely on transtemporal spatial relations between entities that have their location in space relative to other entities that are persisting through the times at which the relation obtains. For suppose that, in two possible worlds X and Z, there are but two particles a and b and a* and b*, respectively. Particles a and b are qualitatively identical to a* and b*. Now compare particle a, which is accelerating and passing the

34

particle b that is in inertial motion, with particle a*, which is not accelerating and is pass-ing the decelerating particle b*. The presentist cannot distinguish between X and Z. It is not even clear how the presentist can maintain that the particles are moving along a con-tinuous path, that is, rather than ‘skipping’ ahead in space (Zimmerman , – ; see also Sider , – ; , – ).

Looking forward, the presentist has at least two options. She might remain confi-dent that substantivalism about spacetime will turn out true. Dean Zimmerman holds this view ( , ). Alternatively, she might argue that worlds X and Z can be distin-guished according to the intrinsic properties of the particles. Thus, whether x is accelerat-ing, in inertial motion or decelerating depends on its intrinsic properties at t. However, Sider argues that such things cannot be determined in this way. Whether x is accelerat-ing, in inertial motion or decelerating at t is “a matter of the positions [that x] occupies before and after t” ( , ). Substantivalism would therefore appear to be the presentist best hope. With that said, the problem of transtemporal spatial relations requires greater consideration than I can provide in this paper.

. Conclusion In this paper, I have argued that unified solutions to the problem of transtemporal rela-tions come at great costs. Few philosophers will take unrestricted presentism seriously because it commits to a radically different kind of quantification over nonexistent entities, and philosophers that hope for a reductive analysis of modality will be sceptical of primi-tive span tense operators.

However, I have demonstrated that careful consideration of each type of transtem-poral relation permits strong partial solutions. What is common to these solutions is that they paraphrase propositions about transtemporal relations. In each case, the paraphrase is slightly different. In the case of transtemporal intentional relations, I have argued for two approaches, namely the overlapper solution and the relational properties solution. Comparative relations are to be shifted to relations between abstracta, such as numbers, or taken to supervene on facts about each relata. The overlapper solution works for some comparative relations but only those that obtain in virtue of similarities between the relata. If presentists deny that causation is a genuine relation, the causal theory of reference is then available to solve the problem of transtemporal semantic relations. Russellian pre-sentists, on the other hand, must appeal to type-names as overlappers. However, I have also argued that Russellian presentists are at odds with the referential use of definite descriptions. As the descriptivist theories of proper names and descriptions allow presen-tists to address problems of constituency, this problem cannot be ignored.

References (Where details of an online version are given, references are to the online version.) Adams, R. M. . “Primitive Thisness and Primitive Identity,” in The Journal of Philosophy, ( ), – . Adams, R. M. . “Time and Thisness,” in Midwest Studies in Philosophy, , – . Adams, F. and Stecker, R. . “Vacuous Singular Terms,” in Mind and Language, ( ), – . Armstrong, D. M. . Truth and Truthmaking. Cambridge: Cambridge University Press. Bach, K. . “Referential/ Attributive,” in Synthese, ( ), – .

35

Bigelow, J. . “Presentism and Properties,” in Noûs, , Supp. Philosophical Perspectives, , Metaphysics, – .

Bourne, C. . A Future for Presentism. Oxford: Oxford University Press. Bourne, C. . “Numerical Quantification and Temporal Intervals: A Span-er in the Works for Presen-

tism?,” in Logique et Analyse, ( ), – . Available online at <https://uhra.herts.ac.uk/

dspace/handle/ / > Braun, D. . “Empty Names,” in Noûs, ( ), – . Brogaard, B. . “Tensed Relations,” in Analysis, ( ), – . Brogaard, B. . “Span Operators,” in Analysis, ( ), – . Burge, T. . “Individualism and the Mental,” in Midwest Studies in Philosophy, ( ), – . Campbell, K. . “The Metaphysics of Abstract Particulars,” in Midwest Studies in Philosophy, , – . Chisholm, R. M. . “On the Observability of the Self,” in Philosophy and Phenomenological Research,

( ), – . Chisholm, R. M. a. “Referring to Things That No Longer Exist,” in Philosophical Perspectives, , –

. Chisholm, R. M. b. “Events Without Times: An Essay on Ontology, in Noûs, ( ), – . Crisp, T. M. . “Reply to Ludlow,” in D. Zimmerman (ed.). Oxford Studies in Metaphysics, Volume ,

– . New York: Oxford University Press. Crisp, T. M. . “Presentism and ‘Cross-Time’ Relations,” in American Philosophical Quarterly, ( ), –

. Crisp, T. M. . “Presentism and The Grounding Objection,” in Noûs, ( ), – . David, M. . “Defending Existentialism?,” in M. Reicher (ed.). States of Affairs, – . Frankfurt:

Ontos Verlag. Davidson, M. . “Presentism and the Non-Present,” in Philosophical Studies: An International Journal for

Philosophy in the Analytic Tradition, ( ), – . De Clercq, R. . “Presentism and the Problem of Cross-Time Relations,” in Philosophy and Phenomenol-

ogical Research, ( ), – . Donnellan, K. S. . “Reference and Definite Descriptions,” in The Philosophical Review, ( ), – . Evans, G. and Altham, J. E. J. “The Causal Theory of Names,” in Proceedings of the Aristotelian Society,

Supplementary Volumes, , – . Forrest, P. . “Ways worlds could be,” in Australasian Journal of Philosophy, ( ), – . Francescotti, R. . “How to Define Intrinsic Properties,” in Noûs, ( ), – . Hinchliff, M. . “The Puzzle of Change,” in Noûs, , Supp. Philosophical Perspectives, , Metaphysics,

– . Hinchliff, M. . “The Identity of the Past,” in J. K. Campbell, M. O’Rourke & H. S. Silverstein. (eds.).

Time and Identity, – . Cambridge, MA: The MIT Press. Hume, D. . A Treatise of Human Nature. L. A. Selby-Bigge (ed.). Oxford: Oxford Clarendon Press.

Inman, R. . “Why so Serious? Non-serious Presentism and the Problem of Cross-temporal Relations,” in Metaphysica, ( ), – .

Kant, I. . Critique of Pure Reason. P. Guyer and A. W. Wood (eds.) of The Cambridge Edition of the Works of Immanuel Kant. Trans. from German by P. Guyer and A. W. Wood. New York: Cam-bridge University Press.

Keller, S. . “Presentism and Truthmaking,” in D. Zimmerman (ed.). Oxford Studies in Metaphysics,

Volume , – . New York: Oxford University Press. Kierland, B. and Monton, B. . “Presentism And The Objection From Being-Supervenience,” in Aus-

tralasian Journal of Philosophy, ( ), – . Kim, J. . “Concepts of Supervenience,” in Philosophy and Phenomenological Research, ( ), – . Kripke, S. . Naming and Necessity. Cambridge, MA: Harvard University Press.

Kuhn, T. S. . “Dubbing and Redubbing: The Vulnerability of Rigid Designation,” in C. Wade Savage (ed.). Scientific Theories, vol. , – . Minneapolis: University of Minnesota Press.

Lewis, D. K. . “Causation,” in The Journal of Philosophy, ( ), – . Lewis, D. K. . “Extrinsic Properties,” in Philosophical Studies, ( ), – .

On the Plurality of Worlds. New Edition. Oxford: Blackwell Publishers. Lewis, D. K. . “Tensed Quantifiers,” in Oxford Studies in Metaphysics, vol. , – . Oxford: Oxford

University Press. Liggins, D. . “Truthmakers and the Groundedness of Truth,” in Proceedings of the Aristotelian Society,

( ), – .

36

Liggins, D. forthcoming. “Truthmakers and Dependence,” in F. Correia and B. Schnieder (eds.). Grounding and Explanation. Cambridge: Cambridge University Press. Available online at <http:// philpapers.org/archive/LIGTAD. .pdf>

Lycan, W. G. . “The Trouble With Possible Worlds,” in M. J. Loux. (ed.). The Possible and the Actual: Readings in the Metaphysics of Modality, – . Ithaca: Cornell University Press.

Lycan, W. G. . “Pot Bites Kettle: A Reply to Miller,” in Australasian Journal of Philosophy, ( ), –.

Markosian, N. . “A Defense of Presentism,” in D. W. Zimmerman. (ed.). Oxford Studies in Metaphys-ics, Vol. , – . Oxford: Oxford University Press. Available online at <http://myweb.facstaff.

wwu.edu/nmarkos/Papers/Defpres.pdf> Mellor, D. H. . The Facts of Causation. London: Routledge. Merricks, T. . “Endurance and Indiscernibility,” in The Journal of Philosophy, ( ), – . Merricks, T. . Truth and Ontology. Oxford: Oxford Clarendon Press. Oaklander, N. . “McTaggart’s Paradox and Crisp’s Presentism,” in Philosophia, , – . Oreste Fiocco, M. . “A Defense of Transient Presentism,” in American Philosophical Quarterly, ( ),

– . Plantinga, A. . The Nature of Necessity. Oxford: Oxford University Press. Plantinga, A. . “On Existentialism,” in Philosophical Studies, , – . Priest, G. . “The Closing of the Mind: How the Particular Quantifier Became Existentially Loaded

Behind Our Backs,” in The Review of Symbolic Logic, ( ), – . Prior, A. . Time and Modality. Oxford: Oxford Clarendon Press. Putnam, H. . “The Meaning of ‘Meaning’,” in Minnesota Studies in the Philosophy of Science, , – . Quine, W. V. . “On What There Is,” in The Review of Metaphysics, ( ), – . Quine, W. V. . “Reference and Modality,” in his From a Logical Point of View, – . Second ed.

Cambridge, MA: Harvard University Press. Routley (Sylvan), R. . Exploring Meinong’s Jungle and Beyond. Canberra: Australian National Univer-

sity. Russell, B. . “On Denoting,” in Mind, ( ), – . Salmon, N. . “The Logic of What Might Have Been,” in The Philosophical Review, ( ), – . Salmon, N. . “Nonexistence,” in Noûs, ( ), – . Sanson, D. forthcoming. “Once Present, Now Past”. Available online at <http://files.davidsanson.com/

research/oncepresent.pdf> Sanson, D. and B. Caplan. . “The Way Things Were,” in Philosophy and Phenomenological Research,

( ), – . Sanson, D. and B. Caplan. . “Presentism and Truthmaking,” in Philosophy Compass, ( ), – . Schneider, B. . “Truth-making Without Truth-makers,” in Synthese, ( ), – . Schaffer, J. . “The Individuation of Tropes,” in Australasian Journal of Philosophy, ( ), – . Searle, J. R. . Intentionality: An Essay in the Philosophy of Mind. Cambridge: Cambridge University

Press. Segal, G. M. A. . A Slim Book About Narrow Content. Cambridge, MA: MIT Press. Shalkowski, S. A. . “The Ontological Ground of the Alethic Modality,” in The Philosophical Review,

( ), – . Sider, T. . “Presentism and Ontological Commitment,” in The Journal of Philosophy, ( ), – . Sider, T. a. Four-Dimensionalism: An Ontology of Persistence and Time. New York: Oxford University

Press. Sider, T. b. “Reductive Theories of Modality,” in M. J. Lowe and D. W. Zimmerman. (eds.). The

Oxford Handbook of Metaphysics, – . Oxford: Oxford University Press. Sider, T. . “Quantifiers and Temporal Ontology,” in Mind, , – . Smith, J. F. . “The Russell-Meinong Debate,” in Philosophy and Phenomenological Research, ( ), –

. Stalnaker, R. C. . “Possible Worlds,” in Noûs, ( ), – . Strawson, P. F. . “On Referring,” in Mind, ( ), – Tooley, M. . Time, Tense and Causation. Oxford: Oxford University Press. Torrengo, G. . “Tenseless Cross-Temporal Relations,” in Metaphysica, ( ), – . Torrengo, G. . “Time, Context and Cross-Temporal Claims,” in Philosophia, , – . Van Cleve, J. . “Three Versions of the Bundle Theory,” in Philosophical Studies: An International Journal

for Philosophy in the Analytic Tradition, ( ), – .

37

Zimmerman, D. W. . “Temporary Intrinsics and Presentism, with Postscript,” in S. A. Haslanger and R. M. Kurtz (eds.) Persistence, – . Cambridge, MA: MIT Press.

Zimmerman, D. W. . “Presentism and the Space-Time Manifold,” in C. Callender. (ed.). The Oxford Handbook of Philosophy of Time, – . Oxford: Oxford University Press. Available online at

<http://fasphilosophy.rutgers.edu/zimmerman/index .htm>

38

A. Declaration No portion of the work referred to in this dissertation has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning.

39

B. Intellectual Property Statement The author of this dissertation (including any appendices and/or schedules to this dissertation) owns certain copyright or related rights in it (the “Copyright”) and he has given The University of Manchester certain rights to use such Copyright, including for administrative purposes. Copies of this dissertation, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has entered into. This page must form part of any such copies made. The ownership of certain Copyright, patents, designs, trade marks and other intellectual property (the “Intellectual Property”) and any reproductions of copyright works in the dissertation, for example graphs may not be owned by the author and may be owned by third parties. Such Intellectual Property and Repro-ductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property and/or Reproductions. Further information on the conditions under which disclosure, publication and commercialisation of this dissertation, the Copyright and any Intellectual Property and/or Reproductions described in it may take place is available in the University IP Policy (see http://documents.manchester.ac.uk/ display.aspx?DocID= ), in any relevant Dissertation restriction declarations deposited in the University Library, The University Library’s regulations (see http://www.manchester.ac.uk/library/aboutus/ regulations) and in The University’s Guidance for the Presentation of Dissertations.