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La métaphysique du temps : perspectives contemporaines

Alexandre Declos
Claudine Tiercelin

III- Temporalité, modes d’être, et constitution

Tense, Special Relativity, and Flow: A Wave Theoretic View

Nikk Effingham


This paper introduces a new tensed theory of time, ‘wave theory’. Wave theorists believe in the same four-dimensional hunks that eternalist-perdurantists believe in, but deny that everyday objects are to be identified with them. Instead, everyday objects are three-dimensional objects constituted by the presently existing temporal parts of those hunks (where ‘constitution’ means just that relation which holds between lumps of clay and statues). This paper combines wave theory with an ‘intentionalist’ theory of constitution, whereby constituted objects partially depend upon the dispositions of agents to have beliefs about them. I then show how the resulting combination can resolve the tension between tensed time and special relativity, as well as explain the passage of time.

Texte intégral

1This paper introduces a new tensed theory of time, ‘wave theory’, explaining how a particular version of it is (a) consistent with special relativity and (b) can explain the flow of time.

2The paper comes in three parts. The first part introduces wave theory. Wave theorists agree with the eternalist that there are four-dimensional hunks of matter. However, rather than identifying everyday objects (e.g. you, me, cars, statues, etc.) with those hunks, everyday objects are instead constituted by presently existing three-dimensional slices of the hunks, much as statues are constituted by lumps of clay (§1). There are different theories of how lumps constitute statues; §2 explains the ‘intentionalist’ view, whereby constituted objects partially depend upon the intentions of agents. Plugging intentionalism into wave theory gets us ‘intentionalist wave theory’, which I summarise in §3.

3The second part of the paper turns to special relativity. I discuss two arguments for thinking that special relativity is in tension with the tensed theory of time. The first argument is that simultaneity is relativised to inertial frames of reference. If we assume time is tensed, existence simpliciter must thus also be relativised to inertial frames of reference, which is allegedly absurd (§4.1). The second argument is that, given special relativity, simultaneity is conventional. Thus, if we assume time is tensed, existence simpliciter is likewise conventional, which is again allegedly absurd (§4.2). In both cases, I explain why intentionalists won’t think these claims absurd.

4The third part of the paper is the shortest, in which I explain how the developed theory can explain the flow of time (§5).

5Note that I don’t argue for time being tensed, nor for wave theory, nor for intentionalism about constitution. In this paper I’m solely concerned with presenting the theory and seeing how it deals with the problems of special relativity and temporal flow—although, of course, solving such problems may itself be taken to be a motivation for the theory in question!

1. Wave Theory

1.1. Temporal Ontology

6The different theories in temporal ontology differ over what things from non-present times exist, e.g. do dinosaurs exist or outposts on Mars? To understand the debate, I’ll distinguish between ‘present existence’ and ‘existence simpliciter’. Define ‘present existence’ by ostension: Barack Obama, Donald Trump, Boris Johnson, Nikk Effingham, and the Eiffel Tower are all examples of things which presently exist; dinosaurs, Napoleon, Joséphine, and outposts on Mars are examples of things which don’t presently exist. ‘Existence simpliciter’, on the other hand, is the concept we use in standard ontological debates about, e.g., whether numbers exist, or whether properties exist, or whether possibilia exist etc. In those debates it is routine to wonder whether some entity—e.g. the number 7 or my non-actual sister—might not presently exist but might nevertheless exist simpliciter. We can say similar of non-present things: presentists say that all and only presenting existing things exist simpliciter; eternalists say that anything that did, does, or will presently exist also exists simpliciter; growing block theorists say that all and only those things that did, or do, presently exist also exist simpliciter.

7I cash out the debate in terms of ‘existence simpliciter’ because it’s fairly standard to do so (Hestevold and Carter 2002, 497-501; Sider 2001, 16-17; 2006; see also Lewis 1986, 3). I recognise that there are problems with this approach (Golosz 2013; Meyer 2005; Savitt 2006), as well as alternative ways of understanding the theories. But in order to get to the main topic of discussion, I will set those worries aside.

1.2 Wave Theory

8Wave theorists agrees with the eternalist that things from both the past and future exist simpliciter. Indeed, they believe in the same four-dimensional hunks of matter that the eternalist-perdurantist believes in. However, they disagree that those four-dimensional hunks are the everyday objects we talk about. Where the eternalist identifies Napoleon with some four-dimensional hunk and Nikk Effingham with another, the wave theorist denies this. Instead, everyday objects are three-dimensional objects constituted by the presently existing temporal parts of those four-dimensional hunks. Nikk Effingham is constituted by the presently existing instantaneous temporal part of the hunk (‘the chunk’) that the perdurantist identifies with Nikk Effingham. Similarly, Napoleon was once constituted by various chunks of the hunk that the perdurantist identifies with Napoleon. Since Napoleon once existed simpliciter but it is not the case that Napoleon exists simpliciter, eternalism is false, even though some things from the past/future exist simpliciter (namely, the hunks).

9By ‘constitution’ I mean just that relation which constitution theorists say holds between lumps of clay and statues (Wasserman 2018, §2). And just as a statue has properties which the lump constituting it does not, the wave theorist says I have properties which the corresponding chunk does not: I have different persistence properties (I will exist tomorrow; my constituting chunk will not); different sortal properties (I’m a person; the chunk is not); different mental properties (I think; the chunk does not). As time moves on, the same object is later constituted by different chunks and, eventually, ceases to be (i.e. ceases to exist simpliciter) when nothing constitutes it.

  • 1 Miller’s ‘cresting wave theory’ (Miller 2019) likewise compares time to a wave. The theories are no (...)

10Given this theory, everyday objects are a bit like a wave. Think of an idealised ocean composed of portions of water which themselves do not move around very much. When, over time, a wave travels through that ocean, changing the properties of those patches (from flat to deformed/bulging), different patches will constitute the wave. My theory says similar when it comes to the ontology of time. The universe is composed of four-dimensional hunks which do not move through time. But over time, the properties of chunks of those hunks change from being non-present to being present; as they become present, they constitute the everyday objects around us, with different chunks constituting those objects, such that the everyday objects do move through time1.

2. Intentionalist Constitution

11Constitution obviously plays a big role in wave theory, so one’s theory of constitution is important. This section introduces a specific theory of constitution, ‘intentionalism’, whilst §3 explains how it can be plugged into wave theory.

2.1. Intentionalism

12Consider the lump of marble, L, which constitutes Michelangelo’s David. Constitution theorists say that L constitutes David (at least partially) in virtue of L having certain properties. Similarly for other cases of constitution. Say that the ‘C-properties’ of an object are those properties it has such that it’s in virtue of its having them that it constitutes some further object.

  • 2 Some philosophers believe composite objects depend upon the intentions of agents (Kriegel 2008; Pea (...)

13Non-intentional and intentional constitution theories differ over whether the C-properties of constituting objects like L have anything to do with the intentions of agents. Non-intentionalists say that they do not; intentionalists say that they do. Intentionalists include Baker (2000, 2002), Einheuser (2011), Renz (2016), and Sutton (2012)2.

14For instance, an intentionalist might think the following abstracted property is a C-property of L:

λx[There exists an agent disposed to believe there is a statue, David, where x is exactly located]

15Call that property ‘Δ’. Intentionalists say Δ is a C-property of L. Thus, were there no agents with the appropriate dispositions, L wouldn’t instantiate L and L wouldn’t constitute David.

16Note two things. First: Δ is not the only C-property of L. Moreover, L’s other C-properties don’t all have to concern the dispositions of agents to form certain beliefs about L. The ‘world has work to do’ when it comes to there being a statue! Other C-properties L might have include it being a certain shape, being a chemical solid, etc., none of which have anything to do with dispositions of agents. Intentionalists believe only that some C-properties of L are to do with the dispositions of agents to form certain beliefs about it.

17Second: Intentionalists aren’t concerned with an agent’s actual intentions and beliefs. Their focus is instead on their disposition to form certain intentions and beliefs. To see why, imagine the C-property was instead:

λx[There exists an agent who currently believes there is a statue, David, where x is exactly located]

18In that case, when we all go to sleep David would cease to exist, only coming back into existence when, e.g., someone wandered past it in the Florentine gallery in which it stands. That’s pretty weird, probably isn’t what intentionalists have in mind, and is why I take properties like Δ to be C-properties. I’ll often talk about such dispositions in the rest of the paper—that said, henceforth let ‘disposition’ be shorthand for ‘disposition of an agent to form the appropriate intentions/beliefs required for the constitution of an object’.

2.2. Objections to Intentionalism

19As noted in the introduction, this paper doesn’t argue for intentionalism. Nevertheless, to help clarify the details of the theory, it is helpful to discuss two objections to it.

20First objection: The ‘infinite regress objection’. People are constituted by lumps of organic matter. Given intentionalism, people therefore exist in virtue of an agent having an appropriate disposition. If that agent is a constituted object, this must continue in a chain ad infinitum. Therefore there must some unconstituted agent, e.g. God, to ground the existence of constituted objects in general.

21This commitment to theism and/or non-well founded grounding can be avoided. The properties of constituted objects correspond to ‘substrate properties’ of the objects which constitute them. Sometimes, those properties are identical. For instance, the height, mass, and shape properties of a statue are exactly the same as those of the lump constituting it; they correspond in so far as they’re one and the same. Sometimes, though, there is correspondence without identity. For instance, the statue may be Romanesque without the lump being Romanesque (Fine 2003), but the Romanesqueness of the statue nevertheless corresponds to other features of the lump, e.g. its having a certain shape (for only lumps of a certain shape can constitute Romanesque statues). Consider another example. I have mental states, whilst my body doesn’t. Nevertheless, my mental states correspond to my body having certain physical/neurological properties.

22An agent’s dispositions are of the latter variety. In order to have a disposition, my body must have a corresponding physical/neurological property. That latter property is not itself a disposition to form beliefs about constituted objects, since it’s had by the lump of flesh and no lump thinks nor can be disposed to think. Nevertheless, that physical/neurological property is the physical substrate of the disposition I have. Call such substrate properties ‘quasi-dispositions’.

23We can now avoid the objection. Don’t say that David exists in virtue of L instantiating Δ. Rather, David exists because L instantiates:

λx[There exists a lump with the quasi-disposition to believe there is a statue, David, where x is exactly located]

24Call that property ‘ΔQ’. It is (partially) in virtue of L instantiating ΔQ that David exists. It turns out that ΔQ, not Δ, is the C-property of L.

25Second objection: The ‘Voldemort objection’. Given intentionalism, we can ‘speak things into existence’. But how we talk and think is not the sort of thing that can cause objects to exist—that’s a power reserved for gods and wizards, not mere mortals like ourselves! Various philosophers have expressed worries along this line (Heller 1990, 361; Olson 2001, 347; Sider 2001, 157; Zimmerman 2002, 333-335).

  • 3 These references, and that to Salmon, all come from Brock (2010, 339-340).

26Solve this by first allowing for a distinction between derivative and fundamental things (Schaffer 2009; Tahko 2018). That we can’t talk things into existence makes sense for fundamental things. That mere words, intentions, or dispositions might affect whether a sub-atomic particle exists (or which spatiotemporal regions are filled, or the nature of the universal quantum wavefunction, etc.) is outrageous. But having distinguished between fundamental and derivative things, it’s less clear to me that derivative things cannot partially depend upon our dispositions. Indeed, it’s already an extant position for fictional objects (Braun 2005, 609; Goodman 2004, 132; Schiffer 1996, 157; Searle 1974-75, 73; Soames 2002, 93; Thomasson 1999, 7; van Inwagen 1977, 308)3. Further, Salmon (1998, 304) explicitly likens fictional objects to constituted artefacts like statues. So it’s much more plausible that derivative, constituted things might depend on our dispositions/the quasi-dispositions of lumps.

2.3. Plenitudinous Ontologies and Existential Relativisation

27There is one final thing I believe intentionalists should say, even though the existing intentionalists don’t appear to say it: They should say that constituted objects exist simpliciter relative to the lumps that have the grounding quasi-dispositions (and relative to the corresponding agents which the lumps constitute). To explain why the intentionalist should make this modification, we must first discuss a motivation for intentionalism. (Again, I am not trying to motivate intentionalism, but instead am merely arguing that, given their probable motivations, the best version of intentionalism is one according to which some objects have a relativised existence).

28Consider a popular non-intentionalist constitution theory which competes with intentionalism: Plenitudinous constitutionalism. Plenitudinous constitution theorists accept:

Plenitude: Wherever there’s an object, x, there’s a distinct object for every possible modal profile of x. (Fine 1999; Hawthorne 2006; Inman 2014; Jago 2016; Leslie 2011; Sosa 1999; Yablo 1987; see also Bennett 2004)

29Where a ‘possible modal profile of x’ is any consistent combination of accidentally/essentially having the non-sortal properties which x has. For instance, I am a male human philosopher. Given Plenitude, where I am there is: something essentially human but accidentally a male philosopher; something essentially male but accidentally a human philosopher; something essentially a philosopher but accidentally a male human; and so on.

30Plenitude entails constitution theory. Imagine a lump of earth located in the ocean, such that the top portion of it is above the water line. That portion has the accidental feature of being above the water line. Given Plenitude there exists, exactly located at both the same spatial region and the same time, an object which is essentially above the water line, i.e. an island. That island is distinct from the lump (since the former is essentially above the water line and the latter only accidentally so) and thus constitution theory is true. And all of this would be true even were there no agents, thus Plenitude entails a non-intentionalist constitution theory.

31Plenitude commits us to lots of weird objects. Imagine Shannon is stood within 10ft of Michelangelo’s David. David thus has the extrinsic property of being such that someone called ‘Shannon’ is within 10ft of it. It has that property accidentally. Given Plenitude there’s a distinct object which has that property essentially; call it a ‘schmatue’.

32Some philosophers find the existence of these weird objects repugnant and believe we should endorse a metaphysics without them (see Korman 2015; see also Effingham 2007, 62 and Markosian 1998, 228) who more specifically worry about composition than constitution, but the same worries carryover). I presume that one of the motivations for intentionalism is that it manages to avoid weird things like schmatues. But intentionalism only avoids the existence of schmatues if there aren’t agents with the appropriate dispositions. Were there an alien race that had dispositions grounding the existence of schmatues (or, more accurately, that their constituting lumps had corresponding quasi-dispositions which ground the existence of schmatues), then schmatues would exist.

33The intentionalist might accept this, arguing that schmatues would no longer be discomforting were there such an alien race. Nevertheless, we’re then left with an epistemic problem. When someone called ‘Shannon’ stands next to David, we can’t know be sure whether there’s a schmatue there or not, because we don’t know whether there is or isn’t an alien race with the appropriate dispositions. I suspect that those who eschew Plenitude will be equally worried about a theory that has this epistemic issue.

34Relativising existence simpliciter helps avoid the problem. We’ve been assuming that what exists simpliciter does so absolutely and that if the schmatue exists, then it exists absolutely, i.e. for everyone. If we say that constituted objects don’t only exist in virtue of lumps having certain quasi-dispositions, but add that they only exist relative to them (and relative to the agents who have the dispositions corresponding to those quasi-dispositions) then the problem is solved. Statues exist simpliciter relative to us, but not the aliens; schmatues exist simpliciter relative to the aliens, but not to us. We can know whether there is a schmatue there or not, at least if we take that question to be about what reality is like from our point of view, i.e. does the schmatue exist relative to us. And we know the answer: It doesn’t!

35Note that not everything exists relatively and some things still exist absolutely. For example, non-constituted things such as fundamental mereological simples (as well as the four-dimensional hunks of matter which they compose) exist absolutely, even if some things exist relatively. Only constituted things exist relatively.

3. Intentionalist Wave Theory (IWT)

36§1 spelled out wave theory in general, saying nothing about how constitution worked, whilst §2 introduced a theory of material constitution and said nothing about wave theory. This section combines the two to arrive at ‘intentionalist wave theory’ (IWT).

37Assume a Newtonian point of view. Into the Newtonian spacetime, there are various four-dimensional hunks. Each hunk is composed of temporal parts (‘chunks’). The core wave theoretic claim is that some chunks constitute three-dimensional objects. Given intentionalism, those chunks constitute those three-dimensional everyday objects because: (a) they have certain gross physical properties (e.g. being of a certain size and shape); (b) there exist other chunks which have certain quasi-dispositional properties; and (most importantly for the wave theorist!) (c) they are present. Further, given §2.3, those everyday objects only exist relative to different agents/chunks.

  • 4 Note that, given enough time, David might only exist relative to cn and not to me. At textinct, an (...)

38Consider L and David. L is a four-dimensional lump of marble which exists absolutely. David is an everyday object that exists (relative to, say, me and you) in virtue of: (a) there being a chunk of L, cl, that has a certain height and weight; (b) there being another chunk (e.g. that chunk which currently constitutes me, cn) which has certain quasi-dispositions corresponding to the disposition to treat cl as constituting an aesthetic artefact; and (c) cl presently exists4.

4. Special Relativity

39IWT can do two interesting things: (i) resolve tensions between tensed time and special relativity and (ii) explain how time flows. This section details (i), whilst §5 details (ii).

40That said, turn to the theory of special relativity. Special relativity entails:

Relativity of Simultaneity: There is no relation ‘__ is simultaneous with __’; instead, there is (at best) a similar relation relativised to inertial frames of reference i.e. ‘__ is simultaneous with__ relative to inertial frame of reference __’.

41Mostly everyone agrees that there’s a tension between Relativity of Simultaneity and:

Tensed Existence: What things exist simpliciter partially depends upon which time is present.

42There are two arguments for such a tension. §4.1 and §4.2 each detail an argument and explain how IWT resolves it.

4.1 The Argument from Relativised Existence

43Consider the first argument. Assume:

Present-Simultaneity Connection: All and only those things simultaneous with a presently existing thing are themselves present.

44Given Present-Simultaneity Connection and Relativity of Simultaneity, what is present is relativised to an inertial frame of reference. Given Tensed Existence, what exists must therefore also be relativised to an inertial frame. But that conflicts with:

Absoluteness of Existence: Things which exist simpliciter also exist absolutely. That is: Nothing which exists simpliciter is such that it exists relative to some x.

  • 5 If my understanding is correct, Gilmore, Costa, and Calosi (2016, 105-111) also have this argument (...)

45One of these principles must go. Those who argue that special relativity favours tenseless theory say that, since we should holdfast physics, the culprit is Tensed Existence and not Relativity of Simultaneity (Baron 2018, 1-2; Hinchliff 1996, 129-130; Read and Qureshi-Hurst Forthcoming, 2-3; Thyssen 2019)5.

46Some tensed theorists try and deny Relativity of Simultaneity. They might argue that an alternative, perhaps more sophisticated, understanding of physics reinstalls the relation of absolute simultaneity e.g. a deeper understanding of quantum physics (for discussion see Callender 2017, 81-97 and Jammer 2006, 271-294), general relativity’s ‘cosmic time’ (Swinburne 2008; see also Read and Qureshi-Hurst Forthcoming), or embracing a Neo-Lorentzian theory (Craig 2001; see also Balashov and Janseen 2003). Alternatively, some deny Relativity of Simultaneity on purely philosophical grounds, looking to metaphysics to reinstall absolute simultaneity [Tooley 1997].

47IWT makes a break from this approach. IWT denies Absoluteness of Existence. It isn’t the first theory to do so. Dolev (2006), Godfrey-Smith (1979), Hinchliff (1996, 130-132), Sklar (1992: 72), and Thyssen (2019, 1344-1345) all deny Absoluteness of Existence. What’s notable is that IWT’s denial of Absoluteness of Existence isn’t, by its own lights, a revision—even in the Newtonian setting, IWT denied Absoluteness of Existence! Einstein may have shown us many things, but nothing ontological, says IWT. The only tweak we must make to a Newtonian version of IWT is that rather than constituted things existing simpliciter relative to agents/chunks, they must now also be relativised to inertial frames of reference. Some might find it impossible to believe that what exists depends upon how fast you’re going and in what direction (Bourne 2006, 168; Fine 2005, 301). I don’t. It’s somewhat crazy to believe that what’s simultaneous with me depends upon what speed I’m going and in what direction. It’s true nonetheless, as Einstein showed. It’s somewhat crazy to believe that what exists depends upon what speed I’m going and in what direction. But if you take Einstein seriously and are moved to endorse both Tensed Existence and Present-Simultaneity Connection, you should think it’s true nonetheless. Tensed theory isn’t causing the crazy result, special relativity is. Blame Einstein!

48Bourne (2006, 168-9) objects to this line of argument. Special relativity demands we revise our views about simultaneity. The tenseless theorist, though, needn’t also revise Absoluteness of Existence, for they can continue to allow that existence simpliciter is absolute. The tensed theorist who denies Absoluteness of Existence is therefore making a revision which can be avoided. There is thus still something dodgy about denying Absoluteness of Existence.

49Firstly, Bourne’s objection only shows that tensed theory can’t be strictly better than tenseless theory, not that it can’t be better. Whilst tenseless eternalism may avoid a revisionary commitment when it comes to existence simpliciter, it fails to accept Tensed Existence. Assuming—as I have done so—that there is some reason to accept a tensed theory of time, the proponent of IWT can argue that allowing for Tensed Existence is a benefit outweighing the cost of revising existence simpliciter.

50Secondly, Bourne’s objection further highlights how IWT is again better than the other tensed theories which deny Absoluteness of Existence. Absoluteness of Existence is the conjunction of two claims:

Absoluteness of Fundamentals: All fundamental existents exist simpliciter and exist absolutely.

Absoluteness of Derivatives: All derivative existents exist simpliciter and exist absolutely.

51Competing theories which deny Absoluteness of Existence will deny both conjuncts. For instance, consider a presentist who denies Absoluteness of Existence and relativises what exists simpliciter to inertial frames. Even fundamental particles would exist relative to an inertial reference frame, so the presentist will deny Absoluteness of Fundamentals (and, obviously, the same applies to non-fundamental composites, so they’ll also deny Absoluteness of Derivatives). But IWT can avoid denying both conjuncts since they allow that some things exist absolutely, namely fundamental temporal parts of mereological simples (as well as the derivative four-dimensional hunks which they compose). Only constituted objects exist relative to an inertial frame of reference. So IWT denies Absoluteness of Derivatives but retains Absoluteness of Fundamentals. It is therefore less revisionary than the competing tensed theories, which deny both.

4.2 The Conventionality of Simultaneity

52The second argument against tensed theory goes as follows. For reasons to be explained later in this section, given special relativity, simultaneity is conventional. Given Tensed Existence, the existence simpliciter of different material objects would therefore also be a conventional matter. Assuming that it’s absurd that material objects existing simpliciter is conventional, we have a problem. Of course, IWT’s solution is obvious. Given intentionalism, the existence simpliciter of material objects is a conventional matter. There’s simply no problem!

53But things are more complicated than they at first seem. To see why, we must first understand why people believe special relativity requires simultaneity to be conventional. It’s easiest to do this by cashing out special relativity using the Poincaré-Einstein ‘radar-time’ understanding of simultaneity.

54See Figure 1. Imagine that a comet is forming its coma as it approaches the sun; call that event of coma formation ‘e’. I am stood on Earth. I shine a beam of light to illuminate the comet, hitting the comet with my beam just as e occurs. The beam then bounces back, so I see e. Between my firing the beam and seeing it return, a certain amount of time elapses according to my watch; call that interval T. Now imagine I’m trying to calculate at what time, according to my watch, e took place. The radar-time understanding of simultaneity says e occurs when my watch reads ½T. Where e is the event of my watch reading ½T then (given radar-time) e’ is simultaneous with e. And this makes a lot of sense—after all, if light travels the same speed in both directions between me and the comet, wouldn’t that be the obvious thing to say?

Figure 1

Figure 1

Coma Formation Relative to Earth’s Inertial Frame of Reference

55Note that Relativity of Simultaneity follows given radar-time. See Figure 2. As I fire my beam, a fast moving spaceship zooms past and likewise fires a light beam at the comet, also hitting it as e takes place. But, since they’re moving away from the comet, it takes longer for the light beam to return back to them. The interval they believe it took is T thus (given radar-time), from their point of view, e occurred when their watches read ½T i.e., where e is the event of their watches reading ½T, e is simultaneous to e relative to those on the spaceship. However—as clearly indicated on Figure 2—from my point of view, e is not simultaneous with e. So even though (in my reference frame) e is simultaneous with e’ and (in the spaceship’s reference frame) e is simultaneous with e, in neither frame of reference is e simultaneous with e’. Thus, given radar-time, Relativity of Simultaneity is true.

Figure 2

Figure 2

Coma Formation Relative to Spaceship’s Inertial Frame of Reference

  • 6 Perhaps we could create a ‘better radar’. In a Newtonian spacetime, defining simultaneity is usuall (...)
  • 7 The conventionality of simultaneity is discussed by Reichenbach (1958, 123-135) (see also Janis 201 (...)

56Return back to the conventionality of simultaneity. People started to suspect that simultaneity is conventional because there are alternatives to radar-time and no empirical way to determine which alternative is ‘correct’. Just consider my frame of reference on Earth. We took the event which occurred at ½T to be simultaneous with e, but there’s no reason why we couldn’t have taken it to be that which occurred at ¼T or ⅛T or, indeed, nT for any n where 0≤n≤1. Connectedly: Why assume light is going the same speed in both directions? There’s no way to tell that it doesn’t ‘speed up’ in one direction and then ‘slow down’ on the reverse journey. So opting for the events at ½T being simultaneous is just an arbitrary stipulation—it’s conventional! It has been established that there are no empirical experiments which would establish which definition is correct, or whether the speed of light is constant in all directions (Jammer 2006: 220-70)6. Thus, it appears to be arbitrary—that is, a matter of convention!— to take the simultaneous event to be that occurring at ½T. So, even having relativised simultaneity to inertial frames, simultaneity is apparently conventional. Given Present–Simultaneity Connection, what things are present would likewise be conventional7.

57Having expanded on the argument, I still won’t expand on IWT’s response. It is enough to point out that IWT openly allows for the conventional existence of constituted things; in already accepting intentionalism, IWT already accepts the very thing that tensed theorists were meant to find repugnant.

4.3 Wave Theory, Conventions, and External Relativisation

58I expanded on the argument because IWT’s response goes on to open up a huge can of worms. Presentness being conventional is problematic in two ways. First, it’s weird in that it’s hard to see how our conventions determine what is or is not present. Second, allowing that simultaneity is conventional gives us good reason to think IWT is actually a tenseless theory of time, not a tensed theory.

59To get a grasp on the first problem, take some instant, tmonk­, in the 13th century and imagine that instant is present. Consider what exists from the point of view of a random monk from that time. Given IWT, there’s a fact —albeit a conventional fact— about which slice of spacetime (which ‘Cauchy surface’) is present relative to that monk’s inertial frame of reference. In other words: There is some fact about which Cauchy surface is to be identified with tmonk, at least from the monk’s point of view. That Cauchy surface must clearly include the monk. Equally, some events clearly cannot be on that Cauchy surface. See Figure 3. The things which are ‘timelike separated’ from the monk cannot be on the Cauchy surface. But it is an open question as to which spacelike separated events are simultaneous with the monk—that is, it’s an open question as to whether the monk’s conventions pick out one set of spacelike events being simultaneous with him as opposed to some other set.

Figure 3

Figure 3

Timelike & Spacelike Separations

60The problem is then obvious: In the 13th century, no-one knew anything about Minkowski spacetime or relativity. No-one in the 13th century has any dispositions to believe anything about Cauchy surfaces or believe anything about presentness relative to their inertial frame of reference. In the absence of such dispositions, is it not unbelievable that the conventions of the people in the 13th century somehow manage to fix those facts?

61There are only two options. Either:

  1. Somehow/someway, even though they’re ignorant of anything to do with spacetime and Cauchy surfaces, the dispositions of the people of the 13th century nevertheless pick out some specific Cauchy surface (and, thereby, select one of the candidate definitions of simultaneity as being correct); or

  2. Their conventions fail to determinately select one Cauchy surface (and, therefore, fail to determinately pick one of the candidate definitions). But we embrace the indeterminacy! It’s a genuine, indeterminate fact about the world as to which surface is ‘the present moment’ (and, given IWT, genuinely indeterminate what things exist simpliciter from the monk’s point of view).

62Both options may seem far-fetched. However, IWT (in having assumed intentionalism) is committed to thinking that at least one of the two options is reasonable. Return to David and consider that interval where Michelangelo chiselled it from the block of marble. At the start of the process, there is no statue. At the end of the process, there is a statue. It appears there must therefore be a moment, tpop, when David ‘pops’ into existence. It seems absurd, though, that there is some specific instant where a statue suddenly appears, so we have a problem. A common solution to this problem is to accept Plenitude and fall back on supervaluationist semantic theories (Lewis 1986, 212-213; Sider 2001, 120-139), but that option is closed off to the intentionalist because they eschew Plenitude. The intentionalist will therefore instead opt for an epistemicist theory of vagueness (Williamson 1994) or a theory of ontic indeterminacy (Barnes and Williams 2011; van Inwagen 1990).

63Consider epistemicism. Before considering the case of David, consider how epistemicists deal more generally with vague predicates, e.g. ‘__ is bald’. The epistemicist says that there is a sharp cut-off between how many hairs are needed to be bald versus how many hairs are needed to not be bald e.g. it may be that 1,000,301 hairs on your head means you’re not bald and any fewer means that you are. Exactly what number of hairs makes for not being bald is somehow determined ‘behind our backs’; epistemicists believe that—no matter how hard we examine our language, actions, dispositions, and conventions—we’ll never come to know what sharp cut-off point was picked out by our conventions. Indeed, back in the distant past, when the speakers of proto-Indo-European first coined their equivalent of ‘__is bald’, they nevertheless managed to pin down a sharp cut off point unbeknownst to themselves. When it comes to David popping into existence, epistemicists will say similar things. Whilst we can’t know when tpop is, something about the way our conventions are nevertheless picks out tpop. So the epistemicist is already saying things in the spirit of option (i). Even though the monks of the 13th century may not have known anything about spacetime and relativity, their conventions nevertheless picked out some Cauchy surface as being present. Moreover, nothing they or we could ever learn about their conventions would key us into which surface that ends up being! Given epistemicism, we should say option (i) is true.

64The other option for the intentionalist was to deny epistemicism and allow for genuine ontic indeterminacy. On this view, reality is itself indeterminate. Whilst there are cases where there’s determinately no statue and cases where, determinately, there is, there are cases where reality itself is indeterminate over the existence of the statue. At such times, even God Himself doesn’t know whether David exists or not! And if you accept the possibility of ontic indeterminacy, then option (ii) will now prove attractive when it comes to which Cauchy surface is present. Whilst it’s determinate that the surface includes where the monk is, and it’s determinate that it doesn’t include things timelike separated from the monk, it’s ontically indeterminate which of the spacelike things are located on the Cauchy surface. Whilst it’s true that some Cauchy surface is present, it’s indeterminate which surface that is and, given IWT, it’s ontically indeterminate (relative to your frame of reference) what things exist. Given ontic indeterminacy, we should say option (ii) is true.

65Since intentionalists will accept either epistemicism or ontic indeterminacy when it comes to David, IWT will accept one of (i) and (ii) when it comes to questions about how our conventions (or the conventions of 13th century monks) select a Cauchy surface as being present.

66That’s one problem solved. But it quickly makes apparent the second problem. If presentness is a conventional feature of reality there are two reasons to believe IWT is a tenseless, not a tensed, theory of time.

67First reason: IWT says presentness depends upon the quasi-dispositions of different chunks; likewise, presentness is relative to those chunks and relative to the agents the chunk constitutes. But relativising presentness to agents is the sort of thing tenseless theorists say. The signature move of tenseless theory is that, when asked what time is present, they answer that it depends who you’re asking. IWT says similar: To know what time is present, we must first know relative to which agent you’re asking it of (or, more accurately, relative to which chunk, where that chunk can constitute an agent).

68Second reason: Given IWT, the only fundamental facts are tenseless facts about the mereological simples which compose the four-dimensional hunks. Whilst there are tensed facts (e.g. about what time is present, or about what constituted objects there are), they are derivative facts holding in virtue of (tenseless facts about) the quasi-dispositional features of chunks. If the world is fundamentally tenseless, it appears we have a tenseless theory of time.

69Both reasons are wrong-headed, though. What they show is only that IWT is a ‘non-standard’ tensed theory, in the sense that Fine (2005) spells out. Fine cashes out different tensed theories in terms of how tensed facts constitute reality. Given I’ve already used the word ‘constitute’ for the specific phenomena of lumps constituting further objects, I’ll instead say facts ‘comprise’ reality. Standard tensed theory says:

  1. The comprising relation is absolute (i.e. non-relativised);

  2. The tensed facts that comprise reality changes over time.

70Fine introduces two non-standard theories, of which we’re interested in just one, ‘external relativisation’ (see also Skow 2015: 67-68). External relativisers deny both (i) and (ii), instead saying:

(i’) The comprising relation is relative;

(ii’) The tensed facts which comprise reality do not change over time.

71External relativisation differs from tenseless theory because there are two ways to relativise ‘comprising’, an internal and an external way (Fine 2005, 279-280). The tenseless theorist is an ‘internal relativiser’ for it is the fact itself which is relativised (for the tenseless theorist ‘[…] there is a single reality, which does not vary over time, but in saying how this reality is we must say how things are at each time.’ [Fine 2005: 280]). The ‘external relativiser’ instead says that the fact itself is tensed and non-relativised but that it is the comprising relation between that fact and reality which is relativised (for the external relativiser, ‘[…] there are different realities at different times and there is no saying how reality is without presupposing a temporal standpoint from which the description is given.’[Fine 2005: 280; my emphasis]).

72Here’s another way of understanding the difference. Consider a non-relativisitic spacetime. Where ‘[[φ]]’ represents the fact that φ, the tenseless internal relativiser says reality is partially comprised—absolutely and not relatively—by:

[[In 1066 AD, the Battle of Hastings is taking place]]

[[In 1565 AD, the Battle of Talikota is taking place]]

(I underline ‘is’ to highlight that I intend the copula to be tenseless).

73The external relativiser denies that there are any such facts. Instead there are tensed facts, such as:

[[The Battle of Hastings is presently taking place]]

[[The Battle of Talikota is presently taking place]]

74Those facts are then related to reality by a relativised comprising relation. The former fact (partially) comprises reality relative to 1066 AD, whilst the latter (partially) comprises reality relative to 1565 AD.

  • 8 Unlike Fine’s external relativiser, IWT allows for some facts absolutely comprising reality, namely (...)

75Those who believe IWT should already be attracted to external relativisation over and above standard tensed theory because external relativisation neatly dovetails with the intentionalist’s relativisation of existence. Return back to the idea that objects exist simpliciter relative to different agents. We might wonder what that actually means! Finean metametaphysics can put some meat on the bones of such claims. Just as Fine’s external relativiser relativises comprising to a time, the intentionalist should relativise comprising to an agent (or chunk). In the same way that Fine describes external relativisers as believing ‘there are different realities at different times’, the intentionalist—in relativising existence simpliciter to agents—should believe there are different realities for different agents. That sounds like exactly the sort of thing that we’re meant to be capturing when we say that existence simpliciter is relativised to different agents and it is the sort of thing easily captured by the Finean metametaphysical system. And once you relativise comprising to agents, it’s easy to see why we might think it is further relativised to times—and if it’s relative to times then external relativisation is true8. (And it’s easy to see why, in a relativistic spacetime, we would again further relativise comprising to inertial frames of reference). Once we see that IWT is a non-standard tensed theory, we see that the first reason to think IWT is a tenseless theory falls short of the mark.

76Turn, then, to the second reason for thinking that IWT is a tenseless theory. Given IWT, at the fundamental level there are only tenseless facts. Given:

Standard Definition: Time is tensed iff there are fundamental tensed facts; elsewise, time is tenseless.

77IWT would be a tenseless theory.

78This will turn out to be a disagreement over definitions, so there’s no genuine debate to be had. Certainly, though, there’s a perfectly respectable understanding of ‘tensed time’, again grounded in Finean metametaphysics, according to which time is tensed. For Fine, the hallmark of a tenseless theory of time is the world being comprised solely of tenseless facts, whilst the hallmark of a tensed theory of time is the world being at least partially comprised of tensed facts. That is, Fine believes:

Non-Standard Definition: Time is tensed iff there are tensed facts which partially comprise reality; elsewise, time is tenseless.

79Given IWT, the world is partially comprised (relative to different times, agents, and inertial frames) of tensed facts, even if those facts aren’t fundamental. Given Non-Standard Definition, IWT is a tensed theory of time—because the comprising relation is relativised to times (something denied by the vanilla tenseless eternalist), IWT (and external relativisers in general) qualify as tensed theorists.

80Debating what a stipulated technical term ‘really means’ is pointless and ‘tensed time’ falls in that category, so I doubt there’s any genuine conflict between Standard Definition and Non-Standard Definition. The phrase ‘tensed time’ is just being used in two different, although somewhat cognate, ways. IWT is tensed on one understanding and tenseless on another. What’s important, though, is that IWT is clearly a different theory than vanilla tenseless eternalism, which is a tenseless theorist according to both understandings.

5. The Flow of Time

81This final section sketches how IWT can (partially) explain the flow of time.

82Time flows. What once was, is no longer. What is, will someday no longer be. And so on. Claims like this are expressed using tense operators, such as WAS and WILL. To metaphysically explain passage is to analyse those tense operators in non-tensed terms. IWT can give a partial analysis. First, define the OCCASSIONALLY operator:


83Given IWT, facts of the form [[OCCASSIONALLY: φ]] partially comprise reality. Because IWT is an external relativisation theory, that partial comprising is (in a Newtonian setting) relative to times and agents/chunks or (in a relativistic setting) relative to Cauchy surfaces, inertial frames of reference, and agents/chunks. That said, IWT can analyse the OCCASSIONALLY operator thusly:

OCCASSIONALLYφ〉 is true (relative to: chunk x; inertial frame of reference ϑ; Cauchy surface R) iff

  1. There are quasi-intentional properties, Xness1, Xness2… which conventionally select relation S as the relation of simultaneity;

  2. x instantiates Xness1, Xness2…;

  3. There exist some ys such that (a) they are all S-related in inertial frame of reference ϑ and (b) were the ys to constitute further things, φ would be true.

84That formal analysis can also be explained more informally. The three-dimensional chunk which currently constitutes me has certain quasi-dispositions. Those quasi-dispositions determine which spatiotemporal events are simultaneous to which other events, relative to my inertial frame of reference. That is: Having fixed the inertial frame, the quasi-dispositions slice and dice spacetime into a series of Cauchy surfaces corresponding to (frame relativised) instants. A proposition φ was true or will be true—i.e. is occasionally true—because, at some such slice n’ diced frame-relativised instant, there are chunks with certain properties such that, were those chunks to constitute further objects, φ would be true.

85This analyses the OCCASSIONALLY operator, but not the WAS or WILL operator. By itself, IWT only allows for an analysis of a ‘direction neutral’ tense operator, i.e. OCCASSIONALLY. This is because IWT has nothing to say about the direction of time. As it stands, IWT lacks the resources to determine which direction time is flowing in. The wave theorist has two options at this stage. First option: Argue that time has no direction and, therefore, there are no WAS and WILL facts, only OCCASSIONALLY facts. Whilst this may seem ridiculous, I note it because we’d end up with a unique theory according to which time is both tensed and directionless (Zimmerman 2011, 166). A second (more reasonable) option: Whilst IWT itself doesn’t have the machinery to explain the direction of time, we could rope in extra machinery—independent of the tenets of IWT—to explain the direction e.g. explaining it in terms of thermodynamics or causal forks. Once that machinery is added we will be able to sort facts which are occasionally true into those that were true, are now true, or will be true.

86That IWT can even partially explain the passage of time is interesting because most other tensed theories of time can’t do that. Take, for instance, growing block theory. It doesn’t explain why time flows, instead assuming that time flows and then building a theory on the back of that, whereby spacetime grows as time flows. Similarly, the classical understanding of moving spotlight theory takes eternalism and then ‘adds in’ a moving present, without explaining why there’s a moving present. Or consider Lucretian presentism (Bigelow 1996; Ingram and Tallant 2018, §6.1; Tallant and Ingram Forthcoming). Lucretians believe, e.g., that WAS: World War II is taking place is true iff the world instantiates the tensed property Being such that World War II once took place. More generally:

Propositions of the form WASφ〉 are true iff the world instantiates a tensed property of the form Being such that φ was once true.

  • 9 In a sense, tenseless eternalism can analyse the tense operators in non-tensed terms. But those ope (...)

87(Similarly for propositions of the form WILLφ〉) That’s an analysis of the tense operators, but it’s an analysis given in terms of tensed properties. The theory hasn’t really explained anything at all, instead ‘moving the bump around under the carpet’ from beneath the tensed operators to being beneath the tensed properties. So IWT’s ability to analyse the operators is an interesting feature of the theory9.


88Wave theory is a new theory of time and lots more could be said about it [Effingham MS]. This paper has focused on just one variety of wave theory, IWT, arguing that it can resolve problems with special relativity and help explain temporal passage. Whilst I’ve not argued that IWT is true, that it can do both of these things is itself some motivation for taking IWT seriously.


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1 Miller’s ‘cresting wave theory’ (Miller 2019) likewise compares time to a wave. The theories are not worlds apart, but do differ. Miller’s theory accepts eternalism and is a moving spotlight theory; the ‘cresting wave’ moves through history as the result of purely qualitative changes to those things which eternally exist simpliciter. It’s a ‘qualitative wave theory’. My theory makes the wave an ontological, not qualitative, matter; it is an ‘ontic wave theory’.

2 Some philosophers believe composite objects depend upon the intentions of agents (Kriegel 2008; Pearce 2017), or even objects in general (Kriegel 2012; Remhof 2017a, 2017b). If you believe such theories, you might also find intentionalism to be appealing.

3 These references, and that to Salmon, all come from Brock (2010, 339-340).

4 Note that, given enough time, David might only exist relative to cn and not to me. At textinct, an instant from a point in time after all agents who care about statues have ceased to exist, L might still exist and be statue shaped. The chunk of L that exists at textinct should still constitute David, but it can’t constitute it relative to me since I don’t exist. But chunks with the appropriate quasi-dispositions still exist, since they exist eternally. For instance, cn still exists simpliciter even when textinct is present—although, at that stage, it’ll exist back in the past. So, when textinct is present, David will still exist simpliciter relative to cn (as well as relative to many other such chunks with the appropriate quasi-dispositions).

5 If my understanding is correct, Gilmore, Costa, and Calosi (2016, 105-111) also have this argument in mind, but don’t present it in the format I have here.

6 Perhaps we could create a ‘better radar’. In a Newtonian spacetime, defining simultaneity is usually thought to be unproblematic because things can move at arbitrarily high velocities (Jammer 2006, 148, 176). We might think that the same isn’t true of relativistic spacetimes and that a similar definition thus can’t work (Salmon 1977: 268). But that would ignore the possibility of ‘tachyons’, which can move at arbitrarily high velocities (Janis 2018, §4; Maund 1974, 406). Some believe that tachyons can’t exist because of the possibility of causality violations, but I’ve extensively argued elsewhere that time travel doesn’t have those sorts of problems (Effingham 2020). Others rally against tachyons because they conflict with the denial of absolute simultaneity (Dainton 2010: 339; Lucas 1990, 9–10; Salmon 1980, 122) but this is wrongheaded (Nerlich 1982, 368; Peacock 2014, 51–52)––given tacyhons, instantaneity just ends up being relative to inertial frames of reference as well (Peacock 2014, 55; Stein 1991, 164–165).

Indeed, it’s irrelevant whether there actually are any tachyons. Consider the Newtonian definition of simultaneity:

Infinite Velocity: Events ex and ey are simultaneous iff were an infinitely fast particle launched from ex it could reach ey, and vice versa.

But that’s a counterfactual fact. A Newtonian spacetime mightn’t contain any actual things moving infinitely fast, but simultaneity is nonetheless fixed by what such a thing would have done. Similarly, even if tachyons don’t actually exist (indeed, even if they’re physically impossible!) that doesn’t mean there isn’t an appropriate counterfactual fact about their behaviour had there been any. Even in a relativistic spacetime, we can define simultaneity using Infinite Velocity. In conclusion, there may be some way to capture non-conventional simultaneity even given special relativity; IWT won’t take this route, but the discussion in this footnote might nevertheless be relevant to other tensed theorists.

7 The conventionality of simultaneity is discussed by Reichenbach (1958, 123-135) (see also Janis 2018 and Jammer 2006, 171-270). As far as I know, only Savitt (2010) explicitly advances the worry from the main text about conventionality being in tension with tensed theories of time.

8 Unlike Fine’s external relativiser, IWT allows for some facts absolutely comprising reality, namely the tenseless facts about mereological simples. Either (i) there are two comprising relations, one relative and one absolute; or (ii) x partially comprises reality absolutely iff x partially comprises reality relative to whatever you care for.

9 In a sense, tenseless eternalism can analyse the tense operators in non-tensed terms. But those operators only feature in sentences for there aren’t any tensed propositions given tenseless theory. That’s why the tenseless theorist is accused of not allowing for robust passage, since their theory has it that tense is rooted in language and not the world. I’ve assumed that we are looking to be tensed theorists who allow for robust passage, so I’ve ignored the tenseless theorist’s success in analysing the operators. IWT, then, remains special when it comes to its power to analyse the operators.

Table des illustrations

Titre Figure 1
Légende Coma Formation Relative to Earth’s Inertial Frame of Reference
Fichier image/png, 3,1k
Titre Figure 2
Légende Coma Formation Relative to Spaceship’s Inertial Frame of Reference
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Titre Figure 3
Légende Timelike & Spacelike Separations
Fichier image/png, 5,0k


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