Persistence Through Time, and Across Possible Worlds 9783110323245, 9783110322828

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Jiri Benovsky Persistence Through Time, and Across Possible Worlds

EPISTEMISCHE STUDIEN Schriften zur Erkenntnis- und Wissenschaftstheorie Herausgegeben von / Edited by Michael Esfeld • Stephan Hartmann • Albert Newen Band 8 / Volume 8

Jiri Benovsky

Persistence Through Time, and Across Possible Worlds

ontos verlag Frankfurt I Paris I Ebikon I Lancaster I New Brunswick

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List of chapters Part I – Persistence through time Chapter 1, Introduction & definitions............................................... p. 19 Chapter 2, Problems with presentism ............................................... p. 27 Chapter 3, The presentist perdurantist view ..................................... p. 35 Chapter 4, The problem of change in temporary intrinsic properties p. 45 Chapter 5, Coincidence and vagueness ............................................ p. 67 Chapter 6, The ship of Theseus ........................................................ p. 85 Chapter 7, The worm view and the stage view................................. p. 91 Chapter 8, Four-dimensionalism and common sense ....................... p. 103 Chapter 9, The modal objection ....................................................... p. 113 Part II – Persistence across possible worlds Chapter 1, Introduction..................................................................... Chapter 2, Modal realism ................................................................. Chapter 3, Straightforward trans-world identity............................... Chapter 4, Modal counterpart theory................................................ Chapter 5, Partial trans-world identity ............................................. Chapter 6, Modal perdurants ............................................................ Chapter 7, Genuine actualism – modal fictionalism......................... Chapter 8, Abstractionism-Ersatzism-Actualism ............................. Chapter 9, Abstractionism and trans-world identity......................... Chapter 10, Abstractionism and counterpart theory ......................... Chapter 11, Abstractionism and modal perdurants........................... Chapter 12, Bundle-bundle-bundle theory .......................................

p. 121 p. 125 p. 129 p. 133 p. 137 p. 153 p. 175 p. 197 p. 207 p. 217 p. 233 p. 241

List of figures ................................................................................... p. 269 Bibliography..................................................................................... p. 271

Foreword David M. Armstrong nicely wrote : "Metaphysicians should not expect any certainties in their inquiries. One day, perhaps, the subject will be transformed, but for the present the philosopher can do no more than survey the field as conscientiously as he or she can, taking note of the opinions and arguments of predecessors and contemporaries, and then make a fallible judgement arrived at and backed up as rationally as he or she knows how" (Armstrong (1989b, p. 135)). In this book, I am trying to follow this recipe. First, I shall try to 'survey the field as conscientiously as I can', and second, I dare to 'make a fallible judgement'. I see this work of mine then, as a guided tour of theories of persistence through time and possible worlds. First, this metaphysical excursion will take us into the land of theories of persistence through time and will try to offer a detailed overview of the standard theories but also of some views that are more original and less widely present in literature. It will be argued that the two traditional accounts of persistence (namely, perdurantism and endurantism) and their variants have to be combined with two doctrines about time (namely, eternalism and presentism) to yield different views. This will turn out to be very important since, for instance, endurantism can very well be defended if one is a presentist, but is much less appealing under the eternalist hypothesis. What we shall arrive at in the end is a 'map' (see p. 12-13) that provides an overview of all of the views discussed here with their advantages and drawbacks. (This map is also supposed to play the role of a table of contents.) After this first excursion shall begin the second : persistence across possible worlds. As in the case of persistence through time, each theory of persistence (trans-world identity, counterpart theory, modal perdurants) is evaluated under different ontologies of possible worlds (modal realism, fictionalism, abstractionism) and this will make us consider different theories, the traditional and well-known ones, but some original ones as well. And again, it will turn out that some combinations are attractive while others are to be rejected – for instance, trans-world identity is much more plausible for the abstractionist than for the modal realist. This yields also a 'map' (see p. 14-15) that gives an overview of all of the different

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views with their pros and cons. One of the purposes of these 'maps' is to give the reader a synthetic look at what alternatives there are and let him or her decide which position's advantages outweighs its drawbacks, and vice versa. What I aim at here is to provide myself and my reader with tools that enable us to evaluate the cost-benefit ratio of the different views under consideration. Is it possible, in the end, to reach a point where one view would come out of these evaluations as 'victorious', and, more importantly, as true ? And is it possible, by the way of evaluations and arguments, to arrive at a position that would be so objectively better than the others that everyone, when facing those arguments, would endorse it ? As frustrating as it can be, I believe this is not possible, perhaps in metaphysics in general, but certainly in the present case that interests me in this work. I have already mentioned the first reason for this : the truth of many particular views about persistence through time and possible worlds depends on the truth or falsity of other views, especially views about the ontology of time and possible worlds. Trans-world identity, to repeat an obvious example, is defendable under abstractionism (actualism), but clearly false under modal realism. Or, to take a bit more controversial example, the truth of endurantism strongly depends on the truth of presentism – if presentism is false, endurantism is, I believe, very unappealing. So what we have are 'only' claims of the form : if such and such view is true, then such and such view is true – and I take it to be one of the main purposes of this work to provide such conditional claims. But of course, these don't tell us anything about what is the case, 'only' about the connections between different inter-dependent claims. Second, there is a difficulty with intuitions – if one wants to reach a definite, 'objectively acceptable' (and perhaps true ?) result. The reason why intuitions yield difficulties, I think, is that (i) they play an important role in many cases, (ii) they cannot be easily refuted by arguments, and (iii) they are not, of course, universally shared. Examples of (i) abound in the chapters you are about to read : Parfit's case of fission, Kripke's objection to modal counterpart theory, the incredulous stare to modal realism – to note here only the most famous ones. And (ii) is true simply because if my intuition is that P, and yours is that non-P, then I can't say

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that you're wrong in having such and such intuition – the best I can do, if I want to make you abandon your intuition, is to show that it is in conflict with other intuitions you have (but that I, perhaps, don't have). But this leads us back to the situation where very often we can only reach an agreement on claims of a conditional form. To end these (unfinished and loose) considerations, let me simply state the meta-theoretical guidelines I followed to evaluate the different theories that I studied, and that I implicitly used to 'make a fallible judgement' in the end: (i) internal consistency (ii) explanatory power (It is perhaps hard to see the appeal of this criterion if one wants to reach a metaphysical truth, for why would great explanatory power of a certain view be a good guide towards truth ? It seems conceivable that a theory could be of magnificent explanatory power, and could even be much stronger than all of its competitors, whilst it is simply false. But still, the criterion is a genuinely interesting one, since what we do in metaphysics in the first place is to build theories that describe at best the phenomena we encounter or that we appeal to in thought experiments – to give an explanation of these.) (iii) intuitiveness (If a metaphysical theory is to be of any use to us, it should not be revisionary about those of our intuitions that we are not ready to abandon.) (iv) parsimony (If you can do it with less, don't do it with more. Unfortunately, clear-cut criteria that would enable us to decide what is 'less' and what is 'more' are still to be found, in many cases. Besides, similar worries as for (ii) appear : the 'cheapest' or simplest explanation is not necessarily the true one.) (v) compatibility with current science (This is perhaps also controversial. But to my mind, it seems that our metaphysical theories should be compatible with what empirical research tells us about the actual world.)

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(vi) honesty ("Never put forward a philosophical theory that you yourself cannot believe in your least philosophical and most commonsensical moments." (Lewis (1986a, p. 135))) Where did all this lead me ? As announced, this tour I am proposing is a guided one : at the end of the day, I do favour some of the views over others and dare to make the fallible judgement that those should be taken as the truth. In the temporal case, the favoured theory is the so-called 'worm view' version of four-dimensionalism, and in the modal case, it is the analogous theory of modal perdurants of which two versions will be examined. A global view of the nature of our world and possible worlds will be argued for : they are all worlds of perdurants. I wish to thank Gianfranco Soldati for his guidance, his helpful comments, his time, and highly interesting discussions. For helpful comments on previous versions of parts of this book and for discussions I would like to thank Ondrej Benovsky, Davor Bodrozic, Fabrice Correia, Fabian Dorsch, Philipp Keller, Jan Lacki, Kevin Mulligan, Martine Nida-Rümelin, Etienne Parrat, David Stauffer, Juan Suarez, and Gian-Andri Toendury. I would also like to thank Achille Varzi and Josh Parsons for their stimulating talks on persistence given during summer 2003 in Montana, and discussions of great interest. Special thanks go to Marie and Vlastimil Benovsky for their support during the time I was writing this book.

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Objects persist by having different temporal parts at different times. (I.1.§2) (Perdurantism)

All times (past, present, future) are equally real. (I.1.§2) (Eternalism)

Four-dimensionalism (I.1.§4) : Advantages : - answers satisfactorily many puzzle cases (I.6) : a) the lump of clay and the statue case (I.6.§2-3) b) the fission case (I.6.§5-7) c) the coincidence in the undetached parts argument (I.6.§8-10-) - avoids the objection from temporary intrinsics (I.4.§1-2) - gives a good treatment of cases of vagueness (I.6.§14) - deals better than other views with the Ship of Theseus case (I.7) - is supported by the view that time is space-like (I.5) Objections : - the view is simply incredible (I.9.§2); reply : I.9.§3 - the view is obviously false (I.9.§4); reply : I.9.§5 - temporal parts are unintelligible (I.9.§9); reply : I.9.§10 - the no-change objection (I.4.§3); reply : I.4.§4, see also I.5.§1 - the modal objection (I.10.§1); reply : I.10.§2-5 - objection to unrestricted mereological composition (I.9.§6); reply : I.9.§7-8 Two versions of four-dimensionalism

Ordinary objects are instantaneous temporal stages. (I.8.§1) (The stage view) Specific advantages to the stage view : - deals even better than the worm view with the problem with temporary intrinsic properties (I.8.§2) Specific objections to the stage view : - its account of persistence is not satisfactory (I.8.§4-5) - it does not answer satisfactorily the no-change objection (I.8.§6) - it does not allow ordinary objects to do the things they do (I.8.§8) - forces us to endorse instantaneous temporal parts (I.9.§11) - in some cases it is required to use the worm view anyway (I.8.§7) - breaks the analogy between time and space (I.8.§3)

Only the present time really exists. (I.1.§2) (Presentism)

Presentist perdurantism (I.1.§7) : Advantages : - allegedly avoids the no-change objection (I.3.§2 and I.3.§5) - allows for a mixed ontology (I.3.§3) Objections : - inherits the objections to presentism (I.3.§4) - problem with parts that don't exist (I.3.§6) - crazy metaphysics objection (I.3.§7)

Ordinary objects are fourdimensional wholes extended in time. (I.8.§1) (The worm view) Specific objections to the worm view : - there remains a semantic worry in the fission case (I.8.§3); reply : I.8.§3

Objects persist by being wholly present at different times. (I.1.§2) (Endurantism)

Genuine endurantism (I.1.§5) : Advantages : - is allegedly an intuitive view Objections : - the objection from temporary intrinsic properties (I.4.§1, §7); replies and discussion : I.4.§8-25 - eternalism and endurantism are incompatible (I.4.§16) - yields problems in some puzzle cases : a) the lump of clay and the statue case (I.6.§2-4) b) the fission case (I.6.§5-6) c) the undetached parts argument (I.6.§8-13) - yields problems in the treatment of vagueness (I.6.§14)

Presentism (I.1.§6) : Advantages : - the view is compatible with non-determinism (I.2.§4) - answers satisfactorily the objection from temporary intrinsic properties (I.4.§5-6) Objections : - problems with truths about the past (I.2.§1-4) - the objection from special relativity (I.2.§5)

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They persist by identity, an object existing in some possible world can be numerically identical to an object existing in some other possible world. (Trans-world identity)

Possible worlds don't exist, but we can pretend modal realism is true because it's useful. (II.6) (Fictionalism)

Possible worlds exist, they are of a different kind than the actual world, they are abstract actual entities. (II.8-) (Abstractionism)

Possible worlds exist, they are of the same kind the spatio-temporal actual world is, they are all equally real. (II.2) (Modal realism)

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General objections : - problem with non-actual objects (II.2.§2); reply : II.2.§3 - problem with modal epistemology (II.7.§1) - the incredulous stare (for instance, II.7.§3, II.7.§12); reply and discussion : II.7.§12

General advantages : - alleged advantage : is ontologically cheaper than modal realism (II.8.§1)

Objections : - straightforward trans-world identity is clearly unacceptable (II.3.§1) - trans-world identity with overlap of worlds yields the objection from accidental intrinsics (II.3.§2)

The first picture is clearly unacceptable (II.9.§2) The second picture is unacceptable (II.9.§3) The third picture :

General objections : - is not ontologically cheaper than modal realism, is perhaps even more costly (II.8.§1) - embraces primitive modality (II.8.§4) - problem with modal epistemology (II.8.§3)

Advantages : - can answer the problem with accidental intrinsics (II.9.§5) Objections : - forces us to embrace world-indexed properties (II.9.§5) - requires primitive modality (II.9.§6) - Cyrano and Roxane's puzzle (II.9.§8); reply : II.9.§9 - can force us to embrace haecceitism (II.9.§9-10)

General advantages : - provides a better account of modal epistemology (II.7.§1-2) - inherits some advantages of the preferred modal realist's view that serves as the fictionalist's fiction (II.7.§2) - is the most intuitive view (II.7.§3) General objections : - modality is primitive (II.7.§4, also II.7.§6) - inherits some problems of the preferred modal realist's view that serves as the fictionalist's fiction (II.7.§2) - the incompleteness problem I (II.7.§5) - the incompleteness problem II (II.7.§6) - the incompleteness problem III (II.7.§7) - arbitrariness of the fiction (II.7.§9) - the Brock/Rosen objection (II.7.§10) - Hale's objection (II.7.§11)

They persist by having counterparts in different possible worlds. (Counterpart theory)

They persist by being stretched across possible worlds, they have 15 different parts in different possible worlds. (Modal perdurants)

L-counterpart theory (II.4) :

Modal perdurants under Lewisian modal realism (II.6) :

Advantages : - avoids the problems with world-bound individuals (II.4.§1) - solves the problem with accidental intrinsics (II.4.§1) Objections : - Kripke's objection (II.4.§2); reply II.4.§3

B-counterpart theory (II.5) : Advantages : - is ontologically less costly than L-counterpart theory (II.5.§2-3) - answers better than L-counterpart theory Kripke's objection (II.5.§12) Objections : - requires four-dimensionalism to be true (II.5.§8-9) - its reply to Kripke's objection, while better than the L-counterpart theory's, is still not satisfactory (II.5.§12) - a problem with origin (II.5.§13-16) - Lewis's objection (II.5.§17); reply : II.5.§18 - strange ontology : splits of worlds and individuals

Advantages : - answers satisfactorily Kripke's objection (II.6.§2) - avoids the problem with accidental intrinsic properties (II.6.§1) - answers nicely a family of puzzles : a) the objection from undetached temporal parts (II.6.§3-4) b) the objection from undetached spatial parts (II.6.§5) c) the statue and the lump case (II.6.§6) Objections : - there is no common purpose to all modal parts of a single modal perdurant (II.6.§2); reply : II.6.§2 - pathology is everywhere (II.6.§8); reply : II.6.§9 - turns out to be equivalent to counterpart theory (II.6.§10); reply : II.6.§10 - difficulties with unification of the different modal parts (II.6.§11); reply : II.6.§11-13

Bundle-bundle-bundle theory (II.12) : - has many features in common with the theory of modal perdurants above (II.12.§14 and elsewhere in chapter 12) Advantages : - avoids problems that the abstractionist theories have because it is a one-category ontology (II.12.§1, §5-6) - avoids the problem of change (II.12.§3) - avoids the problem with accidental intrinsic properties (II.12.§4) - answers satisfactorily the objection from the Identity of Indiscernibles (II.12.§7-11) Objections : - individuals have to be 5D (II.12.§12) - primitive bundling relation, and the glue problem (II.12.§13)

Advantages : - answers the Cyrano and Roxane's puzzle (II.10.§1)

Advantages : - answers the Cyrano and Roxane's puzzle (and others) (II.11.§1)

Objections : a) the first picture : (i) a concrete entity cannot resemble an abstract entity (II.10.§2), (ii) concrete individuals could be abstract (II.10.§2) b) the second picture : is false (II.10.§3) c) the third picture : Cyrano doesn't have any counterparts at all (II.10.§4)

Objections : a) the first picture : (i) objects do not have concrete and abstract parts (II.11.§2) (ii) the problem with unification becomes more acute (II.11.§2) (iii) concrete individuals could be abstract (II.11.§2) b) the second picture : (i) problem with parts that don't exist (II.11.§3) (ii) the problem with unification becomes more acute (II.11.§3) c) the third picture : misses its target (II.11.§4)

S-counterpart theory (II.10.§5-) : Advantages :- answers Kripke's objection (II.10.§5) - solves some puzzle cases (II.10.§5) Objections : - has mysterious primitives (II.10.§6) - problems with representation (II.10.§6) - commits to a world-dependent conception of identity (II.10.§5-6)

Objections : - suffers from a modified version of Kripke's objection (II.7.§8)

Objections : - the theory of modal perdurants is not an available option for the fictionalist (II.7.§8)

Part I Persistence through time

Chapter 1, Introduction & definitions §1. The question I want to address in the first part of this book is : how do objects persist through time ? Note that the question is about how persistence of material objects is to be explained, not whether material objects persist through time – I simply assume, following my strong common sense intuition, that they do. An answer to the question may force us to revise some of our commonsensical beliefs, but this one should certainly be preserved; a reply to the problem of persistence should not deny genuine persistence. Traditionally, in contemporary literature, two accounts of persistence are in competition : endurantism and perdurantism. The terms have been introduced by David Lewis in this way : "Let us say that something persists iff, somehow or other, it exists at various times; this is the neutral word. Something perdures iff it persists by having different temporal parts, or stages, at different times, though no one part of it is wholly present at more than one time; whereas it endures iff it persists by being wholly present at more than one time." (Lewis (1986a, p. 202)). But these two accounts of persistence, as defined here, do not exhaust the realm of possibilities. For, to yield a theory of persistence, endurantism and perdurantism must be combined with a theory about time; traditionally, there are also two rival accounts available : presentism and eternalism. I propose now to state the four views, and explore the possible accounts of persistence one gets by combining them. §2. Let us start with the basic terms : • Perdurantism : The perdurantist's central claim is that a numerically one and the same concrete particular cannot wholly exist at more than one time; rather ordinary material objects are aggregates of temporal parts and it is by having temporal parts at different times that they persist (perdure) from one time to another. • Endurantism : Contrary to perdurantism, the endurantist account of persistence insists on the fact that ordinary objects are wholly there at any time of their

How do objects persist through time?

Definitions

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existence – they persist (endure) through time by existing completely at different times and they don't have temporal parts (but they do have spatial parts). • Eternalism : Eternalism is the doctrine about time which takes future and past objects to exist in the same way present objects do – there is no ontological difference between past, present and future; as Ted Sider puts it : "Just as distant places are no less real for being spatially distant, distant times are no less real for being temporally distant" (Sider (2001, p. 11)). In the eternalist's manner of speaking, future objects "exist", as well as present objects exist, in an atemporal sense of the verb; it is as if one were viewing the universe from a God's standpoint and could contemplate all that happened, happens and will happen laid before his eyes (Arthur Prior calls this "the tapestry view of time" (Prior (1996b, p. 47)). On this view, "now" is an indexical term as well as "here" is. • Presentism : Contrary to eternalism, presentism claims that only presently existing objects are real – "to exist", then, amounts to "to exist now". Typically, presentists are also 'serious tensers' drawing an important distinction between saying that past objects once existed and future objects will exist but only current objects exist. One could think, at a first glance, that presentism, thus formulated, is a non-starter – for how is one to understand the presentist's central claim "The only things that exist are those that exist at present" ? It seems there are two possibilities : either the first occurrence of "exist" in this claim is tensed or it is not. If it is, then it seems that presentism is an uninteresting truth ("The only things that exist now are those that exist at present"), and if it is not – that is, if "exist" is to be taken as a tenseless form of the verb meaning something like "existed, exist, or will exist" – then presentism seems to be obviously false. But presentism certainly is not a trivial truth nor an obvious falsehood, it is a thesis about what there is : "[T]here is only one largest class of all real things, and this class contains nothing that lies in the past or future. Presentism is, in fact, a thesis about the range of things to which one should be ontologically committed" (Zimmerman (1998, p. 210)).

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§3. So far for terminology. This leaves us with four options : (i) The eternalist perdurantist view (ii) The eternalist endurantist view (iii) The presentist endurantist view (iv) The presentist perdurantist view

Four theories of persistence

Let us examine these options more carefully. §4. (i) The eternalist perdurantist view : four-dimensionalism the sandglass t1-part

t2-part

t3-part

t1

t2 now

t3

According to this view, a sandglass, for instance, exists now (at t2) by having a temporal part which exists at t2 (and t2 only). But it also exists at the past time t1 and at the future time t3 by having temporal parts at those times; it is by having those different temporal parts at different times that the sandglass persists from t1 to t3. That's why this view can be called fourdimensionalism since it claims that ordinary material objects are 'spread out' in time as well as in space – they have temporal, as well as spatial, extent; they are genuinely four-dimensional entities. Four-dimensionalism, as I just described it, is also sometimes called 'the worm view', since ordinary material objects turn out, on this account, to be like space-time worms extended in the four dimensions. When speaking about the 'worms' of the four-dimensionalist, one can also speak about an object's 'world line'.

Fourdimensionalism Fig. 1

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The following figure (where, for simplicity, one of the three dimensions of space is left out) shows four sandglasses represented by the arrows that stretch out through time as well as through space. Each of the arrows is the world line of one sandglass, it is its path through space-time. So, if one thinks four-dimensionally, a sandglass is an object extended in all of the four dimensions, it is a space-time worm that crawls its way through a four-dimensional universe. Fig. 2

S1

S2

S3

time

S4 space space

An alternative to the worm view is 'the stage view' according to which ordinary material objects are the (temporal) stages rather than the fourdimensional wholes. The ontology of the two views is the same : both agree on what there is, both agree that there are space-time worms, but the stage view denies that these space-time worms are the ordinary objects we usually name and quantify over. For the time being, I only note that these two versions of four-dimensionalism exist (I discuss them in detail in I.7) and, when speaking about four-dimensionalism, it is always the worm view I shall have in mind. Some proponents of four-dimensionalism are Yuri Balashov (2000a), Mark Heller (1990, 1992, 1993, 2000), D. M. Armstrong (1980), Robin Le Poidevin (2000), David Lewis (1983c, 1986a, 1988, 2002), W. V. O. Quine (1950), Ted Sider (1997, 1999a, 2000b, 2000c, 2001).

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§5. (ii) The eternalist endurantist view : genuine endurantism Endurantism

the sandglass

the sandglass

the sandglass Fig. 3

t1

t2 now

t3

Genuine endurantism denies the temporal parts thesis : material objects do not have temporal parts, and are not temporally extended – this view is a three-dimensional one, since material objects are said to be extended in the three spatial dimensions only. They persist through time then, not by having parts at different times but by being wholly located at different times. As David Lewis puts it : "[According to genuine endurantism] a persisting thing is multiply located in time_: the whole of it is at one time and also at another." (Lewis (2002, p. 2)). This is what the figure above (fig. 3) captures : the sandglass persisting from t1 to t3 exists, not partly but completely, at all times in this interval. Among defenders of this view there are Mark Johnston (1987), Peter Simons (2000a, 2000b), D. H. Mellor (1998) and Josh Parsons (2000).

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Presentism

§6. (iii) The presentist endurantist view : presentism the sandglass

Fig. 4

t1

t2 now

t3

This presentist account combines the endurantist thesis according to which an object exists completely, and not partly, at any time at which it exists with the presentist claim that only present objects are real – this yields the view pictured above (fig. 4) : there is nothing existing at the past time t1 nor at the future time t3; the sandglass exists only at the present time t2, and exists there wholly – all of its parts exist at t2. This is why this view doesn't really deserve the label "endurantism" – remember how the label was introduced by David Lewis : "[something] endures iff it persists by being wholly present at more than one time" (Lewis (1986a, p. 202)). But nothing, according to presentism, exists at more than one time, since there is only one time which is real. This is why, despite the fact that the presentist view shares some features with endurantism (the threedimensionality of material objects, the denial of the existence of temporal parts, the claim that objects are wholly present at any time at which they exist), I will not speak about endurantism here, and will call this view only "presentism". Also, it wouldn't be proper, although it is sometimes done, to call presentism "three-dimensionalism" – this would be ambiguous, since endurantism also holds the three-dimensionality thesis. For a defense of presentism see, for instance, Trenton Merricks (1994, 1999) and Dean Zimmerman (1998).

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§7. (iv) The presentist perdurantist view Presentist perdurantism

t2-part

Fig. 5

t1

t2 now

t3

The presentist version of perdurantism claims, because of its perdurantist component, that at the present time t2 the sandglass doesn't exist completely but exists there by having a t2-part. Its other temporal parts, following perdurantism, exist at other times but, and here comes the presentist's claim, those other times don't exist. So material objects are not really four-dimensional in the sense that an eternalist perdurantist would claim, but they have four-dimensions "in the sense that they have an unfolding temporal dimension in addition to the three spatial ones" (Brogaard (2000, p. 343)). The only defender of this view, as far as I know, is Berit Brogaard (2000). Short discussions are to be found in Haslanger (2003, p. 10-12) and Sider (2001, p. 68-73). §8. Four general accounts of persistence of objects through time are available. The purpose of the first part of this book is to examine them and evaluate their advantages and drawbacks1. I shall begin by discussing the two presentist views.

1

For a summary, see Annexe I.

Chapter 2, Problems with presentism §1. When I say that a sandglass exists, the truth of what I say is grounded in, or accounted for, or made true by the way the world is : I am right if the world contains a sandglass, otherwise I am wrong. Whether one says that the role of what grounds such and such truth is played by a way the world is, or by a certain fact about the world, or by a state of the world at that particular time – this doesn't matter here. What matters is that there must be something which makes my statement true or false. There must be some entity to ground the truth of my sentence, and if my sentence is about a sandglass, this entity should preferably be a sandglass. Would the world be different, in respect to the existence of sandglasses, my sentence would be false; but it is actually true because, for instance, there is a sandglass on my desk. This view, namely that truths need grounding, seems perhaps quite obvious. But it appears that it cannot be accommodated by the presentist. There are, of course, no difficulties in providing grounds, or truth-makers, for propositions like "A sandglass exists"; the problem arises when we consider propositions about past objects or past events (and, similarly, future ones). For if I say "A sandglass existed" there is nothing, according to presentism, to make this proposition true – or, more accurately, there is no sandglass which could serve as a truth-maker – remember that, according to presentism, all there is, is present; quantifiers wide open and entirely unrestricted. The eternalist would not be troubled by such propositions : the existential quantifier involved ranges over all times, past, present and future, and thus it is possible to pick one of the past sandglasses to ground the truth that a sandglass existed. But since, according to presentism, reality does not include past objects, even in the most unrestricted sense, there is no sandglass available to us now to ground the truth of the proposition "A sandglass existed". Another way to put it, as for instance Parsons does (Parsons (2002c, p. 9)), is to note that the eternalist can say what would be different about the world as a whole had the proposition "A sandglass existed" been false. The presentist, unlike the eternalist, seems to have a puzzle to solve here. And as Markosian (2002, p. 3) puts it, there is more : it seems difficult, under the presentist hypothesis, to see how anything could stand in any

Problem with truthmakers

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relation to past (or future) objects. If, for instance, I admire Socrates, it seems difficult (maybe not impossible, but certainly difficult) to see how this could be – how there could be a relation that lacks one of its relata, how I can be related to something that does not exist. The problem is that it seems impossible for the presentist to be able to assert any proposition like "∃x ∃y (Admires(x,y))" where x and y exist at different times, because the presentist's quantifiers range only over things that exist at the present time, which is only one and so cannot range over things existing at two different times. (Such a problem, of course, does not appear if one endorses eternalism for in that case unrestricted quantifiers range over existing past and future times and entities as well as they range over the present ones, and thus provide all the truth-makers for propositions about the past (and the future) we need. This is perhaps one of the main reasons to happily endorse eternalism.) Rejecting the need for grounding

§2. As a general strategy, one could reply that it is not presentism but the truth-making principle, or the principle that truths need grounding, that must be rejected, for other independent problem cases may arise : for instance, negative statements. If I say "There are no dragons" what grounds the truth of this proposition ? Certainly not a dragon, and certainly not a state of the world which would contain dragons ! But this does not mean that the grounding principle should be abandoned. Surely, there are some problem cases concerning the truth-making principle, but here one does not have to have in mind some version of a strict correspondence theory of truth; it is sufficient to use the general principle according to which truth is supervenient on being; this is enough to make clearer what the grounding of truths is : truths supervene on what objects there are and what properties they have – it is thus impossible for there to be a difference in what is true, without there being a difference in what there is (see Sider (2001, p. 36), Crisp (2003, p. 4), and Lewis (2003)). If the presentist takes this line of response, then he or she accepts that there really is nothing to ground or make true propositions about the past (whether positive or negative), and he or she simply endorses it. Such a strategy does not seem to be an appealing one, for again, it does make

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sense to ask what difference there would be in the world, if the proposition "A sandglass existed" were false. (Besides, the problem with relations between present and non-present objects would call for additional theorizing to be solved.) §3. Another possible strategy a presentist could offer to answer the objection is the following (see Sider (2001, p. 37)) : presently, the world instantiates the property of previously containing sandglasses and this provides the missing ground for a presentist's account of the truth of "A sandglass existed". Thus, presently exemplified, but tensed, properties are said to ground past, and presumably future truths. As far as I understand the proposal, the picture it provides is the following. There is a sandglass S on my desk. Suppose it is the last of all sandglasses in the world. Suppose that right now (say, at tn) I smash it and destroy it. So the world at tn+1 exemplifies the property of previously containing S, and also the property of presently not-containing S. Its having the latter has a metaphysical ground : the world, and no sandglass S in it. But its having the former does not seem to have any such ground – or should we claim that the debris of S ground the world's having the property of previously containing S, and so, that such tensed properties are reducible to properties about what there (presently) is (debris of a sandglass, fossils of dinosaurs, history books, …) ? Such a proposal is certainly not very palatable. And it would be an even more difficult position to hold for many other truths ("Socrates had a beard") and would not be applicable to propositions about the future (which perhaps would not be a worry for presentists who hold the view that propositions about the future lack truth-value). The problem here is that the presentist taking this line of argument just seems to postulate ad hoc properties to alleviate a difficulty in his theory – what independent reasons could a presentist have to postulate them ? (An eternalist, of course, has independent reasons to postulate such properties (if he accepts tensed properties at all) : for instance, the past sandglass S that exists at tn-1, in the atemporal sense of the verb.) Every theory has its primitive. But if those tensed properties are the presentist's primitives, then his theory really loses some of its appeal.

A presentist's reply : tensed properties

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abstract entities

Fig. 6

§4. In conversation, Gianfranco Soldati proposed a solution that could be used by the presentist to face the objection. Suppose propositions are abstract entities that exist atemporally in a platonist's heaven, and that have their truth-value atemporally. Suppose further, that all propositions like "The sandglass S existed" have a suitable, logically equivalent, non-tensed paraphrase like "The sandglass S exists at tp", where tp is a past time (intervals of time could, of course, be granted – for instance "The sandglass S exists at t(p)-(p+q)"). Then the presentist could use a strategy pictured by the following figure.

A sandglass existed ↔ A sandglass exists at t1

R

spatio–temporal world

A Platonist strategy for the presentist

the sandglass that does not exist (now)

t1

is true at

t2 now

t3

Now is t2. At this time, the sandglass S does not exist but it existed at a past time t1. It is true then, now, that S existed. But, says the objector, what grounds this truth ? – after all, there is no trace now of S in the presentist's reality since t1, being a past time, does not exist. According to Soldati's proposal, it is enough that the proposition "The sandglass S existed" was made true by S at the time when S existed – i.e. when t1 was present. Remember that we are working under the hypothesis that all tensed propositions can be suitably paraphrased into non-tensed, presumably

31

time-indexed, propositions. Such propositions, as "The sandglass S exists at t1", have their truth-value atemporally, but, here comes the main point, they are made true at a certain time, namely at t1. From the atemporal proposition's standpoint, so to speak, it does not matter whether the time when its truth-maker occurred is present, past or future – rather, it is enough that there is a time at which the proposition enters in the relation of truth-making (or grounding, "R" on the figure) with its truth-maker, and once it is made true, it is atemporally true. Of course, according to this view, this does not mean that the proposition was "waiting" for the truthmaker to occur in order to acquire its truth-value, for this would render the proposition to be in time. The proposition is said to have its truth-value atemporally, so even if I say, at some time prior to t1, that the sandglass S will exist, or equivalently, that the sandglass S exists at t1, the proposition that I express is true. An advantage of this strategy is that it can also successfully deal with the problem concerning my admiring Socrates – since relations (and all properties in general), being ontologically of the same kind propositions are, can have one of their relata at a certain time tj, and the other at another time tk, even if tj ≠ tk, and so the relata never co-exist. The problem with Soldati's proposal lies in its premises. First, of course, one could be unwilling to endorse platonist abstract propositions, but let's say that at least some presentists are happy with them (and further, that they also accept the aforementioned account of relations and the way they have their relata). The second premiss, namely that all tensed propositions can be paraphrased into non-tensed ones, seems to be harder to swallow for the presentist. First, because it is far from obvious that such reduction can systematically be done, and second, because it is part of the presentist's view, and one of the main motivations for it, that reality is fundamentally tensed. So, it would be, to the least, very awkward for any presentist to be tempted by such a view. Besides, the proposal seems to imply determinism, because propositions about the future are atemporally true, as well as propositions about the present or the past. Thus, presentism loses one of its advantages over its competitors – eternalism is often said to imply determinism 2 and it is 2

For arguments that this is not so, see Smith and Oaklander (1995, p. 117-128).

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perhaps one of the drawbacks of the view; presentism in its general form, on the other hand, is compatible with indeterminism, which is maybe an advantage, thus preserving intuitively the idea of free will. But according to the proposal of this section, this advantage seems to be lost, thus diminishing the appeal of such a view. The special relativity objection

The presentist perdurantist view

§5. Another objection against presentism that I wish to mention only briefly comes from physics. According to many, the incompatibility of presentism with special relativity is reason enough to reject it. Sider (2001, p. 42) calls it "the fatal blow to presentism"; according to Merricks (1994, p.180), if the argument against presentism from special relativity succeeds, presentism is "ruled out"; Balashov (2002, p. 3) argues that "anyone who takes relativity seriously cannot take presentism seriously"; and Rea (1998) claims that the most plausible way of resisting the argument against presentism is to reject special relativity. The objection is that since there is no notion of absolute observer-independent simultaneity in the relativistic Minkowski space-time (where it is rejected in favour of relative simultaneity), the notion of a single absolute present is incoherent. And it seems that such a notion of only one absolute present is exactly what is needed in the presentist's ontology. As far as I understand the objection and the empirical basis for it, it seems to me to be a strong one. And since I would not favour Rea's strategy (our ontology should be compatible with current physics), I am inclined to take it seriously. But it seems hard to me to see what metaphysical conclusions relativity theory really entails, and maybe Minkowski's interpretation of it already contains some philosophical premises that could be controversial, so I think it is difficult to ground the rejection of presentism only on this basis. Detailed discussions of the argument from special relativity against presentism (and endurantism as well) can be found in Balashov (2000a, 2000b, 2000c), Brogaard (2000), Johnston (1987), Sider (2001), Merricks (1994), Rea (1998), and Smith (1995, appendix A). §6. What we have seen until now is that presentism seems to suffer from serious drawbacks. But it is worth noting that all of these come only from one component of the view : the presentist's claim that only the present time, and present objects, really exist. But what about the endurantist claim

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that objects do not have temporal parts but persist through time by existing entirely at different times ? It will be argued throughout this book that endurantism is not an appealing view – especially under the eternalist hypothesis. Under presentism, in some cases, it can work better. For instance, we will see in I.4.§5-6 that the presentist endurantist view nicely answers the objection to endurantism from temporary intrinsic properties (whilst its eternalist cousin will be in trouble). Furthermore, as far as the combination of presentism and endurantism is concerned, since it will be argued in the next chapter that perdurantism is unpalatable under the presentist's hypothesis, endurantism is the (only) natural view one can hold if one thinks that only the present time is real.

Chapter 3, The presentist perdurantist view §1. The presentist perdurantist view could easily strike one as very strange and certainly, it is an unusual view that is underrepresented in contemporary literature compared to the three other alternatives. Let us start with a short exposition of issues that could motivate such a view. §2. The presentist version of perdurantism claims that at the present time t2 the sandglass doesn't exist completely but exists there by having a t2-part. Its other temporal parts, according to perdurantism, exist at other times but, here comes the presentist's claim, those other times don't exist. But why claim that objects have temporal parts at other times than the present if these parts don't exist ? According to Berit Brogaard, who is the only one to hold this view as far as I know (see Brogaard (2000)), this is the best way for the four-dimensionalist to avoid what is, according to her, the main charge against four-dimensionalism : that it entails a changeless world. Indeed, it is considered by many as a strong objection to fourdimensionalism that it entails the denial of change in the world. Let us say that a sandglass is full when its top half contains all of the sand and that it is empty when its bottom half contains all of the sand. Surely, being full and being empty are intrinsic non-relational properties of the sandglass 3, and surely any theory should be able to accommodate the fact that a sandglass can change in this respect. But, the objection runs (we will see a more detailed discussion of this objection, and the four-dimensionalist's reply to it, in I.4.§3-4), four-dimensionalism is unable to provide a satisfactory account of change : instead of saying that the sandglass changed from t1 to t3 from being full to being empty, the fourdimensionalist says that the t1-part of the sandglass has (tenselessly) the property of being full and the t3-part of the sandglass has (tenselessly) the property of being empty (remember fig. 1 in I.1.§4). The sandglass being unable to lose or gain any such properties, this is why there is no room for genuine change in the four-dimensionalist view. The presentist variant of 3

Suppose the top of the sandglass is distinguishable from the bottom – by its colour, for instance, or its shape – so that "being full" and "being empty" are not relational properties depending on the fact that "top" and "down" are well defined terms only by relation to other things – like the Earth's centre.

Perdurantism and the no-change objection

36

perdurantism is precisely designed to avoid this objection_: the full t1-part 4 of the sandglass is, by the passage of time, destroyed and replaced by the t2-part which is, in turn, destroyed and replaced by the empty t3-part – thus the four-dimensionalist view that "[the sandglass] has temporal parts with different properties, just as a multicoloured strip of paper has spatial parts with different properties, and neither case involves change in the sense in which this word is commonly understood" (Brogaard (2000, p. 342)) is avoided because there is no such strip, there are no (in any tensed or tenseless sense of the verb) different parts of the sandglass with different properties. And since only one temporal part of the sandglass exists, namely the present one, the only properties instantiated are the properties instantiated by it now – there is no having tenselessly any property and there is genuine change in the world, for, as she puts it "[…] the coming into existence of a new stage [i.e. temporal part] with a different nonrelational property is a real change – and this in a way that captures our most basic intuitions according to which a change has taken place if the object stage that presently exists has different properties from those that existed previously" (Brogaard (2000, p. 348)). A mixed ontology

§3. Another reason to adopt a presentist version of perdurantism is that it could be attractive for presentists who wish to hold a mixed ontology of persistence : they would be endurantist presentists as far as ordinary material objects, like sandglasses, are concerned and perdurantist presentists as far as events are concerned. This is the case, for instance, of L. B. Lombard (1999). Events are entities that many, if not everyone, accept as having temporal parts, even among endurantists. A performance of Rachmaninov's piano concerto n.3 is certainly an entity that has temporal parts – let us say, for the sake of simplicity, the performances of the different notes that compose the concerto. Indeed, the debate between four-dimensionalists and endurantists was sometimes stated as a disagreement over the status of material objects in the following way : four-dimensionalists claim them to be event-like whilst endurantists deny 4

Brogaard would rather speak about 'stages' than 'parts' since she takes "a stage to be an infinitely thin slice of an object along [the] temporal dimension". (Brogaard (2000, p. 343))

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this claim. This is where presentist perdurantism could be of good use to the presentist who would like to hold that events persist by having temporal parts at different times (perdurantism) and that material objects persist by being wholly located at all times at which they exist (endurantism). Likewise, the eternalist endurantist could hold the same claim. As I said, I take it to be almost uncontroversial that events have temporal parts and it is not my aim to defend this view; it is just worth noticing that such a claim is fully compatible with both endurantist ontologies – the eternalist and the presentist – by allowing them to hold a mixed view. Note, however, that the presentist has here one advantage over the eternalist 5 : he can account for an important feature of events – that they are in progress. This feature of event-like entities consists in two claims : first, they have temporal parts, and second, those parts come into existence and then pass out of existence. It seems that only presentism, and not eternalism, can intuitively account for the second of these claims. §4. The presentist perdurantist view inherits the flaws of presentism discussed in chapter 2, and this should perhaps be enough to reject it. But there are further difficulties : first, I don't think that its treatment of the 'nochange' objection is adequate, and, second, there are some additional problems with the view due to the claim that wholes have parts that don't exist. §5. So let us consider the first of these two points : with respect to the 'no-change' objection, I do not see the force of the presentist perdurantist's answer. Suppose that the objection succeeds against four-dimensionalism. The core idea of the objection is that instead of having a case where an object genuinely changes in its intrinsic properties, we have a case where one object (one temporal part) is replaced by another. Peter Simons, for instance, makes this claim when he says that the "four-dimensional alternative is not an explanation of change but an elimination of it, since nothing survives the change which has the contrary properties" (Simons (2000, p. 65)). Now, if this objection applies to four-dimensionalism, it obviously applies to presentist perdurantism as well – what we have, in the 5

David Stauffer raised this point in discussion.

Presentist perdurantism and the nochange objection

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situation as described by Brogaard, is not one and the same object that would change any of its intrinsic properties, but a series of numerically distinct objects coming out and into existence, when one of them is continuously replaced by another. The objection, then, applies here with as much force as before. But perhaps the presentist perdurantist could claim that her view, but not the four-dimensionalist's, can accommodate the claim that there is change in what exists – and this is perhaps why Brogaard thinks that it can answer the no-change objection. Indeed, the four-dimensionalist's ontology is a static one since all times, past, present and future, equally exist, while the presentist component of presentist perdurantism allows for a world where what exists changes, since only the present time is real. But let us be careful about what such a claim is about : what we have here is that there is a difference in what exists, since the reality's stock contains, for example, a full sandglass at some time, and does not contain such an entity at a later time. But how does such a claim answer the no-change objection ? It doesn't. It is true that the total reality's stock is different from time to time – but such a claim turns out to be true even under four-dimensionalism, since the reality's stock at some time is different from the reality's stock at some other time. The only difference is that under presentist perdurantism the reality's stock at a time is the reality's stock simpliciter, but this could hardly provide an answer to the no-change objection – granted, the defender of such a view could claim that "the reality's stock simpliciter changes" but what else could such a claim mean, except, as we have seen, that the reality's stock is different from one time to another ? – which, again, is true even under four-dimensionalism. Furthermore, and most importantly, even if there were a difference between the two views with respect to a 'change' in what exists (the reality's stock simpliciter), there certainly is no relevant difference in the account the two views provide of what we wanted to account for in the first place : intrinsic change of an entity such as a particular sandglass. Exactly as under fourdimensionalism, nothing (that is, no one thing) undergoes intrinsic change under presentist perdurantism – what we have in both cases, to repeat the objector's charge, is not change of an individual, but replacement of one changeless object (one temporal part) by another changeless one. And the same goes, of course, for the world as a whole (the reality's stock at a time)

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– the world is simply replaced by another, with the passage of time. It seems to me then that if the no-change objection succeeds against fourdimensionalism, it succeeds against presentist perdurantism as well. §6. Another point of dissatisfaction with the presentist perdurantist view arises when we contemplate the claim that at the present time t2 the sandglass doesn't exist completely but exists there by having a t2-part (see fig. 5 in I.1.§7). The perdurantist component of this view would push us to say that it also has the rest of its temporal parts existing at other times, but according to presentism, those other times don't exist. But how is it possible to claim that material objects have temporal parts at other times than the present if these parts don't exist ? Of course, following presentism, one could say that they existed and exist no longer, but in what sense would they be parts of the object ? The very plausible principle involved here was put forward by Trenton Merricks : "an object cannot have another object as a part if that other object does not exist" (Merricks (1995, p. 524)). According to Sally Haslanger, this is in no way problematic to the holder of presentist perdurantism (see Haslanger (2003, p. 11)).: her grandmother, says she, is part of her family even though she does not presently exist, so if her family can have a non-existent part, why a sandglass couldn't ? Such a line of argument does not seem to be of great support, since one could very well argue that a deceased member of a family is not a part of it : a family is probably best conceived of as a plurality, like a football team, and exactly as a football team can lose one of its members when this member ceases to exist, a family can lose a member in the same way, and in both cases the lost member is not a part of the team or the family anymore. Besides, Haslanger's example doesn't seem to be a good one since the relation that family members or football team members bear to families and teams is a membership relation rather than a parthood relation, and so this kind of examples cannot establish here that any non-existent object could be a part of anything existent, in the strong sense of "part" required by perdurantism – a doctrine according to which ordinary objects like tables are made up of temporal parts. Concerns about family members set aside, the main ontological difficulty here is that it really seems very hard to admit that the objects (temporal

Problem with parts that don't exist

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parts) that compose another object (the whole sandglass) exist only one after another, and so fail to ever make up the whole, as they should. The sandglass is supposed to be an aggregate of his temporal parts, but there never is a time (or time-span) at which such an aggregate exists. Lawrence Brian Lombard thinks otherwise (see Lombard (1999)). As he points out, rightly, one must carefully distinguish between two senses of "exist" if one is a perdurantist (both presentist and eternalist). First, the straightforward sense in which instantaneous temporal parts (let us admit here that there are such things, even if the perdurantist is not committed to them) exist at a certain time – if such entities exist at a certain time, they exist at this time entirely (they are three-dimensional entities) and they have all of their (spatial) parts at this time. Second, the derivative sense in which the sandglass, a whole composed of all of his temporal parts, exists at some time t – in this sense the sandglass exists at t in virtue of having a temporal part that does; but one is enough, it does not need to have all of his parts at t. Of course, it is the second, derivative, sense that is the interesting one for the perdurantist here, the first one being accepted by everyone : if there are any three-dimensional instantaneous entities, it is uncontroversial that they exist entirely at the time they do. Now, criticising Merricks's claim that an object cannot have another object as a part if that other object does not exist, Lombard says that "what is obvious is only that an object that exists at a time t, cannot have, at t, another object as a part, if that other part does not exist at t. But what the perdurantist wishes to say is not inconsistent with that. […] What exists now in [the derivative] sense – [the sandglass] – is something that does (at some time or other) have parts that do not exist now; but what exists now in that sense does not now have those parts." (Lombard (1999, p. 256)). But let us consider a true statement like "The sandglass has a present temporal part, but it is not identical to it". The problem here is simple : what is the referent of "the sandglass" and the first occurrence of "it" in this statement ? That is, what is this allegedly existent object that we are making reference to by these words ? Does this object exist ? Of course, it doesn't – only a part of it does. Perhaps, the presentist perdurantist would say that the other parts existed and will exist and that there is a sense in which we can speak about the sandglass composed of all of its parts – but such a strategy does not seem to be available here, since it would mean that

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one is taking seriously something like an extra-temporal standpoint from which one refers to an entity composed of different temporal parts existing at different times. The eternalist could do that, of course, but not the presentist, since doing this would be like considering the different times as equally real. It seems that the only thing the presentist can do is to see things from a standpoint of some determinate moment of time (the present) and from this point of view nothing that could be the referent of "the sandglass" is available. So, in what sense the referent of "the sandglass" can be said to exist ? In reply, Lombard would probably say that it exists derivatively – but what does this mean here ? In the presentist's vocabulary, the 'normal' meaning of "exists" is "exists now" – only what exists at the present time 'really' exists; remember that presentism is a doctrine about what there is in reality's stock, and that the doctrine claims that there is nothing more than the presently existing things. But now, the presentist perdurantist is telling us that there is more – that there is another, derivative, notion of existence according to which things composed of nonpresent (non-existent) things exist. But, first, this seems to be a strong departure from one of the central claims of presentism to introduce two concepts of existence – one that sticks to the presentist view, and another that does not seem to; and second, those two senses of "exist" are really distinct and irreducible one to the other. Compare to the case of the fourdimensionalist : she also uses two senses of existence, the 'ordinary' one, and the derivative, but here, the derivative sense does not carry any new ontological commitments – it only tells us that something can exist at a certain time by having a temporal part here, but it does not involve anything more than there already is in the first, non-derivative, sense of existence – so here, the derivative sense of existence is only a device to accommodate ordinary language and perhaps our intuitions, but nothing more. So, it seems that the notion of having non-existent parts seems to carry with it an ill-motivated plurality of notions of existence. But even if such notions of existence were to be accepted and endorsed, this would not leave the presentist perdurantist view cleaned of problems with the having of parts that don't exist. To see this, let us make a small detour and first consider another rescue mission that the defender of the presentist perdurantist view might want to

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undertake to answer the problem we had : that the temporal parts that compose an object exist only one after another, and so fail to ever make up the whole – and so it seems that the sandglass never really exists. Here is a remedy that is readily at hand : deny that the sandglass is a fourdimensional whole made up of temporal parts, and claim, rather, that he is an instantaneous temporal part which persists through time by having other temporal parts at other times as temporal counterparts. This amounts to abandon the more traditional perdurantist 'worm view' in favour of the so-called 'stage view' – since ordinary objects like Cyrano, according to this view, are the instantaneous stages rather than the worms made up of them. It is not my purpose to discuss the stage view here (I will present it and discuss it in detail in chapter 7), I only wish to see how relevant it is to the combination of perdurantism and presentism. And it is obvious that it has the nice advantage to answer our objection : if the sandglass is an instantaneous stage rather than a temporally extended worm, then there is of course no problem about having non-existent parts, since nobody claims that it has any, and there is no problem about how successive stages could make up a whole, since nobody really cares about the wholes (Sider, who defends the stage view, claims that the wholes exist in addition to stages, but that these are not the ordinary objects we usually care about and quantify over – so at least the pressure on the presentist perdurantist becomes here much weaker). So isn't there a good reason for the presentist perdurantist to become a stage theorist ? I think not. Consider the claim that the sandglass is now empty, but was full before. The stage view provides a counterpart-theoretic analysis of such a claim : the sandglass is now empty, but it has a past counterpart that is (was) full. Now, what is needed for the sandglass to have such a counterpart ? Two stages are counterparts iff they are related by the counterpart relation. The counterpart relation is a relation of similarity, and perhaps spatio-temporal contiguity, or causality, or something else. But whatever the counterpart relation is, it simply cannot hold between different stages if one is a stage view theorist who wants to be a presentist as well. Take the full sandglass at t1 and the empty sandglass at t2 (the present time). These two different objects are supposed to be counterpart-related. But how could they ever be? Suppose that to be counterparts, two stages have (at least) to resemble each other – but how could a non-existent object (the sandglass at t1) bear

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any degree of resemblance to an existent object (the sandglass at t2 – the present time) ? Nothing non-existent is sufficiently similar to anything existent for those two things to have any similarities, and so to be counterpart-related (if it makes sense at all to even speak about 'nonexistent things'). And generally, the counterpart relation will never hold between the two objects (the two numerically distinct sandglasses) simply because there never is a time when the two objects both exist – and so there never is a time when both relata of the counterpart relation exist. How could then the counterpart relation ever succeed in doing the job it promises if the relata that it is supposed to relate never both exist ? Of course, one could say here that two objects are counterparts iff, if they were both present (that is, if they both existed), then they would be counterpart-related, but such a situation never is the case, and so the conditional here would always be vacuous6. In short then, the stage view does not really help the business of the presentist perdurantist because, even if it seems to answer the objection about parts that don't exist, it immediately yields a parallel objection about counterparts that don't exist. And it is easy to see how this problem also makes trouble for the presentist perdurantist who wishes to maintain the worm view – exactly as different counterparts need to be related by a counterpart relation in order to be counterparts, different parts of four-dimensional worms need to be 'glued together' in some way in order to make up the wholes that are the objects we are interested in, like the sandglass. Finding such a glue (that is, a unification relation that makes the successive temporal parts of a single four-dimensional worm ontologically stick together) is not an easy task even for the four-dimensionalist, but for the presentist perdurantist, the task just seems impossible to be carried out. For what would such a glue relation be ? Again, it might involve resemblance, or causality, or spatiotemporal contiguity, or something else – in fact, whatever serves the stage theorist to load his counterpart relation can serve the worm theorist as the glue. And so, of course, the same problems as those we have just seen with the stage view will appear for the worm view : how could one existent thing and one non-existent thing be glued together (if, again, I may be allowed to even say such a weird sentence) ? That is, what kind of 6

This parallels what Lewis (1986a, p. 238) says about modal counterparts.

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ontological glue would be needed in order to authorise that mereological composition takes place between a thing that exists and nothing ? Perhaps one could propose here, as a remedy, to follow the line of almost all fourdimensionalist's who are friends of the principle of an entirely unrestricted mereological composition (for independent reasons) – so that the glue relation might not be restricted at all. But however unrestricted, it certainly cannot be that unrestricted – unrestricted mereological composition is restricted to existent things only, and any attempts to take away even this restriction would lead one to weird places where no sensible metaphysician (I hope) wants to go – like commitments to individuals made up of the top half of Cyrano's body today, and all of the tropical fish of the 19th century, and three unicorns, and two fire-breathing dragons. In the light of the above, I cannot see a real motivation for the presentist perdurantist view, especially since, as we have seen, its alleged advantage against the no-change objection turned out not to be very satisfactory in the end. Crazy metaphysics

§7. Perhaps still another way to put this worry is to acknowledge that the combination of presentism and perdurantism merits the label Mark Heller gave to it : "crazy metaphysics" (Heller (1990, p. 17)). Indeed, to say this, is to emphasize that, as we have seen, only a part of the sandglass exists, but the sandglass itself doesn't ! The motivation for the view was to avoid the charge against four-dimensionalism that it denies genuine change. To do this, the presentist alternative rejected the 'strip theory' – the view that "[a sandglass] has temporal parts with different properties, just as a multicoloured strip of paper has spatial parts with different properties" (Brogaard (2000, p. 342)) – but, in doing this, it simply rejected the existence of sandglasses, people, computers, trees, … it rejected the existence of any material non-instantaneous objects. Of course, the fourdimensionalist also claims that none of these objects exist entirely now, but they do exist because their temporal parts genuinely exist at other, past or future, times and are as real as the presently existing ones.

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Chapter 4, The problem of change in temporary intrinsic properties §1. In I.3.§2, I already mentioned the problem of change in properties. As before, let us say that a sandglass is full when its top half contains all of the sand, and that it is empty when its bottom half contains all of the sand. Surely, being full and being empty are intrinsic properties of the sandglass, and surely any theory should be able to accommodate the fact that a sandglass can change in this respect. A sandglass can, for example, change from being full to being empty from t1 to t3, as on the figure below :

The problem of change

Fig. 7

t1

t2

t3

Intuitively, a problem appears when we notice that one single object is said to have the two incompatible properties "being full" and "being empty"; surely, it has them at different times, but then the task of any theory consists in explaining how this 'having at different times' takes the contradiction away and avoids being incompatible with the principle of Indiscernability of Identicals : (Ind.Id.) (∀x) (∀y) ((x = y) → (∀F) (Fx ↔ Fy)) For any objects x and y, if x is identical with y, then for any property, F, x exemplifies F if and only if y exemplifies F. The four-dimensionalist and the presentist, as we shall see, have both a satisfactory account of the phenomenon of change that avoids the contradiction from having incompatible properties at different times. The endurantist does not.

46 The fourdimensiona list's solution

§2. According to the four-dimensionalist, an object exists at different times by having temporal parts existing at different times. The sandglass exists at t1 by having a t1-part and exists at t3 by having a t3-part. The property of being full, then, is exemplified by the t1-part and the property of being empty is exemplified by the t3-part. This is how fourdimensionalism avoids the problem with the principle of Indiscernibility of Identicals – for the different incompatible properties are, in fact, instantiated by different objects : different parts of a four-dimensional whole. And surely there is no contradiction hidden anywhere – different parts of any object can, and do, exemplify different, even incompatible, properties. This is so, uncontroversially, in the spatial case : at a single time t1 for instance, the top (spatial) part of the sandglass has the property of containing sand and its bottom (spatial) part has the property of not containing sand, but no one would claim that there is any contradiction here since the two incompatible properties are had by different parts of the sandglass. The four-dimensionalist's proposal is to treat change through time as analogous to spatial variation; this is so because the fourdimensionalist takes time to be a fourth dimension on a par with the three spatial dimensions and because material objects are said to have temporal, as well as spatial, extent. Those objects are like space-time worms, different segments of which have different properties. In short, there is no spectre of contradiction haunting the four-dimensionalist because the "different intrinsic properties generally belong to different things" (Lewis (1986a, p. 204)). So, on the four-dimensionalist view, change is no more extraordinary and problematic than spatial variation – because the sandglass is extended in space, its spatial parts can have incompatible properties, and because it is extended in time, its temporal parts can have incompatible properties as well.

The 'no-change' objection

§3. But this nice and elegant four-dimensionalist solution is sometimes criticized. Some will say, following, among others, Peter Simons that the "four-dimensional alternative is not an explanation of change but an elimination of it, since nothing survives the change which has the contrary properties" (Simons (2000b, p. 64)). We want to give an account of how a single object, a single sandglass, can persist through change and the fourdimensionalist, according to Simons, is telling us a story about different

47

objects (different parts) having different properties, and this is not the story we wanted to be told. Once it is true that a certain temporal part of the sandglass is full, it will always be true – this is a fact that, according to four-dimensionalism, cannot change. And that's what leads some to call four-dimensionalism a 'static' ontology : everything seems to be just there and no concrete particular can ever genuinely change. §4. What is intrinsic change ? According to Judith Jarvis Thomson, "a thing changes iff it has a feature at an earlier time which it lacks at a later time" (Thomson (1983, p. 210-211)). Berit Brogaard claims that "change takes place when a single entity has two incompatible states at different times" (Brogaard (2000, p. 341)). Both views follow the traditional view of Bertrand Russell that "change is the difference, in respect of truth and falsehood, between a proposition concerning an entity at a time t and a proposition concerning the same entity at another time t', provided that the two propositions differ only by the fact that t occurs in the one where t' occurs in the other" (Russell (1903, §422)). What the three views have in common is that change is the having of different properties at different times. But if this is right, the four-dimensionalist has nothing to fear from the 'no-change' objection : according to the four-dimensionalist's picture, the sandglass, the four-dimensional entity, has at t1 the property of being full, and at t3 the property of being empty (by having a t1-part that is full and a t3-part that is empty); it has a feature at t1 that it lacks at t3 – and that's all that's required to claim that a change occurs. Surely, an instantaneous temporal part of the sandglass does not change (it will, for instance, always be true that the t1-part has the property of being full), but the sandglass does, and this is what we wanted to account for. The fourdimensional sandglass can very well have different properties at different times and can, therefore, change. And yet, the unsatisfied objector would say, the four-dimensional sandglass cannot gain nor lose any properties – once it has them, it has them forever. This is true. But I do not think this should bother the four-dimensionalist at all. First of all, it is worth noticing that this is not a feature of fourdimensionalism – rather, it is eternalism that's under attack here. The eternalist endurantist would have to face exactly the same objection (as, for

Reply to the objection

48

instance, D. H. Mellor, a defender of the eternalist endurantist view, has to (Mellor (1998, p. 84))) : if he's an indexicalist (see §8 below), then it will turn out to be true that any object also has tenselessly all of its properties forever – for instance, if an enduring sandglass has the time-indexed property of being-full-at-t1, it has this property forever. And the same holds for the adverbialist (see §11 below) : once t-ly full, always t-ly full, as Trenton Merricks would say (see Merricks (1994, p.169)). So even if there were a serious objection, it is not the doctrine of temporal parts that is objectionable here, but the doctrine about time : eternalism. But there is no such serious objection. For all eternalists, at one time the sandglass is full and at a later time it is empty – that much is true and always will be. Why would this preclude change ? The fact that the sandglass is full at t1 does not change, but why would this lead to deny that the sandglass changes ? Even the presentist, I think, would say that "At the past time t1, the sandglass was full" will always be true. There is also another way to put this 'no-change' objection against fourdimensionalism that is to claim that the view takes change to be too much like spatial variation. Yes it is, a four-dimensionalist would reply – but why is this an objection to my view ? Indeed, it is part of my view that time is spacelike and that material objects are extended in time as well as they are in space. As Sider puts it, "the objections may simply be met head-on. Change is analogous to spatial variation. […] There are no good arguments to the contrary." (Sider (2001, p. 214)). A typical four-dimensionalist claim concerning this analogy is that an object's carrier through time is like a road's extension across space. An illuminating explanation can be found in Heller (1992, p. 703 (my italics)) : he suggests that "we do in fact sometimes describe an object as changing in virtue of its having different properties at different places". When I give instructions to a friend for him to find my house, to take Heller's example, I can tell him : "It's exactly two miles after the road changes from paved to dirt" and, so, I am speaking about the road as if it changed, while, in fact, I am speaking about dissimilarity of its spatial parts. If I were viewing the road from a bird's eye view (from a helicopter, for instance) I would not describe it as changing. The difference between the two cases, as Heller points out, is that in the latter I have a neutral perspective (in the eternalist case, this is sometimes called "a God's standpoint") while in the former I have given my friend a

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direction : following this direction, the road is first paved and then dirt, and this is why I said it changed. Now, it seems to be a physical fact that time has a direction, and this is why, in the temporal case, an object's having different properties at different times is genuine change, while an object's having different properties at different places is not (it just can seem to be because of our human perspective, as the road case shows). So, not only four-dimensionalists aren't moved by such an objection but some would even claim that there is a reason in favour of four-dimensionalism – that time is analogous to space and that temporal parts of a material object are parts of it in the same sense spatial parts are – as Armstrong (1980, p. 6768) puts it, "they are temporal parts rather than spatial parts, but the adjectives 'temporal' and 'spatial' do not modify the meaning of the word 'parts'". The general argument the four-dimensionalist wants to raise here is that since ordinary objects are spatially extended and have spatial parts, and since time is spacelike (it is just another dimension on a par with the three spatial ones), they also are temporally extended and have temporal parts. This is plausible (and, perhaps, supported by relativity theory), but I don't see any way to put this claim as an argument for four-dimensionalism or against its competitors. For the competitors could happily accept that there are analogies between time and space, and they could happily accept that objects are spatially extended, while denying the conclusion of the argument : they could claim that the argument fails because something that is true in the spatial case is not true in the temporal case, simply because, precisely, the latter is a temporal case. Sider calls this "a particularly stubborn […] response" (Sider (2001, p. 92)), but it still remains a response that the anti-four-dimensionalist could give and it would be hard to prove him wrong. It would be hard to prove him right as well. Perhaps, Sider is right when he says that we usually accept that objects are spatially extended and have spatial parts7 – even the endurantist usually accepts that – but then, there is perhaps pressure on him, not on the fourdimensionalist, to show why he runs for spatial parts but not for temporal parts. He must, as Sider puts it, "positively commit to an argument for parts 7

This is not universally accepted though (see my discussion of Parsons' view in I.4.§22-25).

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in the spatial case, and so has the burden of explaining why that argument does not carry over to the temporal case" (Sider (2001, p. 92)). The presentist's solution to the problem of change

Lewis's objection

Endurantism and the problem of temporary intrinsic properties

§5. Presentism, as argued in I.2, has serious drawbacks. But it is interesting enough to notice that it has the advantage to provide an obvious solution to the problem of incompatible temporary intrinsic properties. The perdurantist presentist could, probably, use a version of the fourdimensionalist's strategy but presentism itself avoids the problem in a different way. According to presentists, all we have to do is to keep our tenses straight : if t2 is the present time, then the sandglass was full when t1 was present and will be empty when t3 will be present but those past and future times don't really exist – they are like "false stories" (Lewis (1986a, p. 204)) – so there really is nothing to exemplify incompatible properties, and, therefore, no contradiction can arise; the only properties an object has are the properties it has now. §6. According to David Lewis, this solution is untenable because "it goes against what we all believe. No man, unless it be at the moment of his execution, believes that he has no future, still less does anyone believe that he has no past" and "[this solution] rejects persistence altogether" (Lewis (1986a, p. 204)) – for, as I understand him, there is no good in saying that an object persists through time, which means that it can exist at different times, if only one time exists. Lewis, in his (2002, p.2), makes it clearer that this is not an objection to the presentist's account of intrinsic change but to presentism in general. This is why I say I find the solution satisfactory : under the presentist's hypothesis, no contradiction arises from the fact that the sandglass is full at t1 and empty at t3 and the principle of Indiscernibility of Identicals. §7. According to endurantism, the sandglass at t1 is numerically identical to the sandglass at t3. At t1, the sandglass is full, at t3, it is empty. But if we follow the principle of Indiscernibility of Identicals, the sandglass at t1 and the sandglass at t3 are numerically identical only if they exemplify all the same properties. But this leads to the untenable claim that the sandglass, the very same object existing at t1 and t3, has the two incompatible properties of being full and of being empty. This objection – that

51

endurantism fails to give an account of how persisting objects can have incompatible properties at different times – was raised by David Lewis who considers it to be "the principal and decisive objection against endurance" (Lewis (1986a, p. 203)). To avoid the contradiction resulting from the sandglass's having the incompatible properties "being full" and "being empty", fourdimensionalism and presentism are revisionary about the object that exemplifies those properties; the former by analyzing it as an aggregate of temporal parts and the latter by denying its past and future existence. Typically, endurantists try to reach this result by being revisionary not about the object but about the properties or the having of properties. Let us consider the statement "The sandglass is full at t1". It can be parsed in different ways, giving birth to different responses to the objection8 : (i) The-sandglass-at-t1 is full. (perdurantism) (ii) The sandglass is full-at-t1. (indexicalism) (iii) The sandglass is-at-t1 full. (adverbialism) or The sandglass is t1-ly full. (adverbialism) It will be argued that (i) is preferable to (ii) and (iii). §8. Solution (ii), Indexicalism The indexicalist solution to the puzzle consists in temporalizing the properties an object can have. If instead of the properties "being full" and "being empty", we have the time-indexed properties "being full at t1" and "being empty at t3", no contradiction arises from the endurantist claim that the sandglass at t1 is numerically identical to the sandglass at t3 and the principle of Indiscernibility of Identicals – for the new time-indexed properties are not incompatible, and "The sandglass is full-at-t1 and empty8

How would a presentist parse "The sandglass is full at t1" (where t1 is a past time) ? It seems a difficult task to me, since, according to presentism, no sandglass exists at t1. (i) is clearly not available and (ii) and (iii) would have to predicate a property of a nonexisting object. Probably, a presentist would simply refuse such a sentence and would say that only "The sandglass was full at t1" is true.

Indexicalism

52

at-t3" is a consistent claim. So, surely, this is a way to avoid the objection from §7 above. Objection : having a property simpliciter

§9. But according to some 9, following David Lewis, this analysis should be rejected because the cost of it is too high. There certainly are timeindexed properties such as "being full at t1" but, paraphrasing Lewis (see Lewis (2002, p.4)), where have the monadic intrinsic properties "being full" and "being empty" gone ? Is it not possible to say that the sandglass is full, or empty, simpliciter ? – that it has not only the property of being full at t1, which no one denies, but that it can also have the property of being full ? Can't the sandglass just be full or empty_? It seems reasonable that it should be allowed that it can. But indexicalism doesn't allow that; indeed, according to this view, all properties turn out to be time-indexed – I cannot have, for instance, the property of having two eyes, I can only have the series of properties "having two eyes at t1", "having two eyes at t2", "having two eyes at t3", and so on. But, I want to say, I have two eyes, not two-eyes-at-tn. (Besides, another worry also seems to be that such timeindexed properties are not really monadic properties but rather disguised relations between monadic properties and times.)

Objection: duplicates at different times, and problem with objects when they don't change

§10. Another claim, raised by Mark Johnston (see Johnston (1987)), objects to indexicalism that it cannot deal with a case of two duplicate objects at different times. If a sandglass S1 exists at tn and if a duplicate sandglass S2 exists at tm, then they both have the property of being, for example, full. But, on the indexicalist account, it is not possible for such two duplicate sandglasses to exemplify the same property, for S1 has the property of being-full-at-tn and S2 has the property of being-full-at-tm. In a parallel case of two simultaneous duplicate sandglasses, both would turn out to exemplify the same property (for instance, being-full-at-tn). But, first, there doesn't seem to be any good reason to claim that only simultaneous duplicates can exist, and not duplicates at different times; and, second, duplicates, simultaneous or not, should be allowed to 9

See, for instance, Rea (1998) and Merricks (1994, p. 168) who take to be a first desideratum of any reply to the objection that it "should allow for the exemplification of non-time-indexed and non-relational properties like 'being bent'".

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exemplify the same properties (at least some), but this is precluded by indexicalism in the case of non-simultaneous duplicates. A somehow similar problem, I think, can also arise for one single sandglass only. Suppose, for instance, that a sandglass S exists at t1 and is empty. Suppose that it does not change in this respect until some later time t14. What we'd like to claim here, intuitively enough, is that the sandglass keeps having the same property of being empty all along between t1 and t14 – but indexicalism precludes this, since at any times in this interval the sandglass has to lose all of its properties and gain new ones : it first has the property "being-empty-at-t1", then the property "being-empty-at-t2", then the property "being-empty-at-t3", and so on. Under indexicalism, because a sandglass cannot simply have the property of being empty, it has to change its properties all the time, and it just cannot keep any, it just cannot stay the same. Another way to see this problem, suggested by Achille Varzi 10 , is to remark that if an object is said to be F-at-t1 and F-at-t2 then those two timeindexed properties have something in common – namely, F. But an indexicalist cannot account for such a similarity between those two properties, simply because F is not a property available to him. And this becomes really something one should worry about if one wants to make sense of claims such as "The lizard on my desk at t1 is just as green as the lizard in the forest at t2" since on an indexicalist account of what it is to be green (green-at-t1, green-at-t2), such sentences will systematically turn out to be false. Before going further, let us examine the alternative (iii). §11. Solution (iii), Adverbialism The adverbialist solution to the problem of temporary intrinsic properties proposes not to temporally modify the property but the having of it. Thus the adverbialist will say that "The sandglass is full at t1" should be analysed as "The sandglass is-at-t1 full" or, more elegantly, as Johnston would put it, "The sandglass is t1-ly full" (see Johnston (1987, p. 128-129)). This strategy is, I would say, more respectful of ordinary language than 10

During his lectures at the summer school on persistence in Montana (Switzerland) in 2003.

Adverbialism

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indexicalism, since we would easily say "The sandglass is presently full" and not "The sandglass is full-at-the-present"; this is also supported by the fact that familiar terms like "now", "yesterday", "tomorrow", "always", etc. are all adverbs. Furthermore, this view saves the existence of non-timeindexed properties such as "being full". According to adverbialism, there is not just the having of a property, there is always the t-ly having of a property. This will provide a solution to the problem of temporary intrinsics, because the principle of Indiscernibility of Identicals will be modified in such a way that it will not only be required that two objects are numerically identical if and only if they have the same properties, but also if they have those properties in the same way. So if the sandglass is full at t1 and empty at t3, it has both the incompatible properties of being full and being empty, but it has the former t1-ly and the latter t3-ly and this is how the contradiction is avoided. Adverbialism and duplicates at different times

§12. According to Johnston, adverbialism also has the advantage over indexicalism that it gives a satisfactory account of the duplicate objects at different times problem (see §10 above), because the two sandglasses S1 and S2 can both have the property of being full and not the different properties "being full-at-tn" and "being full-at-tm". This, I think, is better than indexicalism but it still is perhaps not entirely satisfactory : it could be reasonable to claim that genuine duplicates would require not only the exemplification of the same properties, but also that they exemplify them in the same way – for otherwise they would simply not be duplicates, since they would have different properties such as "having tn-ly F" and "having tm-ly F". But, if this requirement is justified, only the first condition is met by adverbialism, not the second: the different duplicate sandglasses, granted, exemplify the same properties but in different ways. So one could argue that even if adverbialism is to be preferred on this matter to indexicalism, it still fails to provide a completely satisfactory solution to the problem. (The same remark applies to adverbialism and the second objection from §10 above : between t1 and t14, S can, unlike under indexicalism, keep the same property of being empty, but has to change all the time the way it is having it.)

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§13. If one rejects indexicalism, one will probably reject adverbialism for similar reasons. To me, as I said, adverbialism seems more attractive because of its compatibility with ordinary language, because it saves nontime-indexed properties, and because of its better treatment of the duplicates problem, but the fact remains that, exactly as the indexicalist, the adverbialist denies that it is possible for the sandglass to have the property "being full" simpliciter. The sandglass can have it t1-ly, but it cannot just have it 11. As David Lewis puts it : "If a relation [that is, the relation having t-ly] stands between you and your properties, you are alienated from them" (Lewis (2002, p. 5)).

Adverbialism and having a property simpliciter

§14. A possible reply (see Sider (2001, p. 92-)) for an endurantist (whether he be an indexicalist or an adverbialist) to the objections in §9 and §13 is to claim that "to be full" is equivalent to "to be full now". This would save at least an appearance of how we can predicate properties simpliciter and analyse such claims in terms of the favoured time-indexed properties or time-indexed ways of the having of the properties.

A reply for endurantists

§15. But this will not work for claims such as "I have two eyes" because it is not only meant by this claim that "I have two eyes now" – that's only a part of the meaning – what I want to say when I make such a claim is more precisely that I have two eyes for a certain period of time, which would lead us, following indexicalism, to properties such as, for example, "having two eyes from t15 to t243" or "having two eyes during my whole life" and, following adverbialism, to time-indexed exemplifications of properties such as in "I have t15-to-t243-ly two eyes" or "I have two eyes during my whole life". And, again, there is nothing to object to such properties and such ways of having them but what about the property of having two eyes ? Is it equivalent to a conjunction of time-indexed properties ? Or to some interval-of-time-indexed property ? I think not. Having two eyes is a

On having a property simpliciter

11

Another unwelcome consequence of both indexicalism and adverbialism is that in a timeless world nothing could exemplify a property like "being full". As Sider puts it : "If being straight-shaped is a relation to times, nothing would remain straight-shaped if you cut away all the times from a world. And surely objects in a timeless world could be straight-shaped." (Sider (2001, p.99)).

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property I have simpliciter without being committed to any claim about at what time it is the case or for how long it is the case. Suppose there is only one sandglass in the world (only one in the endurantist's sense), that it is used only once and then destroyed (so that the sandglass is full only once and empty only once). Then it would be possible for us to have non-ambiguous names such as "the full sandglass" or "the empty sandglass" or "the exactly half-full sandglass", and so on. Such names would be genuine proper names for they would pick out exactly one object, an object existing completely at some time, and it would not be necessary at all to use any temporalizing device to name the object and to predicate anything of it. We could say "The full sandglass is full" without being committed to implicitly meaning something like "The full sandglass is full-at-t1" or "The full-at-t1 sandglass is full-at-t1". Indeed, the former paraphrase would not be an analytic truth, as it should be, and the latter would amount to embracing an ontology of temporal parts because the temporalizing element is built in the subject. Nor would it be necessary for "The full sandglass is full" to implicitly mean "The full sandglass is t1-ly full" (as the adverbialist would say), for why should it be? – since there is only one object denoted by the subject of the sentence, it does not seem required to me that any temporal specification is needed (and, here again, the original sentence is an analytic truth, whilst the adverbialist's paraphrase is not). My point is that it is not necessary that claims such as "The full sandglass is full" involve any hidden or implicit temporal qualification; and if this is the case, then there are objects that have properties such as "being full" and "being empty" simpliciter. Besides, as remarked in §10 above, it seems that we need non-indexed properties that are had simpliciter if we want to say, for instance, that if I had two eyes yesterday and that I still have two eyes today, then I have a property now that I also had yesterday; that is, I want to say that I kept having this one and very same property – but I cannot say this if the only properties available are properties like having-two-eyes-at-t1 and havingto-eyes-at-t2. So it seems that we need non-indexed properties that are had simpliciter after all. If this is the case, and if, furthermore, it is claimed by the endurantist that the full sandglass is numerically identical to the empty sandglass, then, really, there is a problem for the endurantist with the principle of

57

Indiscernibility of Identicals. To avoid this, one could claim that the full sandglass and the empty sandglass are not identical, but this would lead to an ontology of temporal parts which is, of course, unacceptable for the endurantist. So the only option for the endurantist is to maintain that it is not possible for the full sandglass to be just full, to have this property simpliciter. For Peter van Inwagen to say that I have the property of having two eyes is to say, precisely, that I have it at certain times or, to take his example, "to say that Descartes had the property of being human is to say that he had that property at every time at which he existed" (van Inwagen (1990, p. 116)). At this point, it is unclear how the debate should be settled since there is a major disagreement about a central premise : the objector will claim that intrinsic properties such as "having two eyes" or "being full" are monadic and can be exemplified simpliciter, whilst the indexicalist or adverbialist endurantist will deny this assumption. I think the objector is right, but here one must probably agree that the charge against endurantism on this matter is not, contrary to Lewis' claim, decisive. As Sider says, this argument against indexicalism and adverbialism is only as strong as the claim on which it is based, that some sandglasses are just, simpliciter, full or empty (see Sider (2001, p. 97)). It seems we have reached deadlock. Endurantists could claim to have at hand replies to the objection from temporary intrinsic incompatible properties that the objector cannot refute without being dogmatic or begging the question against his opponent. §16. Still, even if indexicalism and adverbialism are accepted, I cannot get rid of the felling that the endurantist 'cheats' somewhere. For how can there be numerical identity between objects having different properties, and being located at different times ? According to my intuition, objects exemplifying different properties are just different objects. My problem here is that even if indexicalism and adverbialism were accepted as plausible semantic solutions to the problem, a metaphysical question would still remain : as E. J. Lowe (who favours adverbialism as the right semantic solution) puts it, "It is the problem of how there can be objects for the description of which the semantic problem arises – that is, how there can exist objects such that we need to be able to say, without fear of

A metaphysical worry

58

contradicting ourselves, that one and the same such object may undergo a change from possessing one intrinsic property to possessing another incompatible one" (Lowe (1988, p. 76)). Lowe's own solution will be discussed in §17-§18 bellow. Here, he is right to say that after the indexicalist and adverbialist have given their analysis, thus avoiding the contradiction they were charged with, there still remains a problem. Look again at the endurantist picture :

the sandglass

the sandglass

t1

t2 now

the sandglass

Fig. 3

t3

The same name denotes what really seem to be different objects : one of them is full, another half-full-half-empty, and the third empty. Remember we are working here under the eternalist hypothesis : all times genuinely exist and are equally real, as real as the present. If we had the epistemic ability to do so, we could contemplate the whole of time, and all the things that happened, happen and will happen would be laid in front of us. Furthermore, according to the endurantist, the sandglass exists completely at all times at which it exists, so we would 'see' a series of sandglasses, a series of entire objects. And now the endurantist claims that those objects are numerically identical – this is something I just cannot believe. Any eternalist, even the endurantist eternalist, will agree, I think, that things can be located in time (which exists in extenso in an atemporal sense of "exists") as well as they can be located in space and can exist at different times as well as at different places (remember that, according to the endurantist, things exist wholly and completely at different times, they are really entirely located at all times at which they exist). Contemplating the whole of the time containing all the sandglasses existing at different times

59

which form a 'temporal series', is like contemplating a garden where a series of sandglasses is laid – and in that (spatial) case, presumably, no one would bet on numerical identity between the sandglasses which form the series. This is why it is so hard for me to believe that, under the eternalist hypothesis, complete things (not parts) located at different times can be numerically identical – a fortiori if they exemplify incompatible properties. And this is why I would agree with some, for example Trenton Merricks (Merricks (1999)) and Michael J. Loux (Loux (1998, p. 231, footnote 5)), that the only viable option for the endurantist is presentism, not eternalism. Of course, the endurantist could defend himself here by saying that the analogy between time and space is not justified; but why not ? – it is the eternalist's own central claim that all times exist, and exist in the same way, and – here comes the endurantist's claim – that material objects are multiply located in time and exist completely at those different temporal locations. Such a picture simply precludes numerical identity. §17. E. J. Lowe's solution (see Lowe (1987a, 1988)) to the problem of temporary intrinsic properties is interesting in the sense that he gives two solutions_: first, a solution to the semantic problem which avoids, according to him, all problems with the principle of Indiscernibility of Identicals – adverbialism. Second, a solution to what he calls the metaphysical problem : the problem of explaining how one and the same object can undergo change in its intrinsic properties. If I understand him well, adverbialism is the right solution to the problem of specifying the logical form of sentences like "The sandglass is full" but it has not, and must not have, any commitment on the ontological level – here, another solution is required. This solution is to claim that the relation of identity over time of a material object supervenes upon spatial relations between the constituent parts of the object. In the case of a sandglass, the grains of sand it contains bear some spatial relations to each other (and to the rest of the structure of the sandglass) at some time, and other spatial relations at other times. This is why the sandglass can be full at certain times and empty at others; this is how it can undergo change and stay one and the same – it is the same sandglass but its structural relationships can differ from one time to another, up to a certain degree. I guess that what Lowe wants to say is that whenever some degree of rearrangement of the

Lowe's solution

60

components of the sandglass is reached, it is no longer one and the same sandglass or simply, it ceases to exist. To avoid a vicious regress (because the grains and the other parts of the sandglass themselves persist and can undergo change in their intrinsic properties, which, in turn, has to supervene upon their own structural relationships), Lowe claims there is a fundamental level, the level of fundamental particles "which all have their intrinsic properties unchangeably" (Lowe (1987a, p. 154)) and, thus, have no temporary intrinsics. So it is in terms of fundamental particles and their relations to one another that change of the macroscopic objects composed of them is to be explained. As Lowe claims, "modern physics offers us a solution to the problem of change which renders superfluous Lewis' solution in terms of temporal parts" (Lowe (1987a, p. 154)). Reply to Lowe

§18. In Lewis (1988), David Lewis gives a reply to Lowe's solution that can be briefly summarized as follows. First, the claim from modern physics that fundamental particles have no temporary intrinsics could be false which would rule out Lowe's solution immediately. If, one day, someone discovers that quarks and electrons can undergo change in their alleged intrinsic unchangeable properties (charge, rest mass, …), it will undermine the basis of Lowe's claims. Second, I am not my particles. There certainly is a relation between me and my particles but it is not one of identity. I lose and gain particles all the time, the particles that compose me now existed before I did and can exist after I cease to. It is more obvious in my case, because I am a living being, but for a sandglass, and for any material object, it is just the same. So, at any time, I am composed by a different set of particles. But then, my relation to those particles is temporary, and it is an intrinsic relation. So the problem with temporary intrinsics is back again : it will have to be explained how I bear the one-many relation of composition to different particles at different times. The problem of change in intrinsic properties is not solved by Lowe's proposal.

SOFism

§19. Another strategy available to the eternalist endurantist that is a variant of adverbialism is exposed in detail by Sally Haslanger (in Haslanger (2003)) and is called "SOFism" (for "state-of-'fairs-ism"). The SOFist picture looks like this :

token states of affaires

type states of affaires

61

Fig. 8

the sandglass's being empty

the sandglass's being full

obtains at

obtains at

the sandglass

the sandglass

t1

t2

the sandglass

t3

now

According to SOFism, in agreement with the endurantist central claim, there are sandglasses wholly existing in token states of affairs obtaining at different times. Here for instance (fig. 8), there is a sandglass existing at t1 by being in a token state of affairs obtaining at t1 and existing at t3 by being in a token state of affairs obtaining at t3. There are also type states of affairs (I suppose they are some sort of abstract entities) that can have tokens at some time : here for instance, there is the type state of affairs "the sandglass's being full" that has a token at t1 and another type state of affairs "the sandglass's being empty" that has a token at t3. In the type states of affairs, the properties "being full" and "being empty" are exemplified by the sandglass simpliciter; they are not relations to times and are not exemplified t-ly. These properties are incompatible but the contradiction is avoided because the two type states of affairs have tokens at different times. This is, in short, the SOFist's picture. §20. I think this strategy is not very palatable. First, it is complicated, or, to be more precise, less respectful of Ockham's Razor than the other alternatives. I would say that a good theory of persistence of sandglasses

Objection to SOFism: Ockham's Razor

62

changing with respect to their properties should be able to provide an explanation using just sandglasses and properties. To appeal to a realm of abstract type states of affairs to solve the puzzle looks to me like 'cheating' and ad hoc. Where other theories, let it be presentism, fourdimensionalism, adverbialism or indexicalism give an account of persistence in terms of sandglasses and properties (or relations), SOFism needs a bigger metaphysical apparatus that is not, I think, justified, since other simpler and ontologically more parsimonious accounts exist, such as four-dimensionalism. This can be seen also in the following way : the SOFist claims (see §19 above) that in type states of affairs, such as "the sandglass's being full", the property "being full" is a property the sandglass has simpliciter. I have difficulties even to understand this claim : a type states of affairs is presumably an abstract entity, a sandglass is not. So, certainly, no sandglass can exist in a type state of affairs and, a fortiori, it cannot exemplify any property there. Objection to SOFism: it doesn't solve the problem

§21. This leads me to another objection to SOFism : I don't think it hits its target, I don't think the contradiction is solved. If I look at the SOFist's picture, I see the type states of affairs that, let's give the SOFists that, do not contradict themselves because they do not have tokens at the same time. But there still is the sandglass – the concrete material object I am interested in, the one that changes over time, the one I have on my desk. This entity exists at different times and is, according to endurantism, numerically identical over time. And this entity has incompatible properties – once it is full, later it is empty – and I do not see at all how the fact that, at different times, the sandglass is said to be in a token of a different type state of affairs takes the contradiction away. The SOFist, I think, simply does not say anything new and interesting for our purposes about the sandglass, rather, he tells a story about type states of affairs, but this is not what we wanted. Haslanger points this out when she says : "SOFism [suggests] that the principal job of an ordinary subject-predicate sentence is not to express a primitive predication between an object and a property […]. Instead, it takes an ordinary statement to be making claim about a state of affair's type obtaining, or alternatively about a token state of affairs being of a certain type" (Haslanger (2003, p. 35)).

63

§22. The last strategy I am going to examine that is available for the eternalist endurantist to face the problem of change in intrinsic properties was developed by Josh Parsons (see Parsons (2000)). First, he introduces the notion of a distributional property : if a poker is hot at one end and cold at the other end, it has the (intrinsic) distributional property of having such and such heat distribution. Let us call this poker "p1" and the distributional property it has "Da" and let us call "p2" another poker with another distributional property "Db" – the property of being uniformly hot, for example. It is then possible, as Parsons points out, to define the property of being hot at one end as the (intrinsic) disjunctive property "Da or Db or …", where a series of distributional properties that ascribe heat at one end of the poker is specified. This disjunctive distributional property of being hot at one end is spatially indexed. To apply this strategy to the temporal case, let us consider the persisting sandglass again. Remember, in short, the eternalist endurantist picture : the sandglass persists through time by being wholly present at more than one time, and all times are equally real. It is full at t1, half-full at t2, and empty at t3. If one were a four-dimensionalist, one could easily see that the sandglass has a certain distributional property of being full at its earlier 'end' existing at t1 and of being empty at its later 'end' existing at t3. Let us call this sandglass "s1" and the distributional property it has "Dc", and, as in the spatial case of the poker, let us call "s2" another sandglass with another distributional property "Dd" – the property of being empty for the whole interval of time from t1 to t3. Now, we can define the time-indexed property of being empty at t3 as the disjunctive property "Dc or Dd or_…", where a series of distributional properties that ascribe emptiness to the t3-part of the sandglass is specified. Just as in the spatial case, Parsons claims, this disjunctive property is intrinsic and non-relational. Up to now, we worked under the four-dimensionalist hypothesis, but Parsons sees a way to apply such a strategy to the eternalist endurantist case : he claims that "we ought to accept the possibility of extension without parts" (Parsons (2000, p._412)). By this, he means that ordinary objects such as sandglasses, tables or roses, entend – they are extended in time by existing completely at different times. And if this proposal is accepted, if the sandglass can be said to have a temporal extent even under the endurantist hypothesis, it is then possible to ascribe to it the disjunctive

Parsons' solution

64

distributional property "Dc or Dd or …". Such an account, then, provides us with time-indexed properties (that takes away the contradiction resulting from the principle of Indiscernibility of Identicals) which are genuinely intrinsic and non-relational. Change, then, as he makes it clear later, "does not consist in objects temporally having changeless properties, but in objects permanently having changing [distributional] properties" (Parsons (2002b, p. 6)). Objection : there are no entending objects

§23. I am not really sure whether I can understand the notion of an object that endures and has temporal extent. I know what the four-dimensionalist means when he says that sandglasses have temporal extent because he takes extension in time to be spacelike and because I know what extension in space is : one object is extended in space by having different spatial parts located at different places; applied to the temporal case, this claim is perfectly well understood in the four-dimensionalist picture. Parsons proposes that "analogous to perdurance, we have pertension, filling space by having distinct parts in distinct places; analogous to endurance, we have entension, filling space by being wholly located in each of several places" (Parsons (2000, p. 404)) and provides an argument to support the claim that there are entending simples (namely, quarks and leptons). I do not wish to discuss his argument in detail, for one thing is clear (he claims this himself) – its key premises are empirical and so, it is subject to surprises from science : if it is discovered that quarks and leptons are not mereologically simple, or that it is not clear that there are mereologically simple particles at all, his argument will be undermined. Furthermore, as he himself points out, current physics is simply silent on whether mereologically simple objects are extended or not. This is why, even if the argument were successful, I do not take it to be of great support for the claim that ordinary material objects, like sandglasses, can be spatially or temporally extended without having spatial or temporal parts. Indeed, it seems obvious to me that spatial extension without spatial parts is not possible, at least, I cannot imagine how it could be. And if this is right, there is no support for the analogous claim in the temporal case. And if this is right, it does not seem plausible that the endurantist's ordinary material objects can exemplify the disjunctive distributional properties Parsons wants them to.

65

§24. There is another worry concerning Parsons' theory. How big are the disjunctions of distributional properties ? There are probably infinitely many ways an empty-at-t3-sandglass can be at other times of its existence. If a sandglass is guaranteed to have temporal extent (let us suppose this) that includes t3, there are probably infinitely many possibilities for it to be such and such at other times. So, there are infinitely many distributional properties which ascribe emptiness at t3 to the sandglass. But then the disjunctive property "Dc or Dd or …" would contain an infinity of disjuncts. Ontologically, this does not seem very satisfying to me : we were looking for an account of how the sandglass can be full at some time and empty at another and we end up with a sandglass that has the time-indexed property of being-full-at-t1-and-half-full-at-t2-and-empty-at-t3-OR-empty-at-t1-andempty-at-t2-and-empty-at-t3-OR-… and so on, ad infinitum. As for some other endurantist accounts, I would then ask where have the properties "being empty" and "being full" gone ? What has them ? Besides, there would also arise an epistemological problem, that is whether we can know and grasp such infinite (or, at least, very large) disjunctions, and if this is what we are speaking about when we say "At t1, the sandglass is full".

Objection : how big the disjunctions of distributional properties are ?

§25. A last objection to Parsons' view is that it is circular. The timeindexed property of being empty at t3 is analysed as a disjunction of distributional properties. What are those distributional properties ? Dc tells us something about the distribution of sand in the sandglass for some interval of time, Da tells us something about the distribution of heat in the poker. What are those properties Dc and Da ? Well, as it appears in the objection from §24 above, I would say a distributional property such as Dc is a conjunction : it's the property of being-full-at-t1-AND-half-full-at-t2AND-empty-at-t3-… Likewise, in the poker's case, the property Da is a conjunction : it's the property of being-hot-at-one-end-AND-mildly-hot-inthe-middle-AND-…-AND-cold-at-the-other-end. It is easy to see that, ultimately, distributional properties are conjunctions of space- or timeindexed properties and this is why it is circular to define, for instance, "being empty at t3" or "being hot at one end" in terms of such properties.

Objection : the analysis of timeindexed properties is circular

66 Conclusion

§26. In this chapter, I have examined some classical and some more original accounts of change in intrinsic properties and it seems that while there is no decisive objection to be drawn against eternalist endurantism on this matter, there certainly is a good reason to favour four-dimensionalism or presentism.

Chapter 5, Coincidence and vagueness §1. A good reason to adopt four-dimensionalism is that it solves nicely a family of problems that all involve puzzles with coincident entities. I shall examine here three such problems and shall try to show that the fourdimensionalist's treatment of them is superior to the endurantist's. A detailed discussion of these problems is to be found, for instance, in Sider (2001, p. 5- and p. 140-), Heller (2000) and Rea (1998). §2. Let us say that at t1 there is a lump of clay that at t2 an artist forms into a statue. Thus at t2 a statue is created. Let us say that it persists until some later time t3 and is then destroyed. At some time after its destruction, at t4, the statue of course does not exist anymore but the lump of clay still does. The lump of clay persists from t1 to t4 : it existed at t1 in a certain (let's say cubic) form, then it was shaped into the form of a statue and, after the destruction, it was shaped again into some other form. A puzzle arises here because it seems that in the interval of time from t2 to t3, the lump of clay and the statue are one and the same object : they have the same form, the same location, they are made up of the same particles. But, if they were the same object, they should, according to the principle of Indiscernibility of Identicals, share all their properties. But this is not the case : the lump of clay has, for instance, the property of being cubical at t1 that the statue has not. So, after all, the statue and the lump of clay are different objects. But then, how can they, from t2 to t3, coincide ? How can they be made of the same particles, how can they have the same spatial location, etc. ?

The lump of clay and the statue

§3. The four-dimensionalist has a simple reply. The t2-part and the t3-part of the statue are numerically identical, respectively, to the t2-part and the t3part of the lump of clay. For instance, the t2-part of the statue and the t2part of the lump of clay do share all of their properties – they have no different historical properties such as being cubic at t1 because none of them existed at t1. But, of course, this does not entail that the statue and the lump of clay are identical : the lump of clay, for instance, has parts at t1 while the statue does not. So they are not identical but they share identical temporal parts; one could say that they overlap. Thus, as Sider points out (Sider (2001, p. 6 and p. 152)), if we accept temporal parts, the puzzle with

The 4D solution

68

the 'coincident' statue and lump of clay is no more remarkable than the spatial case of two overlapping roads, one of them being a sub-segment of the other. Problem with endurantism

§4. For the endurantist, the puzzle is genuine. Since it is the entire statue, and not a part of it, that is wholly present at t2 or t3, since the same holds for the lump of clay, and since they are distinct objects because they do not share all of their properties, the endurantist must endorse the claim that, between t2 and t3, two numerically distinct objects co-exist at the same spatial location, that is, that they coincide. Such a claim being unacceptable, this puzzle of coincidence provides us with a reductio against endurantism.

The fission case

§5. A second case involving a puzzle with coincident entities is the case of fission. At t1, Jean-Luc Picard, captain of Star Trek's starship Enterprise, enters the transport device in order to teleport himself on a planet's surface. Usually, the device is supposed to disintegrate Picard on Enterprise and 'rebuild' him exactly as he was on the planet; but let us now suppose that, due to a malfunction of the mechanism, two of them appear on the planet when only one person should have been transported. At some later time t2, there are then two persons instead of the one that entered the transport room – a plausible way to describe this accident would be to say that the original Jean-Luc Picard has undergone fission. If you don't like Star Trek transport stories, and if you prefer the more usual 'philosophical surgery' examples, think of Jean-Luc at t1 as entering the Enterprise's sickbay and undergoing an operation that would put one half of his brain in a brainless body and the other half of his brain in another brainless body. Suppose, further, that his original body is annihilated and that both halves of his brain survive the operation, and you'll have a similar result as in the transport accident case : there seem now to be two persons who both have exactly the same right to claim to be the captain Jean-Luc Picard. Again, this seems to be a case of fission, where one person undergoes a certain process and becomes two – let us call, from now on, "Jean-Luc" the person before the fission and one of the resulting post-fission persons "Jean" and the other "Luc", as shown on the figure bellow.

69 Fig. 9

Jean Jean-Luc Luc

t1

t2

As far as Jean-Luc's survival is concerned, there are four possibilities 12 : (i) Jean-Luc did not survive the accident (or the operation) and died, Jean and Luc being then two new accidentally-born persons, or (ii) Jean-Luc survived as Jean, and Luc is a new accidentally-born person, or (iii) JeanLuc survived as Luc, and Jean is a new accidentally-born person, or (iv) Jean-Luc survived as both Jean and Luc. I think that (iv) is to be preferred. The trouble with possibilities (ii) and (iii) is that since there is no reason to prefer one to the other (both Jean and Luc, in the transport case as well as in the operation case, have an equal right and the same reasons to claim to be the surviving Jean-Luc), neither of them is attractive – because each choice would simply be ad hoc. And let's ask Jean-Luc himself (that is, let's imagine ourselves as Jean-Luc before the accident or the operation, knowing what's going to happen) : would Jean-Luc say that he cares about what will happen to Jean and Luc if we asked him before the fission ? Would he fear future pains of Jean and Luc, and hope for their happiness ? Would both Jean and Luc be right in claiming Jean-Luc's salary at the end of the month ? The answer to these questions is, I believe, yes – and this is enough to show that Jean-Luc would not consider the fission to be his death, but on the contrary he would think of himself as surviving the 'accident' (so (i) is ruled out). Both Jean and Luc would have Jean-Luc's past experience, skills, memories, and so on. Furthermore, if there hadn't been an accident, and if the transporting mechanism had worked properly – that is if the transport process yielded 12

See, for instance, Parfit (1971, p. 375). Parfit says there are only three possibilities but this is just because I develop his second possibility into two, to be more explicit.

70

no more than one person – we wouldn't have any doubts about Jean-Luc's survival and personal identity, and there is no reason for this to change just because another candidate for being Jean-Luc is there. In the surgical case, the same holds : if only one half of the brain had been transplanted and the other destroyed, we wouldn't have any doubts that our patient survived as the individual that has the undestroyed half-brain – but how could the conservation of the other half of the brain change the situation and make that he did not survive ? I think these considerations show it to be very plausible that in a case of fission of a person, the person survives as all of the resulting individuals of the fission. (A case of fission of a non-conscious material object will be discussed in I.6. Different considerations have to be brought out there.) But note that this does not mean that, after the accident or the operation, there is one person that has the weird experience of being located in two separate bodies, or one person that is bi-located and has no unity of consciousness, rather this case of fission should be conceived of as a case where, after the fission, there are two distinct persons which will from then on evolve in entirely different ways. Problem with endurantism

§6. But, if this is right, there is a problem for the endurantist. If Jean-Luc survives as Jean, he is then, according to endurantism, numerically identical to Jean. Likewise, if Jean-Luc survives as Luc, he is numerically identical to Luc. But, by transitivity of identity, we get as a result that Jean is numerically identical to Luc, which is absurd. But the only way to avoid this result would be to endorse the existence of coincident persons; in this case, it would be to endorse the claim that there were two persons even before the fission occurred. But, surely, this is not something anyone would be willing to accept. Thus, the fission case seems then to provide us with another reductio against endurantism.

The 4D solution

§7. As in the statue and lump of clay case, the four-dimensionalist has nothing to fear from the fission case – for, according to fourdimensionalism, there is no numerical identity between Jean-Luc and Jean, and Jean-Luc and Luc. Survival, on this view, is not a matter of numerical identity, but rather, as Mark Heller says "for x to survive as y is for x and y to be an earlier and later part of a single object" (Heller (2000, p. 363)). On

71

the four-dimensionalist account, Jean-Luc is then a temporal part of the whole four-dimensional person we could call "Jean-Luc-Jean" and he is also a temporal part of the four-dimensional person we could call "JeanLuc-Luc". Jean-Luc-Jean and Jean-Luc-Luc are four-dimensional beings that share a temporal part – namely, Jean-Luc. Again, this is a case of overlap that is analogous to the spatial case of a road that forks – and this, certainly, is not an objectionable case. One could object that there is a problem with denotation. If, just before the fission, Jean-Luc says "Next week, I'll visit my friend Worf" and if, after that, Jean meets Worf but Luc does not, what should we say about JeanLuc's statement? Is it true ? False ? Does it have some other, indeterminate, truth-value, and so are we committed to use a many-valued logic ? I think there is a more natural solution at hand : when Jean-Luc seems to speak about one person, his future self, he really speaks about two. The meaning of his sentence has what Mark Heller calls "multiple contents" (Heller (2000, p. 376)). Heller provides us with a nice crossword example (Heller (2000, p. 375)) : This sentence contains exactly sentence contains exactly three words.

six

words.

In this case, as Heller points out, the word "this" has a multiple content : it denotes the horizontal sentence, and the vertical sentence. Once this is accepted, there is no problem in Jean-Luc's case : the "I" in his sentence works similarly – there are two contents, two meanings expressed, one of them being true and the other false. (This discussion will also be continued in I.7.§3.) §8. The third puzzle that involves coincident entities can be stated as the famous 'undetached parts' argument against endurantism. A very clear exposition of it is to be found in Loux (1998, p. 222-231), discussions can

Undetached parts

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be found in Heller (1990, p. 2-4; 19-20), Sider (2001, p. 142; 152-153), and van Inwagen (1981, p. 79-84) who was the first to consider such an argument (but for a different purpose, see §11 below). The argument runs as follows. It is well known that some lizards can release a part or all of their tail when they are grabbed by a predator. Once the tail is broken off, the lizard quickly runs for shelter and is safe for the moment, leaving a squirming tail to confuse or distract the predator. Let us imagine that, at a certain time t, such an adventure happens to my pet lizard Jean-Luc. Certainly, Jean-Luc can undergo such an accident and survive it, so, favouring trans-temporal numerical identity, the endurantist would claim that (i) Jean-Luc-before-t is numerically identical to Jean-Luc-after-t But, the argument goes, there is, before t, an other object that is the whole of Jean-Luc except its tail – it is what can be called an undetached part of Jean-Luc. Let us call this thing, this part of Jean-Luc, simply, "Jean" (and we could call "Luc" its undetached part that consists in its tail), as pictured here :

Fig. 10

Jean

Jean-Luc

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Certainly, Jean, as well as Jean-Luc, survives the predator's attack, but then, according to endurantism it is to be accepted that (ii) Jean-before-t is numerically identical to Jean-after-t If we don't want to endorse coincident entities, we'll have to say that after t (iii) Jean-Luc-after-t is numerically identical to Jean-after-t for they occupy exactly the same space-time location and seem to be, in short, just one and the same thing, as pictured here : Fig. 11

Jean

Jean-Luc

But, by transitivity of identity, we get from (i), (ii) and (iii) that (iv) Jean-Luc-before-t is numerically identical to Jean-before-t which is obviously false. As mentioned, a way to avoid this conclusion would be to claim that (iii) is false because, after t, there are really two coincident non-identical things : Jean-Luc and Jean, but this line of response is unpalatable, it is precisely

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what we want to reject. So, again, this argument seems to provide us with another reductio against endurantism. The 4D solution

§9. And, again, the four-dimensionalist has a nice treatment of this case – he will, of course, reject (i) and (ii) while accepting (iii). There are, on his account, two space-time worms – one of them (WormBIG, on the figure below) is the aggregate composed of Jean-Luc-before-t and the thing that is there after t (call it "Jean-Luc-after-t" or "Jean-after-t" – it does not matter since those two names have the same reference) and the other (WormSMALL, on the figure below) is the aggregate composed of Jeanbefore-t and the very same one thing that is there after t. The aggregates (the space-time worms) are not identical (because, for instance, they do not occupy the same space-time region) but they share a post-t part. So here is how this case looks under four-dimensionalism :

75 Fig. 12

Before t

Jean

Jean-Luc

WormSMALL

WormBIG

After t

Jean

Jean-Luc

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§10. Of course, endurantists reject those objections and have replies to them. It is the purpose of the following sections to examine those replies. Van Inwagen and undetached parts

§11. In Peter van Inwagen's hands, the undetached parts argument is not a reductio against endurantism (the premises (i) and (ii)) but rather one against the needed further premise that Jean exists – according to him, there are no undetached parts such as Jean(-before-t) or Luc(-before-t) 13 (see van Inwagen (1981, p. 82)). There are two things I wish to say about this strategy here. First, I think it flies in the face of our common sense intuitions. I can see Jean(-before-t). I can touch it. I can talk about it – for instance, I can say that it's dark green, that it has a certain mass, a certain size, that it occupies some region of space. And the same holds for Luc, the ‘undetached’ tail, as well. I see no good reason to deny the existence of these things. We can speak about undetached parts of material objects as well as about the objects themselves and they certainly exist. As Mark Heller puts it : "When not being swayed by specific philosophical arguments, we have no doubt that my hand is a physical object." (Heller (1990, p. 11)).

13

As a reductio not against endurantism but against undetached spatial parts, the argument can be formulated as follows : (i) Before a time t, Jean-Luc had a tail. At t, it released its tail to escape a predator's attack. (ii) Before t, there was un 'undetached' spatial part of Jean-Luc that is the whole of Jean-Luc except its tail. Let us call this thing "Jean". (iii) Jean-Luc survives the accident, but doesn't have a tail any more after it. (iv) Jean survives the accident, because nothing really happened to it. (v) After t, Jean-Luc and Jean occupy the same spatio-temporal region, are made up of the same particles, have the same mass, shape, colour, … (vi) So, after t, Jean-Luc and Jean are numerically identical, if we don't want coincident entities. (Jean-Luc-after-t is numerically identical to Jean-after-t) (vii) Jean-Luc-before-t is numerically identical to Jean-Luc-after-t – see (iii). (viii) Jean-before-t is numerically identical to Jean-after-t – see (iv). (ix) But then, by transitivity of identity, it turns out that Jean-Luc-before-t is numerically identical to Jean-before-t – which is false. (x) So, there is no such thing as Jean-before-t (a spatial 'undetached' part of JeanLuc).

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Second, this solution, even if one were ready to accept it, would not be of any help with the other puzzles involving coincidence (the fission case, and the lump and the statue case) – it is worth noting that only fourdimensionalism provides a unified solution to all of them. §12. In my exposition of the three cases involving coincidence that are supposed to provide with arguments against endurantism, I always insisted that coincident entities should be avoided. But some philosophers think otherwise – the most important proponent of the view that takes coincidence to be acceptable and non-problematic is David Wiggins. According to Wiggins' view, when considering the statue and the lump of clay case, we can happily accept that, at the time of coincidence (between t2 and t3), there really are two objects that are located in the same region of space. As he puts it, "[…] a portion of space may be co-occupied at a time by distinct things (provided, at least, that the things in question belong to different basic or individuative kinds)" (Wiggins (2001, p. 22)). The reason why he takes this to be acceptable is because the coincident things are of a different kind, and indeed he claims that "[…] for each thing that satisfies a predicate […], there must exist some known or unknown, named or nameable, kind to which the item belongs and by reference to which the 'what it is' question could be answered. Everything that exists is a this such" (Wiggins (2001, p. 21-22)). It is because a statue is a statue and a lump of clay is a lump of clay, and not a statue, that their coincidence is non-problematic. The only principle of non-coincidence that should be accepted is, as stated in Wiggins (1968, p. 93), that "no two things of the same kind (that is, no two things which satisfy the same sortal or substance concept) can occupy exactly the same volume at exactly the same time". But, why ? Why should we subscribe to a general principle that allows two things of a different kind to coincide, while it forbids coincidence for things of the same kind ? Indeed, such a general principle sounds quite bizarre because it seems to claim that a sandglass and a lizard can coincide, while two sandglasses cannot. But why should a sandglass and a lizard be allowed to coincide just because they are not things of the same kind ? As Sider also puts it : "Why should a difference in the kinds of the objects mitigate any implausibility in their coincidence ?" (Sider (2001, p. 154)).

Allowing for coincident entities

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Besides, such a strategy, even if one were ready to embrace it, would not provide a solution to all three puzzles exhibited above. In the captain Picard's fission case, for instance, all entities involved fall under the same sortal term (like 'person' or 'human being') and accepting coincidence in this case would be accepting coincidence of entities of the same kind; and this is unacceptable even for Wiggins. Chisholm's view

§13. Perhaps, a way for an endurantist to face the three puzzles involving coincidence would be to follow Roderick Chisholm's view of persistence of material objects through time, which exploits his doctrine called "mereological essentialism". The general thesis of mereological essentialism is defined by Chisholm as follows : "for any whole x, if x has y as one of its parts then y is part of x in every possible world in which x exists" (Chisholm (1973, p. 581-582)). Relevantly to the case of persistence of material objects through time, this entails that "if y is ever part of x, y will be part of x as long as x exists" (Chisholm (1973, p. 582)). Intuitively, I think this is quite acceptable : if a certain sandglass is made of some particular pieces of wood and glass, then it seems that, had the sandglass been made with other pieces, it wouldn't, simply, be this particular sandglass, but some other, maybe very similar but different, sandglass. This is, indeed, the very same claim Saul Kripke holds in Kripke (1972, p. 113). So I think there is no immediate problem in accepting mereological essentialism. What is unacceptable, I believe, is the combination of mereological essentialism with endurantism. Chisholm himself provides us with an argument that exhibits this problem, but instead of taking it to be an argument against endurantism, he takes it to be a problem for mereological essentialism. His argument is the following (Chisholm (1973, p. 584)) : (i) My automobile had parts last week that it does not have this week and it will have parts next week that it never had before. (ii) But the principle of mereological essentialism implies that, if anything is ever a part of my automobile, then that thing is a part of my automobile as long as the automobile exists. (iii) Therefore, the principle of mereological essentialism is false.

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There seems to be a reductio against mereological essentialism. But if one rejects the endurantist hypothesis contained in premise (i), this is not so. For, if one is a four-dimensionalist, one will claim that "my automobile last week", "my automobile this week", and "my automobile next week" do not refer to the same object; each of these objects, which are temporal parts of a space-time worm we can simply call "my automobile", has its parts essentially as long as it exists, but the four-dimensional whole does not. For instance, let us suppose that the next week's temporal part of the automobile has a fifth wheel, but not the four-dimensional whole automobile – certainly, it has a fifth wheel next week, but it has it, as we have already seen, precisely by having its next week's temporal part there. So far, it would just seem to me that mereological essentialism is designed to go together with four-dimensionalism. But if we accepted some further claims of Chisholm, then maybe, as Sider suggests (see Sider (2001, p. 180-)), endurantists could use mereological essentialism to face the puzzles involving coincident entities. The further claim to endorse is that "[…] it is likely to be only in a loose and popular sense that we may speak of the identity of a physical thing through time" (Chisholm (1970, p. 174)). Let us remember the case of the statue again. The statue persists from t2 to t3. According to Chisholm, we have to distinguish carefully between two ways of describing such a case : If we speak in a "strict and philosophical sense", there are two statues, one existing at t2, and another existing at t3. But, in a "loose and popular" sense, there is only one thing – one statue persisting from t2 to t3 in an endurantist way (Chisholm would call such an entity an "object series", or, as in his (1976, p. 98), in which he talks about a table whose parts were successively replaced, he says : "there is what might be called the ens successivum – the 'successive table' that is made up of different things at different times"). The problem with coincident entities in the interval of time from t2 to t3 is avoided because, to paraphrase Chisholm, that which constitutes the statue at t2 is identical to that which constitutes the lump of clay at t2; that which constitutes the statue at t3 is identical to that which constitutes the lump of clay at t3 but not to that which constituted the statue at t2; and that which constitutes the lump of clay at t4 is not identical to that which constituted the statue at t2 or to that which constituted the statue at

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t3. I think it is not difficult to imagine how such a strategy would apply to the two other puzzles. The reason why it is not difficult to imagine this is also the reason why I think that such an account is not an available strategy for the endurantist to face the puzzles from coincidence. The reason is that we have already seen those replies – they are, more or less, the four-dimensionalist's. Indeed, it seems to me that, fundamentally, Chisholm's view amounts to a variant of perdurantism – at least in the "strict and philosophical sense"; his 'object series' seems to me just like an aggregate of instantaneous temporal parts, in the end. What about the "loose and popular" claim that one and the same object, an automobile for instance, can persist from last week to next week? The four-dimensionalist would say that it can be true in a derivative sense – because a thing persists through time by having different temporal parts at different times – but to the endurantist, such a reply is unavailable; indeed, it would go against his central claim. The Chisholm-endurantist view would then be that, in a sense (the loose and popular one), such a claim is true because the enduring automobile is an object series14, and we can speak about the automobile from next week as being the same automobile as the one from last week, supposing that they are similar enough or that they are connected by a series of automobiles that are pairwise similar. But, as Sider points out, the "entia successiva persistence is not persistence in the fullest sense" (Sider (2001, p. 184)), and strictly and philosophically speaking, no material object can undergo a loss of parts after all, even very small parts. In the end, it just seems that the combination of endurantism and mereological essentialism misses its target. The best that Chisholm's strategy could do for an endurantist is to provide him with loose and popular endurantism, but this is certainly not satisfactory and I cannot imagine that any serious endurantist would be willing to endorse it. Vagueness

§14. Another argument in favour of four-dimensionalism that involves coincident entities is grounded in the treatment of cases of temporal vagueness. The version of the argument as I present it here is extracted 14

An "ontological parasite" that is composed of, and has all of its properties in virtue of things that "do duty for" it. (Chisholm (1976, p. 104))

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from Heller (2000, p. 366-), Forbes (1987, p. 152-), Sider (2001, p. 120-), and Le Poidevin (2000). The claim to defend is : (i) If one wants to treat vagueness as semantic indecision and if one does not want to endorse coincident entities, then one is committed to accept four-dimensionalism. To see the truth of this claim, let us consider a puddle. Since the weather is fine and hot, the puddle evaporates progressively. But since it evaporates slowly and progressively, it is a vague matter to decide when exactly it ceases to exist. The kind of vagueness involved here can be given three accounts. In short : (a) Vagueness is semantic indecision. The term "puddle" has no definite and precise extension, it has a vague meaning. (b) Vagueness is metaphysical. Puddles, and all material objects, are intrinsically vague. The world is vague. (c) Vagueness is epistemological. "Puddle" has a definite and precise meaning but we ignore it. If one wants to treat cases of vagueness as cases of semantic indecision, one will claim that it is not the case that there is an object whose boundaries in time are vague, rather, one will say that there are several objects with precise temporal boundaries – that those objects cease to exist at slightly different times, one after the other. (Compare the spatial case : a cloud does not have definite and precise spatial boundaries. On this view, there are many objects, some smaller, some bigger, that are candidates for being "the cloud". It is not possible to say which candidate to choose, because the term "the cloud" is vague.) Thus the vagueness here is not rooted in the puddle itself but rather in the meaning of the term "the puddle" : this meaning being vague, we cannot say with precision when exactly the thing we are considering still exists and when it goes out of existence because the extension of the term is not precise enough to pick just one of the series of very similar objects that cease to exist at slightly different times. Let us say that the puddle persists from t1 to t2 and that it is only then that the temperature begins to rise and the puddle starts to

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evaporate. Let us suppose that at t9 all of the water evaporated, so the end of the existence of the puddle is vaguely located somewhere between t2 and t9. Let us take two things that are candidates to be the referents of "the puddle" (two candidates from the series of slightly different objects that cease to exist between t2 and t9) : puddle1 is the puddle that exists from t1 to t4 and puddle2 is the puddle that exists from t1 to t6. If one is an endurantist, one will have to accept that the puddle at t1 and t2 is a thing that is numerically identical to the puddle that exists at t4, and the puddle that exists at t1 and t2 is numerically identical to the puddle that exists at t6. But puddle1 is not identical to puddle2 because they cease to exist at different times. But, at t1 and t2, both of those were present – so, there must have been two coincident puddles at those times (in reality, much more than two). But we don't want to accept coincident entities. So endurantism must be rejected. The four-dimensionalist has a nice account of the puddle case : puddle1 is simply a temporal part of puddle2. Every puddle-candidate whose temporal extension is smaller that another's is its temporal part (exactly as a bigger candidate in the cloud's case has a smaller one as a spatial part). Coincidence is avoided. How can an endurantist face this objection ? First, he could accept brute coincident entities (the Wiggins-style explanation of them being unavailable because only entities of the same kind are involved). I will suppose that no serious endurantist would take this line of response. Second, he could reject the thesis that vagueness is semantic indecision and pick one of the other two alternatives, (b) or (c). What must be noted first is that four-dimensionalism is neutral as to which account of vagueness one should choose, whereas endurantism, as we have just seen, forces one to renounce to the semantic approach. This alone makes four-dimensionalism superior to endurantism. Further, according to many, the semantic approach is probably the right one – if this is true, the endurantist's position is clearly to be rejected. (This sounds reasonable – I don't think that puddles, sandglasses or lizards are vague. There is a certain, quite definite, amount of particles, cells, droplets of water, … it's just that no one ever decided to give a precise enough definition of the

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terms to see whether a certain cell, particle or droplet belonged to such and such object.)

Chapter 6, The Ship of Theseus §1. The well-known Ship of Theseus puzzle, that also involves issues of coincidence and vagueness as will be made clear below, can be dealt with more easily if one adopts four-dimensionalism than if one works with endurantism. This does not mean that four-dimensionalism provides a nice and complete solution, as argued in the other cases in preceding chapters. It will only be argued here that four-dimensionalism can do better than endurantism. The puzzle starts with the ship of Theseus that is made of wooden planks. Since Athenians wanted to preserve the ship for next generations, they carefully repaired the ship as soon as it was necessary. If one plank was damaged, they made another just like the damaged one and replaced it. After some time, all of the planks of the ship had been removed and replaced by duplicates. Let us call the original ship, before any replacements had been made, "Theseus-Original" and let "TheseusRepaired" be the ship all of whose planks have been replaced one by one. But there is another, third ship : let us imagine that the Athenians kept all of the planks that were removed from the original ship and when all of them were replaced they put them all together to reconstruct Theseus's ship. Let us call this ship, the one re-made with the original planks, "Theseus-Reconstructed". Now, a puzzle of course arises because we have here two ships, Theseus-Repaired and Theseus-Reconstructed and we can reasonably ask the question : which one of them is the original ship ? There are, as in Jean-Luc Picard's fission case from II.6.§5, four possible replies : (i) Theseus-Repaired is the original ship, and Theseus-Reconstructed is not. (ii) Theseus-Reconstructed is the original ship, and Theseus-Repaired is not. (iii) Both Theseus-Repaired and Theseus-Reconstructed are the original ship. (iv) Neither Theseus-Repaired nor Theseus-Reconstructed is the original ship.

The ship of Theseus puzzle

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In Jean-Luc Picard's case, it was argued that the alternatives (i) and (ii) were to be rejected because there simply seemed to be no reason at all to prefer one to the other. But this is not so in the case of the ship of Theseus – traditionally both of these views have been defended. (The difference between the two cases lies in the difference between the processes that yield the two post-fission candidates (the same process twice for Jean-Luc and two distinct processes for the ship), and also in the fact that Jean-Luc is a conscious being, while the ship of Theseus is not.) The criterion of spatiotemporal continuity

§2. First, let us examine the alternative (i) which claims that TheseusRepaired is the original ship in virtue of the fact that it satisfies a criterion of spatio-temporal continuity – we could have literally 'tracked' the ship from Theseus-Original to Theseus-Repaired, we could always have pointed a finger at it. Surely a ship can survive the replacement of one of its planks. So, after replacement of one plank, we are still pointing at the same ship. Then, another plank is replaced, and so on. At each time when a plank is removed, we will claim that it is the same ship as before the removal of the one plank and, by transitivity of identity, we'll obtain as a result that Theseus-Original = Theseus-Repaired. What matters in the survival of material objects such as ships is not that they must be made up of the same matter, but that they must be linked by a continuous uninterrupted spatiotemporal trajectory. But there are problems with this approach. We can easily imagine that a transport device used in I.5.§5 to teleport captain Picard could be used (without malfunction this time) to transport the ship from one place to another, without any spatial continuity. And further, if we used a timetravel device to transport the ship from today to next week, there would be no temporal continuity either. But, I think that in both of these cases we would claim that there is the same ship before and after the transport. Although the possibility involved here comes from science-fiction, it should nevertheless be taken seriously as a logical possibility in a case where it is our concept and understanding of survival and identity that is under examination. Besides, there are actual objects that are spatially discontinuous_: the territory of the USA including Alaska, to take Quine's example (Quine (1950, p. 69)), or my pen, for instance, that has two parts – the top and the

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main part. Most of the time, those two parts of the pen are adjacent but when I use it to write I take the top away. Would this mean that I destroyed the pen ? I think not. I think that it is more likely that a pen can be spatially discontinuous, in fact many ordinary objects are (probably all material objects are, if something like a simplified picture given to us by physics is right – at the atomic level, all objects are composed of particles with a lot of space in between). This all seems to lead to the rejection of the criterion of spatio-temporal continuity as a criterion of identity of material objects through time. §3. Now, let us examine the alternative (ii) where it is argued that Theseus-Reconstructed is identical to the original ship because it is made of the same planks – this is the criterion of compositional unity. For a material object to survive and be the same is to keep all of its material parts – it is to be made up of the same matter. But is this a necessary condition of survival and identity ? It seems hard to argue that it is : under this hypothesis, if I go to have my hair cut, I cease to exist, and if one single atom is replaced on Theseus-Original, it is destroyed. Such a claim just seems to be too strong to be true. So perhaps we could weaken it a bit to achieve a more satisfactory result : it could be said, perhaps, that small changes do not matter for the survival and identity of material objects, whereas bigger changes do. But immediately, two problems appear with such a claim. First, the choice of what are big changes that matter and what are small changes that do not matter would have to be an arbitrary one. How many planks can be replaced on Theseus-Original for it to remain the same ship ? One ? Two ? Fifty percent of the planks ? But why ? Second, even if we were able to choose such a limit – let us say fifty percent of the planks – we would face the following unwelcome result. It is claimed here that the replacement of one single plank preserves the identity of Theseus-Original. Thus, Theseus-Original is identical to TheseusOriginal-2 which is the result of the replacement of one plank on TheseusOriginal. And if we follow such a reasoning, we will face the following series of identity claims :

The criterion of compositional unity

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Theseus-Original = Theseus-Original-2 Theseus-Original-2 = Theseus-Original-3 Theseus-Original-3 = Theseus-Original-4 Theseus-Original-4 = Theseus-Original-5 . . . Theseus-Original-(n-1) = Theseus-Original-n where Theseus-Original-n is the ship with all of its planks replaced – namely, it is Theseus-Repaired. By transitivity of identity, we then get that Theseus-Original is Theseus-Repaired. But what was wanted here was the claim that while small changes preserve the identity of the ship, big changes (such as the replacements of all of its material parts) do destroy it – and so, that Theseus-Original is not Theseus-Repaired but, rather, Theseus-Reconstructed. But then such a view simply leads us into a contradiction. (Besides, such a view also has trouble in accommodating the claim that I am the same person I was 10 years ago, as all or most of my cells have died and have been replaced by new ones since then and are now part of me.) So it seems that the criterion of compositional unity is not a necessary condition for the survival and identity of material objects. Is it a sufficient one ? Is it sufficient for a concrete particular to be made up of the same matter as another concrete particular to be just one and the same particular ? It seems hard to believe so. Suppose you take all of the planks that compose Theseus-Original and use them to build a wooden house. Would the ship and the house be the same concrete particular ? Hardly so. Fourdimensionalism and the metaphysical puzzle

§4. So, let's ask again : which one of the two ships Theseus-Repaired and Theseus-Reconstructed is the original ship ? It seems that the answer to this question is far from being obvious, as choosing between the two resulting ships is difficult. So, perhaps, we could use the same strategy we used in Captain Jean-Luc Picard's fission case (I.5.§5-) : there it was argued that the two Picards resulting from the fission were the same person

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as the original Picard before the fission – and the criterion that was put forward in favour of this conclusion was the who-would-he-care-for criterion. And since it seemed reasonable that Picard-before-the-fission would care for what happens to both Picards resulting from the fission, both of them could then claim to be him. (And we have seen how this does not yield any problems for the four-dimensionalist.) But it seems that, unlike in the case of conscious objects like Jean-Luc Picard, in the case of the ship of Theseus, which is a material nonconscious object, we do not have any such reason that would allow us to claim that both Theseus-Repaired and Theseus-Reconstructed are the original ship. It is not my aim here to provide a solution to this puzzle – the fourdimensionalist does not have to. In the four-dimensionalist picture there are simply two space-time worms, one of them going from TheseusOriginal to Theseus-Repaired, the other from Theseus-Original to TheseusReconstructed, and the two space-time worms share a temporal part : namely, Theseus-Original (thus, the picture one would get from an atemporal point of view would be similar to the one given in Picard's fission case). As Sider puts it, "there exist space-time worms corresponding to each answer" (Sider (2001, p. 8)) – to each of the two possibilities I examined shortly above. So, at least metaphysically, the picture is clear. There are several four-dimensional worms that are candidates for the label "the Ship of Theseus". Which one of them is the better candidate is then an interesting matter, but it is not metaphysical matter. So a puzzle still remains (which candidate is the right one ? or, perhaps, there is no determinate answer ?), but it is a conceptual puzzle – the advantage of four-dimensionalism is to dissolve any metaphysical worries. This is not so for the endurantist whose metaphysical solution presupposes a defense of one of the two views (or any variants) sketched above. The endurantist could not endorse the alternative (iii) that both TheseusRepaired and Theseus-Reconstructed are the original ship, since he would then have to claim that since Theseus-Original is numerically identical to Theseus-Repaired and Theseus-Original is numerically identical to Theseus-Reconstructed, Theseus-Repaired is numerically identical to Theseus-Reconstructed, which is obviously false.

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(If he wanted to claim that Theseus-Repaired and Theseus-Reconstructed are numerically different, but that Theseus-Repaired is Theseus-Original, and Theseus-Reconstructed is Theseus-Original, he would then have to embrace the claim that at the time when Theseus-Original was there, there really were two coincident entities.)

Chapter 7, The worm view and the stage view §1. Until now, I tried to show the reasons to believe that fourdimensionalism is to be preferred to its three other competitors – endurantism, presentism, and perdurantist presentism. It is time now to examine two competing versions of four-dimensionalism, as promised in I.1.§4. The first of them, the 'worm view', is the one I've presupposed in all preceding chapters. The second is called the 'stage view' and is defended by Ted Sider (Sider (2001, p. 188-)) and also supported by Achille Varzi (Varzi (2003)). Let us first remember the worm view picture :

Two 4D views

the sandglass Fig. 1

t1-part

t2-part

t3-part

t1

t2 now

t3

According to this view, the sandglass is a four-dimensional entity that is extended in time as well as in space, and perdures through time by having temporal parts at different times; likewise, its extension across space is achieved by its having spatial parts in different places. The stage view is also a four-dimensionalist one but the picture it provides is different :

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counterpart

counterpart

Fig. 13

t1-stage

t2-stage

t3-stage

t1

t2 now

t3

According to this view, the sandglass existing at t1 is an instantaneous stage and it persists through time by having different temporal counterparts at other times. The ordinary object we refer to as a sandglass is not a four-dimensional entity, rather, there is a series of stages interconnected by a counterpart relation, and ordinary objects are conceived of as being the stages rather than the whole composed of them. Strictly speaking, the stages of the sandglass are only momentary entities but they are nevertheless said to persist through time by having counterparts at other times. This doctrine is analogous to David Lewis' modal counterpart theory. In short (I will come back to this in detail in II.4), modal counterpart theory claims that it is possible for the sandglass which is actually black to be, say, red not because the sandglass itself exists in another possible world where it's red but because it has an other-worldly counterpart that is red. Similarly, if we follow the stage view of persistence through time, we can now say that, at t3, the sandglass is (will be) empty because the stage of the sandglass that exists now has a temporal counterpart that exists at t3 and that is empty. To draw this analogy even further, one might adopt Yuri Balashov's (2002) terminology : if, instead of speaking of a temporal stage of a single material object like a sandglass, one 'cuts across' the whole (actual) world, one would get an entire world-stage at a certain time that one could call a temporal world, since, according to the stage view, objects are stages, and so the world is also a (bigger, the biggest) stage that has temporal counterparts at other times. Following this lead, if one considers

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all of the stages of small ordinary objects like sandglasses within a single temporal world, one could call those stage-mates, analogously to Lewis' world-mates 15. To sum up, both views are genuinely four-dimensionalist since both claim that temporally extended objects persist through time by having temporal parts or stages, and both claim that the extended objects – the fourdimensional entities that are aggregates of their parts or stages – exist as well as the parts or stages do. It's just that, according to the stage view, the objects we ordinarily name and quantify over are stages rather than worms. Sider defends the stage view for three major reasons. First, he claims that the stage view provides an even better account than the worm view as far as the problem from I.4 about temporary intrinsic properties is concerned (Sider (2000c)). Second, he also claims that it provides a better account of some problem cases, especially the case of fission (in fact, all cases from chapter 5 involving coincidence are concerned) (Sider (2001) and (1996)). Third, because he endorses modal counterpart theory (Sider (2001)). While I find the first reason genuinely interesting, I think that the other two are both bad reasons, and that ultimately the stage view fails. I shall start with a short discussion of the first reason. §2. Remember the objection to indexicalism and adverbialism from I.4 : none of those accounts allows objects to exemplify temporary intrinsic properties simpliciter. They cannot just have any such property, they can only have them relatively to times. Now, it seems that the worm view can do better than those views but it still carries a problem – for, according to this view, there are things that can have temporary intrinsic properties simpliciter, namely temporal parts, but those are not the ordinary objects we want to talk about. If I want to say that a sandglass has the property of being full, I cannot say it, because the

15

One disanalogy between the modal and the temporal case comes from considerations about the nature of time : if time is continuous or dense it seems difficult to have a clear idea of what it is for an object to be 'followed' by its temporal counterpart, since between any times there are others, infinitely many others, perhaps. In the modal case such complications do not arise since the structure of Lewisian possible worlds is discrete.

The stage view and temporary intrinsics

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sandglass, the four-dimensional entity, does not have such a property itself, it only has it in a derivative way, by having a temporal part that has it. The stage view, unlike the worm view, can guarantee the having of temporary intrinsic properties simpliciter by the ordinary objects themselves. This is easily achieved since, according to this view, ordinary objects like sandglasses or lizards are (instantaneous) stages, and those, in agreement with the worm view theorist's claim, can have such properties. So such a view allows the sandglass to have simpliciter the property of being full itself, in a non-derivative way. I think that this is a genuinely interesting advantage of the stage view that can be put forward in its favour. I will now examine the other two reasons Sider provides in favour of the stage view, which I think give less satisfaction. The fission case

§3. Let us remember our fission case from I.5.§5. The captain Jean-Luc Picard enters the transportation device and two persons result from a malfunction of the transport mechanism.

Fig. 9

Jean Jean-Luc Luc

t1

t2

According to Sider, the worm view provides a satisfactory metaphysical solution to this case but a semantic worry remains. The metaphysical solution, of which the aim was to avoid coincident entities, claims that the pre-fission parts are numerically identical; thus, there are two space-time worms that share a part and so, as we've seen, such a case is no more mysterious than overlapping roads. Indeed, this was also Sider's own claim. But now, he objects that "even if we knew that fission was about to occur, we would not say that there are two persons before us" (Sider (2001,

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p. 189)). As I understand him, he claims that Heller's multiple content solution (see I.5.§7) is wrong. Nobody, he says, would agree to count as two persons the pre-fission part in our case. Well, I think one would sometimes agree on this counting, and one should. My reason to think this is that often, in the analogous spatial case, one does. When I travelled across France this summer, I took a road from Poitiers that, when one arrives in Bellac, forks : Fig. 14

The (metaphysically) one road that comes from Poitiers, on the left, is referred to by two names "N 147" and "E 62". Then it forks, in Bellac, and its 'post-fission' parts are each called by one of the two names. So, before the road forks, and precisely because we know that it's going to fork, the road that goes from Poitiers up to the place where it forks bears the two names of the two 'post-fission' roads. But this doesn't mean that there are, metaphysically speaking, two roads (before Bellac), there is only one, in fact there is only one part of a road that is shared by the two roads "N 147" and "E 62". And this point is perfectly well taken by our commonsensical intuitions : despite of the fact that we do say that there are two roads by giving them two different names, when it needs to be repaired we'll sent equipment that is needed for the repairs of one road only. So, metaphysically speaking, there is only one road, but that road is part of two and this is why it bears two names, and no non-philosopher is ever puzzled by this. And philosophers shouldn't either.

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Now, the worm view theorist can provide a solution to the temporal fission case that is analogous to the one we have just seen in the spatial case. Metaphysically, there is only one person at t1, namely Jean-Luc, but if we knew that a fission were about to occur we could happily claim that JeanLuc is part of two persons and we could even give those two names, if this were of any use. Because we do claim this in the spatial case, and because the worm view theorist takes persistence through time as analogous to extension in space, I claim that it is entirely justified to say that we would make the same claim in the temporal case. (If we only have one name like "Jean-Luc" for two non-identical persons, such a name is then, from an atemporal standpoint, ambiguous. But as David Lewis points out, such an ambiguity is perfectly harmless, as long as its two bearers are indiscernible (see Lewis (1983c, p. 64-65)). The need to distinguish the two persons arises only after the fission.) Sider's own view is that ordinary objects are momentary stages that have temporal counterparts at other times. Thus, before the fission occurs, there is only one thing that has two counterparts at a later time. This one thing is not part of any two objects and deserves only one name. This is how the count of persons before fission agrees with the claim that there is only one person. Maybe this is not very objectionable. But one thing can be objected to easily : such a strategy breaks the analogy between persistence across space and time (unless one would be willing to embrace spatial counterparts), that is for many one of the four-dimensionalist's central claims. Maybe this is not an objection, really. But if a four-dimensionalist accepts the stage view, he deprives himself of any arguments in his favour based on this analogy. This is a first drawback of the stage view. Sider thinks that such an approach saves "the intuition that just one person is present before fission" (Sider (2001, p. 189)), but we have seen that the worm view can deal without any difficulties with this intuition. Objection to the stage view : its account of persistence is not satisfactory

§4. Modal counterpart theory suffers from Saul Kripke's famous objection. Sider thinks that the objection is satisfactorily answered by David Lewis. I don't think so. But since I am going to discuss this in detail in Part II, I will concentrate now only on the analogous objection to temporal counterpart theory, and to Sider's defense of it.

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The objection runs as follows : if Jean-Luc says now that he will visit his friend Worf tomorrow, then the sentence turns out to be true iff he'll visit Worf tomorrow. But this is, according to the stage view, simply impossible, because the person that says now that he'll visit Worf tomorrow is a stage, a momentary entity that will not itself persist until tomorrow and thus, will not be able to visit anyone. Jean-Luc, the person who is doing the speaking, is simply not identical, in any sense, to the person who's supposed to do the visiting. Certainly, Jean-Luc has a counterpart tomorrow that'll visit (or not) Worf. But what is a counterpart ? Sider does not provide with a clear analysis or definition of the counterpart relation, he takes it here as a primitive. (Very well, I do not object to this here. I agree with Sider that it may be analyzed, but it's not necessary in the present debate that opposes the worm view and the stage view. Whatever the worm view theorist chooses to unite his four-dimensional beings with may be available to the stage theorist to define the counterpart relation.) But whatever the counterpart relation is, it is not identity. But if Jean-Luc says he'll visit Worf tomorrow, why would Worf care about someone else, similar to Jean-Luc and linked with him by the counterpart relation, to visit him ? Note that the "someone else" claim is very strong here : if one endorses the stage view, there is no sense in which Jean-Luc from today is identical to Jean-Luc tomorrow. Compare to the worm view : as in the stage view case, the entity that is doing the speaking is not numerically identical to the entity that is doing the visiting because they are different temporal parts but, according to the worm view, those temporal parts are parts of a unique and self-identical four-dimensional object (Jean-Luc) that persists (extends) from today to tomorrow – so, according to the worm view, there is a sense, a very clear one, in which it is Jean-Luc himself (the four-dimensional Jean-Luc) who's going to visit Worf. If one generalizes this objection to the stage view, one can simply claim that it denies persistence altogether. For the stage view ontology provides us only with instantaneous entities and, because Sider accepts unrestricted mereological composition, aggregates of those, but it rejects 'worms', it rejects the view that sandglasses, starship captains, or lizards are fourdimensional entities. The stage view persistence is not genuine persistence.

98 Sider's reply to the objection, and a rejection of the reply

§5. Sider defends his view against this objection as follows : "[It] is wrong to say that the stage view denies that 'You will do it' means that you will do it. 'Ted was once a boy' attributes a certain temporal property, the property of once being a boy, to me, not to anyone else. Of course, the stage view does analyse my having this property as involving the boyhood of another object, but I am the one with the temporal property, which is the important thing. The stage view is consistent with stages having temporal properties; it's just that temporal properties are given a counterpart theoretic analysis." (Sider (2001, p. 195)) This reply, I think, is not satisfactory. Granted, the stage view is consistent with stages having temporal properties, but not the ones we want. To take Sider's example, if we say "Ted was once a boy", we are ascribing a certain temporal property to Ted (who exists now). But if we want to endorse the stage view, it is not the property of "once being a boy", but rather, the property of "once there being a counterpart of Ted that is a boy". If the stage view theorist allows these two properties to be equivalent then he is, I think, mistaken – for if it is the former that we ascribe to Ted, it is solely about Ted that we are speaking, but if we ascribe him the latter, we are speaking about Ted and someone else, and that makes all the difference. I think that Sider's response can only appear to be satisfactory if one takes the expression "once being a boy" to be a suitable paraphrase of the expression "once there being a counterpart of x that is a boy", but such a strategy, let me agree with Sally Haslanger, "strains the limits of credibility" (see Haslanger (2003, p. 23)).

The stage view and the 'nochange' objection

§6. The fact that the stage view appeals to different counterpart-related objects to provide an account of persistence also makes it weaker against the 'no-change' objection from I.4.§3. Remember shortly the objection : four-dimensionalism does not account for genuine change of persisting material objects like sandglasses, because it tells us a story about different objects (temporal parts of a sandglass) existing at different times and having different properties, but none of those objects can change. The reply that the worm view theorist gave to defend his view was that there is something that changes, namely the four-dimensional sandglass that is composed of all of its temporal parts. Once one of its parts has any intrinsic property, it cannot change, and it will always be true that it has

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(tenselessly) this property, but the four-dimensional entity can undergo a change by having different parts at different times. But if one endorses the stage view, such a reply seems unavailable – for there is no one thing that ever has the different properties. The worm view theorist claims that the four-dimensional sandglass has them in a derivative way (avoiding by that the objection from I.4), but the defender of the stage view does not have room for this in his theory : he cannot show anything that could be said to undergo a change. Of course, he can say that a certain stage, at t1, is F and will be ¬F at t2 in virtue of being a temporal counterpart of another stage existing at t2 that is ¬F. As a semantic solution, this could maybe sound satisfactory, but ontologically speaking these two stages are just two different things. "Change needs identity as well as difference" claims D. H. Mellor (1998, p. 89). But there is only difference in the stage view, there are only different things with different properties. §7. There is another objection to the stage view that Sider himself draws and that makes him say that his view requires a concession. I think his objection is a good one and I will simply state it here shortly, as he does (see Sider (2001, p.197)). The objection is about counting : Sider objected to the worm view that it provides a bad count in some cases (we have seen in §2 below the case of fission where the worm view seems to count "two" whilst the stage view counts "one" before the fission occurs). We have seen that such an objection does not really apply. Now, the concession will be that in some other cases, the worm view's count is to be preferred to the stage view's. Consider the (true) sentence "Fewer than two billion persons have set foot in North America throughout history". The problem is that, according to the stage view, because it takes people to be instantaneous stages, the sentence turns out to be false (there are many more people-stages than people). Following the worm view, we get the right truth-value because we get the right count – people, in this case, are worm-people. So, as Sider concedes "in some cases we need a worm-theoretic account after all" (Sider (2001, p. 197)). So there are cases in which we should use the worm-count and in all other cases we should use the stage-count. As I said, I think Sider's objection is good – the only thing I don't agree with is his

Sider's objection to the stage view

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claim that "the stage view's advantages outweigh this defect" (Sider (2001, p.197)). Objection to the stage view : it does not allow ordinary objects to do the things they do

§8. "All continuants are stages", Sider claims (Sider (2001, p. 191)). Lizards, sandglasses, or people are stages rather than temporally extended space-time worms. But stages are instantaneous entities, they do not have temporal extent. Then, according to Sider, people and lizards are instantaneous entities. The unwelcome consequence of this is that people or lizards cannot do many of the things we would expect them to be able to do. For instance, it seems that a person should normally be able to utter a sentence. But, on the stage view, this turns out to be impossible, strictly speaking : the utterance of a sentence takes some time and a stage does not last long enough to make such a performance. Normally, a lizard can run, but again, not on the stage view; strictly speaking no lizard can run because a lizard is an instantaneous entity and running takes time. No such problem would even arise if one chose to accept the worm view, since the temporal parts that do the speaking or the running are temporally big enough to guarantee the possibility of such performances. The obvious reply of the stage view theorist to this is that a person can utter a sentence and a lizard can run because they have counterparts at 'neighbour' times and if we take several counterparts together, they can achieve such a performance. It takes more than one single stage to run or to speak. But then, what do we really mean when we say that a lizard runs ? What do we refer to by "this lizard" ? We have seen that it seems that if we refer to the instantaneous stage (as we should, if we follow Sider's recommendations : space-time worms "are not ordinarily named or quantified over" (Sider (2001, p. 191))) it is impossible for our sentence to be true (an instantaneous entity does not have enough time to run). Then maybe we refer to a sum of successive lizard-counterparts, which is a thing that lasts long enough to do the performance. But what is this sum ? I see two possibilities : first, that it is a set of numerically distinct entities (the distinct temporal counterparts), or second, that it is a whole composed of the different counterparts. The first possibility seems really unpalatable to me : it would take much philosophical work to try to defend a view according to which a set can run – indeed, such an idea seems absurd. We

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are then left with the second possibility; but this just amounts to embracing the worm view, for the thing that has the properties we are interested in (running, speaking, and so on) is a temporally extended four-dimensional entity – and so, those properties are really had by a 'worm' rather than by a stage; and this turns out to be the worm view. So, since this way out (a way that nobody takes, as far as I know) is closed, the stage theorist will have no choice but stick to his original claim : "this lizard" refers to an instantaneous stage, and it has the property of running in virtue of having temporal counterparts at neighbour times – and this is how a lizard can run. Very well. But what this claim commits the stage view theorist to, is to endorse the further claim that since the lizard has the property of running in virtue of its relations to other lizards (his past and future counterparts), this property turns out to be extrinsic, contrary to what we'd usually say. And for the same reasons, a lot of properties that we usually take to be intrinsic, turn out to be extrinsic, according to the stage view. So if one wants to account for the fact that lizards can run, that people can speak and think, and that the properties involved here are intrinsic, one should embrace the worm view rather than the stage view16.

16

It is worth noting that both Sider and Varzi accept this consequence of the stage view (personal communications, 2005). So, to settle the debate and see how strong this objection is, it would be necessary to establish what independent reasons we have to think that properties like running or thinking are intrinsic or extrinsic. Since the intuitive thing to say is that they are intrinsic, I think that the burden of proof is now on the stage theorist to show that they are not.

Chapter 8, Four-dimensionalism and common sense §1. Until now I've tried to show that four-dimensionalism has many advantages over its three competitors (presentism, endurantism, and presentist perdurantism) and that between the stage-view variant and the worm-view variant of four-dimensionalism it is the latter that should be favoured. It is time now to examine objections that have been raised against this view. One important objection, the 'no-change' objection, has already been answered in I.4.§3-§4. Now it is time to deal with the worry that four-dimensionalism is not compatible with some of our commonsensical beliefs. The complaints against four-dimensionalism on this ground can be divided into two groups. First, some philosophers claim that the four-dimensionalist's ontology is crazy and that everyone, even the four-dimensionalist, takes intuitively material objects as three-dimensional (at the end of this chapter we will also see a reply to the objection that temporal parts are unintelligible). Second, it is the principle of unrestricted mereological composition, held by most four-dimensionalists, that will be said to lead us to accept bizarre entities we normally don't believe there to be.

Objections to fourdimensionalism

§2. Claiming that only events but not material objects have temporal parts, D. H. Mellor objects to the four-dimensionalist's view as follows : "No one else [than the four-dimensionalist] would say that only [temporal] parts of Sir Edmund Hilary and Tenzing Norgay climbed only a part of Everest in 1953. The rest of us think those two whole men climbed that one whole mountain, and that all three parties were wholly present throughout every temporal part of that historic event" (Mellor (1998, p. 86)). Similarly, Peter Simons complains that "outside philosophical seminars a four-dimensionalist never says 'a two-hour phase of me last night was a waking phase'; he says, with the rest of us, 'I was awake for two hours last night'." (Simons (2000b, p. 62)).

Simons and Mellor's objection

§3. There are two ways a four-dimensionalist can react to such complaints. First, he could follow Mark Heller who admits that indeed three-dimensionalism is our normal pre-philosophical view but says that he puts very little weight on this advantage (see Heller (1990, p. 3)). In fact,

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following this line of response, the four-dimensionalist could claim that even if his view is, at a first glance, counter-intuitive, it becomes more palatable even for the common sense once one thinks more about it and once one recognizes the advantages of it. It will then be the competing views that'll suffer from counter-intuitive consequences (commitment to coincident entities, for instance) – consequences that are much more annoying than any pre-philosophical prejudice against temporal parts. The second way a four-dimensionalist could defend himself here is to claim that it does not really matter what we normally say about Hilary or our night activities since "we are now much more sympathetic than we were to the view that ordinary language need not define the underlying metaphysics" (Le Poidevin (2000, p.383)). Besides, as Mellor and Simons themselves showed in their examples quoted above, it is always possible, if needed, to paraphrase any usual sentence to accommodate the temporal parts ontology. We can say, for instance, that my pet lizard Jean-Luc exists now. If four-dimensionalism is true, such a claim is, strictly speaking, false. Jean-Luc is simply temporally too big to exist now – only a part of it does, and so it's only in a loose sense that we can say that it exists now. This is analogous to the spatial case : if all of Jean-Luc except its tail is hidden behind my computer, I'll normally say that Jean-Luc is hidden behind my computer, ignoring the fact that not all of his body is hidden. Surely, there is something counter-intuitive in four-dimensionalism, and one can agree then, at least partly, with the objectors. But this is just inevitable. Any of the theories of persistence through time I have examined are committed to claims that common sense would reject or simply has no opinion about. When solving the problem of temporary intrinsic properties, one just have to be revisionary about at least some of our beliefs. I think that four-dimensionalism is the alternative that makes the best choices here. Thomson's crazy metaphysics objection

§4. Another, metaphysical, objection was raised by Judith Jarvis Thomson in the following famous passage : "The [four-dimensionalist's] metaphysics yields that if I have had exactly one bit of chalk in my hand for the last hour, then there is something in my hand which is white, roughly cylindrical in shape, and dusty, something which also has a weight, something which is chalk, which was not in my hand three minutes

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ago, and indeed, such that no part of it was in my hand three minutes ago. As I hold the bit of chalk in my hand, new stuff, new chalk keeps constantly coming into existence ex nihilo. That strikes me as obviously false." (Thomson (1983, p. 213)) §5. This objection was answered by Heller (1990, p. 16-) and Sider (2001, p. 216-). The point is that temporal parts of material objects do not come into existence ex nihilo, as Thomson says. This would mean that they would just pop into existence independently of any previous events or things. But this is simply wrong. According to four-dimensionalism (I am going to say more about this in §7 below), temporal parts of objects like chalk are causally interrelated – previous temporal parts of it cause later temporal parts to exist. Also, persistence through time is, according to four-dimensionalism, analogous to persistence across space. If you look at a poker, hot at one end and cold at the other, and, while examining it, say, from left to right, your eye runs across the object, you'll first see the hot part of it and then, as you look further, the hot part 'ceases' to exist (you don't see it any more) and you see the cold part. For the fourdimensionalist who endorses eternalism, persistence through time is analogous. "Present" is just an indexical term that does not bear any ontological commitment, it is just, as Sider says, "a particular perspective in time" (Sider (2001, p. 218)) and other times exist as really as the present, exactly as do all the spatial parts of the poker exist, even those we're not currently looking at. Objects do not come into existence ex nihilo 17. 17

There is also another view, put forward by René Descartes in the Third Meditation, that answers Thomson's objection by simply biting the bullet. Indeed, Descartes claims that "tout le temps de ma vie peut être divisé en une infinité de parties, chacune desquelles ne dépend en aucune façon des autres; et ainsi de ce qu'un peu auparavant j'ai été, il ne s'en suit pas que je doive maintenant être, si ce n'est qu'en ce moment quelque chose me produise et me crée, pour ainsi dire derechef, c'est-à-dire me conserve. En effet, c'est une chose bien claire et bien évidente [...] qu'une substance, pour être conservée dans tous les moments qu'elle dure, a besoin de même pouvoir et de la même action, qui serait nécessaire pour la produire et la créer tout de nouveau, si elle n'était point encore. En sorte que la lumière naturelle nous fait voir clairement, que la conservation et la création ne diffèrent qu'au regard de notre façon de penser, et non point en effet." (Descartes (1963, Med. III))

Reply

106 Objection to unrestricted mereological composition

§6. I am now going to turn to an objection that arises against the fourdimensionalist's ontology because of the principle of unrestricted mereological composition. The principle of unrestricted mereological composition, defended by most four-dimensionalists, claims that there is a material object corresponding to any mereological sum of any other material objects, even if they are not connected in any particular way. Sometimes, the principle is also stated as the claim that there is a material object for any filled region of space-time. According to this principle, the mereological sum of all of today's temporal parts of all the green lizards, the top half of Mont-Blanc the 26th of October 1765 from 13.00 PM to 13.47 PM, and yesterday's temporal part of a certain sandglass is a material object – and we could, if needed, give it a name, let's say "Bernard". If there are objects such as Bernard, then it means that there are in reality far many more material objects than we usually believe there to be, like lizards, mountains or sandglasses – there are many more objects than we actually have names for and that we usually quantify over. We have already seen (see I.6.§2 above) that the fact that Bernard is spatiotemporally scattered does not disqualify it as a regular material object. Certainly, some wouldn't agree; Van Inwagen, for instance, does not even accept the top part of Mont-Blanc as being an object, as we have seen in I.5.§11. But the objection I want to consider now consists in a more commonsensical worry : common sense does not seem to be ready to believe that Bernard exists, more precisely, common sense doesn't usually tell us that Bernard is a single material object. The problem here is, in fact, to show what it is that makes us normally believe in lizards or mountains but not in Bernard-like entities. Unrestricted mereological composition granted, how are we to explain that some of the four-dimensionalist's objects are privileged by common sense ?

Reply

§7. The first thing to note is that, after all, there seem to be reasons to think that common sense sometimes does believe in at least some Bernardlike objects – I mean by that temporally and spatially scattered objects. We have already seen the case of my pen in I.6.§2, this would be an example of the spatial case. But there are others, even in the temporal case : "St. Petersburg" for instance, is a name we can use to denote a certain city, but only at a certain scattered period of time, since St. Petersburg bore this

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name only until 1924, when it became Leningrad, and then was given the name back in 1991 and is called St. Petersburg again since then. What this example shows is that we do sometimes have names for temporal parts of objects and even for scattered temporal parts; one could easily say, for instance, that St. Petersburg contains more inhabitants than Leningrad did, and it would then seem that our everyday talk is not prejudiced against temporal parts of objects, scattered or not. But still, for common sense, there is something odd in accepting Bernardlike entities. What is it that unifies familiar objects like lizards or mountains that Bernard lacks ? The standard four-dimensionalist reply is that the small minority of objects we usually believe there to be, the objects that are familiar to us, are just aggregates of parts that obey certain criteria_: they are, usually, spatio-temporally continuous and related by causality and similarity relations. It may also be added that familiar objects are usually, unlike Bernard, objects of only a unique kind. The successive temporal parts that make up a familiar object like a lizard are usually similar to each other, causally interrelated, continuous, and they all fall under the same sortal term. But maybe other relations would also do; in the case of people, for instance, some relation of mental connectedness and continuity should probably be postulated. But this is not really the job of the four-dimensionalist to determine with precision what these relations are that unify the objects we take as familiar – even the endurantist must have some account of what it is that makes a certain particular existing at some time identical to that other particular existing at another time, and whatever it is, whatever identity and individuation conditions the endurantist chooses to play this role, it will also be available to the four-dimensionalist as the 'glue' that makes the successive temporal parts of familiar objects stick together. What exactly the glue is will all depend on what kind of objects one is ready to accept. The principle of unrestricted composition simply tells us to be liberal and accept more objects than the familiar ones. The picture it provides is one of a space-time filled with matter. Any filled region of space-time is then a material object. Some of the regions seem, to us humans, to stick together better than others and stand out from their environment because they are connected by certain privileged relations. Those are our familiar objects.

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Another way to put this worry about Bernard-like bizarre entities was raised by Achille Varzi (2003). Varzi takes it to be a very unpalatable feature of the four-dimensionalist worm view that it makes sentences such as "Some philosopher was a table" turn out to be true. Indeed, according to the worm view fortified by the principle of unrestricted mereological composition, there is a space-time worm that corresponds, for instance, to the temporal parts of my table yesterday and the temporal parts of Achille Varzi today. So, we have here an entity that is now a philosopher but was a table. The stage view, according to Varzi, behaves better because the counterpart relation that holds between different stages that are philosophers need not hold between those stages and some stages of a table – and so, the problem does not appear. What is doing the job here is the counterpart relation that selects only those series of stages that are philosophers, because the counterpart relation is, presumably, some relation of similarity, and perhaps causal connectedness and spatiotemporal contiguity, or whatever you like. But then, if this is a solution for the stage view, it can also serve very well the worm view : first, the worm view theorist must bite the bullet – strictly peaking, it is true that there is an entity that is now composed of philosopher-parts and that has past temporal table-parts. This must just be endorsed. But, following what I have said above, the worm view theorist can claim that if one is interested in commonsensical objects (among which there are no table-philosophers) one can choose to strengthen the glue that unifies the different parts of the worms (indeed, exactly the same glue that the stage theorist uses to define his counterpart relation is available) and thus also select only those worms that are philosophers, and do not have table-parts. So, one can say that there is an entirely unrestricted relation that 'glues together' the different temporal parts of a single space-time worm, and second, that this relation can be qualified and can be given any constraints we want it to have to pick out the 'interesting' worms and discriminate them from the unrestrictedly composed Bernard-like entities, like table-philosophers 18 . 18

Another way to put this is to say that it is true that there are table-philosophers if one is speaking with quantifiers wide open, but that one can choose to restrict them to quantify only on ordinary (that is, "interesting") objects, in which case it will be false that there are table-philosophers. (It's like when one truly says "There is no beer" meaning that there is no beer in the fridge.)

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Granted, such qualifications and constraints are strongly human-dependent and have no ontological force at all, but this is only for the good since fourdimensionalists will typically claim that Bernard-like entities are ontologically on a par with, and are every bit as real as 'ordinary' objects that seem to stick together and stand out from their environment, like my table or Achille Varzi. Besides, I do not find the idea that the way we see the world as being cut up into people, lizards, sandglasses, clouds, and so on, is a genuinely human-dependent way, and I can easily imagine there being different intelligent beings in our world that would not cut up the world (the spacetime regions filled with matter) in the same way we do, maybe because their sensorial apparatus would not be similar to ours, or for other reasons. And, as far as common sense is concerned, one can ask : are our ordinary beliefs really incompatible with the four-dimensionalist ontology and the principle of unrestricted mereological composition ? In fact, I think that common sense just does not have any determinate opinion about Bernardlike entities. No one, unless he or she is pushed to it by philosophical considerations, would even think about such entities. But does this mean that common sense includes a certain positive belief against them ? I don't think so. I think that common sense is just entirely neutral on this matter, it has no opinion either way. For, acknowledged, it has no opinion that favours Bernard-like entities neither. The worries raised here against this principle arise at least partly from the fact that natural languages do not have names for Bernard-like entities and the common sense thinker does not usually think about them, but while this is certainly interesting from the epistemological and psychological point of view, it is hardly an objection to the metaphysical principle of unrestricted composition. §8. To philosophically motivate the principle of unrestricted mereological composition, David Lewis showed (see Lewis (1986a, 212213)) that there is a good reason not to restrict composition (here, to accommodate an ontology of familiar objects only). The problem with such a restriction would be that it would have to be a vague one. We have already seen this above (see I.5.§14) : it is a vague matter to determine spatial and temporal boundaries of ordinary material objects like lizards (Is this molecule or particle a part of the lizard or is it a part of the surrounding

Unrestricted mereological composition motivated

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environment ? When exactly does the lizard cease to exist ?). But then, as Lewis points out, it would be a vague matter whether composition takes place or not, and this is not acceptable if one wants to reject metaphysical vagueness, and take vagueness to be semantic indecision. So it cannot be that whether there is a certain mereological sum is vague, there is such a sum or there is not. This is not vague. But this is where restricted composition would lead us, and so restricted composition is better to be rejected. In general, any theory that would restrict composition will have to face the problem of where to draw the limits of it. Objection : temporal parts are unintelligible

Reply

§9. The last objection against the four-dimensionalist's ontology I am going to examine in this chapter is not exclusively an objection from common sense; but while it was, of course, raised by some philosophers and it is a philosophical worry, its complaint is very straightforward and based on intuitive and ordinary (dis)beliefs. Put forward by Peter van Inwagen, the objection is simple : "I simply don't understand what these things [temporal parts of material objects] are supposed to be, and I do not think this is my fault. I think that no one understands what they are supposed to be, though plenty of philosophers think they do." (Van Inwagen (1981, p. 90)). His worry, as he makes it clear in Van Inwagen (2000), is mainly that he does not see how a thing could have temporal proper parts. §10. I think the four-dimensionalist picture given in §7 above can provide solid grounds to enlighten such worries. But first, let my give just one everyday example of what an instantaneous temporal part is (of course, not all temporal parts are instantaneous). When my father travelled for a long time from home to work in Seoul, he put a webcam in his office – a small camera, pointed towards his desk, that was programmed to take one picture every two minutes and put those on a specific web page on the Internet. There was then a picture of my father working that was 'refreshed' every two minutes. Well, those pictures were pictures of successive noncontinuous temporal parts of my father. Non-instantaneous temporal parts are just like those, except that they have bigger extent along the temporal dimension. A proper part of any physical

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object is itself a physical object. That principle is accepted, almost uncontroversially, in the spatial case. I say "almost" uncontroversially, because as we have seen, not surprisingly, Van Inwagen is one who does not accept it. He thinks that my lizard Jean-Luc's tail, while still attached to Jean-Luc, or my non-amputated hand, are not material objects in their own right. I suspect it is because of this, because he just does not even accept spatial proper undetached parts of material objects, that he claims not to understand what a temporal proper part would be. A non-instantaneous proper temporal part of a material object is a fourdimensional object that is smaller in respect to the temporal dimension than the whole of which it is a part. This is, among others, Mark Heller's view. We can take a picture of them, we can talk about them, we can point to them, we can smell them, touch them, see them, so why would it be difficult to understand what temporal parts are ? They are the same kind of entities than are material wholes. If one stipulates that objects are fourdimensional, that they have temporal extent, then it is surely easy to understand the notion of temporal parts – it is as easy as to understand what spatial parts are, once we recognize that material objects are spatially extended. One can disagree on the premise, and thus reject the claim that there really are such things, but the notion of a temporal part is, to my mind, a very clear and intelligible one, and should be even for opponents of four-dimensionalism. §11. In the previous section, I have talked about instantaneous temporal parts. That could seem to be problematic for the four-dimensionalist – wouldn't they be three-dimensional entities ? And so, wouldn't there be a more basic three-dimensionalist ontology supporting four-dimensionalism? And are there any three-dimensional objects ? It seems clear that there can be instantaneous objects only if time is discrete, not continuous. I don't know whether time is discrete or continuous, and this is why I think it is a further advantage of the worm view over Sider's stage view that it is neutral towards the question whether there are instantaneous temporal parts or not – on Sider's view, clearly, his 'stages' are instantaneous entities. Indeed, this problem is at the bottom of my objection against the stage view from I.7.§7-8 where it is argued that there are many roles stages cannot play simply because they don't last. The worm view theorist, I

Are there instanttaneous temporal parts ?

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think, is not committed concerning instantaneous temporal parts either way. Maybe there are, maybe not, the worm view is compatible with both alternatives. Is it possible for there to be such entities ? They are certainly no less possible than two-dimensional objects like the surface of a cube. Can there be such two-dimensional objects ? I don't see any reason why not, but I like better to leave that question open, and the worm view allows us to do that19.

19

D. M. Armstrong goes a bit further and claims that whether there are instantaneous temporal parts or not is not even a philosophical question. (Armstrong (1997, p. 107)) If he is right, Sider's stage view has then the unpalatable consequence of being subject to surprises from science, since, according to Armstrong, the issue has to be settled by physics, or perhaps cosmology.

Chapter 9, The modal objection §1. The objection to four-dimensionalism that I am going to examine now is a modal analogue to the objection raised against endurantism in I.5.§8, and it also involves a problem with coincident entities. The objection was developed by Peter van Inwagen (1981, p. 92-). Statements and discussions of it can be found in Heller (1990, p. 27-28) and Sider (2001, p. 218-). Let us consider again my pet lizard Jean-Luc.

Van Inwagen's modal objection to fourdimensionalism

Jean-Luc Fig. 15

Jean-Luc-8

t0

t8

t10

The argument runs as follows : (i) (ii)

Jean-Luc actually lived for 10 years. There was an 'undetached' temporal part of Jean-Luc that existed from t0 to t8 (see figure above) – it lived for 8 years only. Let us call it Jean-Luc-8. (iii) Jean-Luc could have lived only 8 years. (There is a possible world, W, where Jean-Luc was killed at the age of 8.) (iv) So, Jean-Luc could have had the same temporal extent as Jean-Luc-8 has. (In the possible world W, Jean-Luc has the same temporal extent as Jean-Luc-8 has in the actual world.) (v) Jean-Luc-8 could exist in W with the same temporal extent it actually has (even if Jean-Luc does not exist for more than 8 years in W). (vi) Jean-Luc and Jean-Luc-8 would occupy exactly the same space-time

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region in W. (In W, Jean-Luc and Jean-Luc-8 would coincide.) (vii) But coincident entities are impossible. (viii) So, there is no such thing as Jean-Luc-8 (a temporal part of JeanLuc). As I have remarked in I.5.§8 when discussing the objection against endurantism, in van Inwagen's hands the objection was not raised against endurantism but against undetached spatial parts. His claim was that there is no such object as the top half of Mont-Blanc or my right hand. The modal version of the argument I am now considering is strictly analogous – the conclusion is just that there are no undetached temporal parts of any material objects. The only temporal parts that can make sense, according to van Inwagen, are, as we have seen in I.8.§9, improper temporal parts that would not be menaced by the present argument. I shall consider two possible replies a four-dimensionalist can use to answer this objection. One of them is recommended by Ted Sider, the other was proposed by Mark Heller. But let me first point out something important Sider says (see Sider (2001, p. 220-221)). The objection is for everyone

§2. The fact is that this objection is not an objection to fourdimensionalism only. The argument can be adapted as follows, without any involvement of temporal parts, and leads to the same unwelcome conclusion (commitment to coincident entities) by the same means – by considering modal properties. (i)' Jean-Luc actually has its tail. (ii)' There is an 'undetached' spatial part of Jean-Luc that consists of all of it except its tail. Let us call it "Jean". (iii)' Jean-Luc could lose its tail. (There is a possible world, W, where JeanLuc is grabbed by a predator and loses its tail.) (iv)' So, Jean-Luc could have had the same spatial extent as Jean has. (In the possible world W, Jean-Luc has the same spatial extent as Jean has in the actual world.) (v)' Jean could exist in W with the same spatial extent it actually has (even if Jean-Luc does not have its tail in W). (vi)' In W, Jean-Luc and Jean would coincide.

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So, as Sider points out, since the unwelcome conclusion can be reached without appealing to temporal parts, it seems that the modal version of the argument is an objection to everybody, and not only to the temporal parts theorist. It is not, then, an objection to four-dimensionalism. But still, it needs to be answered. We are now going to see two ways available to the four-dimensionalist to deal with the objection. §3. Sider's reply to the objection is in reality provided by Van Inwagen himself (see Van Inwagen (1990, p. 120)). What, in Van Inwagen's mind, is a reductio against four-dimensionalism (although he does not explicitly claim this that way), is, in Sider's mind, a good reason to adopt fourdimensionalism. The point is that a four-dimensionalist can easily answer the objection if he endorses a counterpart-theoretical analysis of de re modal statements. Since Van Inwagen takes modal counterpart theory to be unacceptable, here is the reductio 20 . Since Sider welcomes modal counterpart theory (as well as temporal counterpart theory (see I.7)), here is his defense. The dialectical situation is then simple : if one accepts modal counterpart theory, one can answer the objection. The reply goes as follows. Counterpart relations are similarity relations. Different objects can be similar in different ways, and so, there are different counterpart relations at hand. There can be, in our case, a lizard counterpart (L-counterpart) relation, and another temporal-part counterpart (T-counterpart) relation. Surely, those are different relations. The L-counterpart relation involves different criteria for similarity than the T-counterpart relation. For instance, it matters for T-counterparts that they must have the same temporal extent – if not, they would not be similar enough to be T-counterparts. And it could be claimed that two objects are L-counterparts if and only if they are sufficiently similar maximal aggregates of temporal parts of lizards. So, in W, there is just one thing (and not a coincident entity) that has two counterparts in the actual world – under different counterpart relations. It has Jean-Luc as an L-counterpart and Jean-Luc-8 as a T-counterpart. As a 20

Van Inwagen claims further that this is the only way for the four-dimensionalist to answer this objection, and so, four-dimensionalism is to be rejected. We will see that there are other possible replies. Sider also provides us with other possible replies whilst favouring the counterpart-theoretical one. See Sider (2001, p. 221).

Sider's reply

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lizard, Jean-Luc can have a smaller temporal extent, but not as a temporal part. Heller's reply

§4. Mark Heller answers the objection by denying premiss (iii). JeanLuc, according to him, could not live any longer nor shorter than he in fact did. To make this claim clearer, we must examine more deeply his fourdimensionalist ontology. Heller distinguishes between conventional and non-conventional objects (see Heller (1990, chap. II)). Most of the objects we usually believe there to be, like lizards, sandglasses, mountains, the wisest of philosophers, or Manhattan (those are Heller's favourite examples) are conventional. This means that, strictly, ontologically speaking they don't exist. This can strike as quite bizarre and false. But in fact, I think the view is appealing. Let us consider Heller's Manhattan case. Again, there is no such object, he claims. Nothing, as Heller puts it, came into existence when Manhattan was 'created'. There was a certain land mass that existed before and that will exist after Manhattan will cease to be – this land mass really exists. Manhattan is just a product of some human conventions, some legislative activity. Manhattan is not identical to the land mass and has different modal properties. This does not mean they are coincident entities: first, because Manhattan is just a convention and so does not really exist, and second because, as Heller sees it, there never are coincident entities, there is just a filled space-time region to which we can refer to by different conventions (like "statue", which is a conventional object, or "lump of clay" which is, maybe, non-conventional (see below)). So, what there really is, is a certain physical object that fills the space-time region to which we refer to as "Manhattan". But this object is not Manhattan. Persistence conditions and modal properties of conventional objects then are not real properties of any existing objects, but rather they depend upon some of our conventions that make us act as if there were such objects with such and such modal properties and persistence conditions. (A further reason to motivate the claim that most of the familiar objects are conventional is grounded in vagueness (the reader will recall the discussion of vagueness from I.5.§14) – for, all of the conventional objects like lizards, philosophers, sandglasses, and so on, are vague, and they have non-precise spatio-temporal boundaries and persistence conditions. Heller's

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strategy allows us to account for vagueness as semantic indecision, not as a metaphysical feature of the world.) What are the non-conventional objects ? Well, maybe the lump of clay is, maybe the land mass that fills the space-time region we call "Manhattan" is. In general, non-conventional objects are what Heller calls hunks of matter. All there really is are hunks of matter that fill space-time regions. Thus, those hunks of matter have their spatio-temporal boundaries essentially – and those boundaries are precise, they are not vague objects. So, for instance, none of them could exist for any shorter period of time that it in fact did. None of the non-conventional objects has the modal properties that we ascribe to Jean-Luc – this is why Heller denies premiss (iii). I find this a little bit confusing : after all, Heller just told us that JeanLuc, as well as all lizards, is a conventional object. But I think the point is that conventional objects don't really exist and that they do not have really any modal properties, and that the non-conventional object that fills the space-time region we refer to as "Jean-Luc" has its temporal boundaries essentially, and so could not live any shorter. There is, then, no way for a really existing object to have a shorter existence than it does, and this is how the rejection of premiss (iii) is motivated. (The premiss only seems true because we do not have a precise definition enough of "Jean-Luc", our conventions are not precise enough to stipulate exactly the necessary and sufficient conditions for being Jean-Luc. It is this vagueness grounded in our language and thoughts that allows us to act and talk as if it were possible for Jean-Luc to have the modal properties we usually ascribe it. "A conventional object is counted as existing at just those worlds that our conventions allow us to describe as including that object's existing" (Heller (1990, p. 63))). As bizarre as Heller's view seemed to my mind at the beginning, I must say I find the argument from vagueness quite convincing. Objects like lizards are vague, and vagueness is not metaphysical. The further step, the claim that objects like lizards do not really exist, seems to be a big step but maybe it is not : all it proposes is that the world contains matter distributed across space-time in a certain way and that we, human beings, have conventions to cut it up in a certain way. I can imagine there being different intelligent beings in the world that would not cut up the spacetime filled regions in the same way as we do, maybe because their

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sensorial apparatus would not be similar to ours, or for other reasons. Heller's view allows for a very simple ontology, the ontology of hunks of matter, and provides an account of what our familiar objects are in terms of our conventions. §5. We have seen two ways available to the four-dimensionalist to answer Van Inwagen's modal objection. Since the objection relies on modal properties, an appropriate treatment of de re modal statements is crucial to deal with it (and this is maybe a point in Heller's reply that could be objectionable : he does not provide any arguments supporting his ontology of modality – the view that possible worlds are, if I understood him well, merely conventional). It will be the task of Part II to show how such statements should be understood and interpreted, and among other results, we'll then possess a better and more complete answer to the objection of this chapter.

Part II Persistence across possible worlds

Chapter 1, Introduction §1. My neighbour Cyrano has a big nose. He could have a small one, though. When I say this, that he could have a small nose, but actually has a big one, what are the truth-makers for such a statement ? Presumably not Cyrano himself since he has a big nose. So where should we look for a truth-maker ? Where should we look, so to speak, for a small nose ? Many contemporary philosophers look for it in possible worlds. It is possible that Cyrano has a small nose if and only if there is a possible world in which Cyrano has a small nose. But what does that mean ? Does this mean that Cyrano lives in two worlds (or (many) more) ? A puzzle arises quickly. What is wanted is to provide an analysis of de re modal statements in terms of quantification over possible worlds in the following way : (i) (X is possibly F) ↔ (There is at least one world where X exists and X is F) (ii) (X is necessarily F) ↔ (In all worlds where X exists X is F) There are two immediate possibilities. First, X (let us say Cyrano) can exist in several worlds and can have a big nose in one whilst having a small nose in another. Or second, Cyrano is a world-bound individual – he can inhabit one world only. Both ways seem to lead to trouble. The first strategy fails because of a problem analogous to the problem of temporary intrinsics from I.4. For if Cyrano from our world is numerically identical to the Cyrano from another world then, being the very same individual, he should obey the principle of Indiscernibility of Individuals : (Ind.Id.) (∀x) (∀y) ((x = y) → (∀F) (Fx ↔ Fy)) For any objects x and y, if x is identical with y, then for any property, F, x exemplifies F if and only if y exemplifies F. But he doesn't. For Cyrano, one and the same individual, has both the properties of having a big nose and of having a small nose, which are incompatible. So, we have a contradiction, similar to the one raised against endurantism in I.4.§7.

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The second strategy does not seem to do any better. The problem is that if Cyrano is a world-bound individual, then the right-hand side of (ii) is always satisfied for any property Cyrano actually happens to have, even the most contingent and insignificant one. For instance, if Cyrano has actually a big nose, then, according to (ii), it is a necessary feature of him – but that is certainly false. So it seems, at a first approach, that the first strategy yields a contradiction and the second is just false. One can then start to appreciate the problem : it is a problem of persistence of individuals through possible worlds. And this is the main task of the second part of this book : to examine different accounts of persistence of material objects across possible worlds and thus provide a satisfactory analysis of de re modal statements. Persistence across possible worlds

§2. As in the temporal case, there are several strategies available. Analogous to endurantism, there is the trans-world identity view. Analogous to perdurantism, there is the claim that all individuals are world-bound – exactly as nothing can exist at more than one time, nothing can exist at more than one world. Also, analogous to presentism, there is genuine actualism (also called fictionalism), the thesis that only the actual world exists, whilst other worlds, exactly as other times, are not real, they are only useful heuristic devices. In contrast to this view, there is genuine modal realism analogous to temporal realism – eternalism – all times are real, no matter how distant they are; likewise, all possible worlds are every bit as real as the actual one. And there is also abstractionism, a so-called 'moderate' version of modal realism, that takes possible worlds to exist, but not in the same way the actual world does. By combining these thesis about persistence and about the nature of possible worlds, we get the following six views : (i) (ii) (iii) (iv) (v) (vi)

Modal realism with trans-world identity Modal realism with world-bound individuals A genuine actualist (fictionalist) view with trans-world identity A genuine actualist (fictionalist) view with world-bound individuals Abstractionism with trans-world identity Abstractionism with world-bound individuals

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Of course, the six possibilities just listed are not the only plausible alternatives – the trans-world identity view, for instance, can be articulated in different ways or, analogously to perdurantism in the temporal case, the world-bound individuals modal view shall come in versions that are parallel to the worm view and the stage view. And for reasons that will be given, the same holds for modal fictionalism. The simplest of the three types of ontological views of possible worlds – modal realism, fictionalism, abstractionism – is certainly modal realism. For what can be simpler than to imagine that possible worlds are just worlds, exactly as our own world is ? I do not say that the view is intuitive, it's just the simplest one, and so this is where we shall start our tour of theories of persistence across possible worlds.

Chapter 2, Modal realism §1. Modal realism is the thesis according to which there are possible worlds, and they are of the same kind the actual world is – they are spatiotemporal concrete entities – and they are every bit as real as the actual world we inhabit. Our world does not have any ontological privilege over the possible ones, the possible has the same ontological status as the actual. The main defender of this doctrine is David Lewis (1986a, 1973b, 1968, 1983a, 1983b, 1983c). He claims, further, that possible worlds (including the actual world) are all isolated one from each other, they are neither causally nor spatio-temporally related. But is not our world the actual one, whilst the others are merely possible, and so, isn't there an important distinction to be made ? Yes, our world is the actual world, but this does not make it ontologically any different from the others, Lewis claims. "Actual" is to be analysed as an indexical term. Exactly as the temporal realist (the eternalist) analyses "present" as an indexical term that just picks up one of all the existing times – the time of utterance of the word – the modal realist analyses "the actual world" as "our world" or "the world we inhabit", and nothing more. Other inhabitants of other possible worlds can do the same, but in their mouth "the actual world" will just refer to another world, the one they inhabit. So Lewis really believes, and invites us to believe too, in a plurality of worlds – the actual world being just one of them. One good reason he provides to support this doctrine is that other accounts that try to provide an analysis of modal de dicto and de re statements do not succeed, and so we are left with his view. The other argument is that modal realism is consistent, plausible and serviceable (see Lewis (1986a, chap. 1)). Before I turn to my main interest, the problem of persistence across possible worlds, let us first examine a general objection to modal realism that I think must be answered to gain the view's credibility and that will also permit a better understanding of what modal realism is.

Modal realism

126 Problem with nonactual objects

§2. The worry arises when we start thinking of non-actual objects (see Loux (1979, p. 44-)). It seems that the genuine modal realist must endorse the following claim : (i) It is possible that there exists an object distinct from every actually existent object. It is clear that if one commits oneself to genuine real existence of possible worlds, one must then accept genuine real existence of objects that inhabit them, objects that are distinct from any object existing in the actual world. But then, one could suspect a contradiction – the modal realist claims that there are objects (the possibilia) that don't exist actually. In short, as Plantinga puts it, the view suggests that "there are things that do not exist" (Plantinga (1976, p. 256)).

Solution

§3. Lewis answers this objection by showing that it is grounded in a confusion. There is an important distinction to be made regarding the existential quantifiers involved in (i). For, of course, possible non-actual worlds do not exist actually, and the same holds for their inhabitants – the only thing the modal realist says is that there are more things than those that exist actually. This is how Lewis puts it : "Likewise some things exist here at our world, others exist at other worlds ; again, I take this to be a difference between things that exist, not a difference in their existing. You might say that strictly speaking, only this-worldly things really exist ; and I am ready enough to agree ; but on my view this ‘strict’ speaking is restricted speaking, on a par with saying that all the beer is in the fridge and ignoring most of all the beer there is. When we quantify over less than all there is, we leave out things that (unrestrictedly speaking) exist simpliciter. If I am right, other-worldly things exist simpliciter, though often it is very sensible to ignore them and quantify restrictedly over our worldmates." (Lewis (1986a, p. 3)) So, according to Lewis, we have to admit two distinct existential quantifiers – one of them (∃) ranging over an unrestricted domain (over the

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totality of all possible worlds, including the actual world) , while the other restricted quantifier (∃@) will only range over the actual world. The claim that there are objects that don't actually exist will then be understood as "∃x ¬∃@y (x = y)" which is a consistent claim. The restricted existential quantifier ∃@ is definable in terms of the unrestricted one with the help of the indexical analysis of "actual" (see above) : ∃@x Fx =df ∃x (Fx ∧ Actual(x)). So, all Lewis says here is that to avoid that an ambiguity in our ordinary language yields a contradiction, we should give ourselves two distinct terms : one to speak about our actual world, and the other to speak about all of the possible worlds. Similarly, if we want to speak about what exists in a certain possible world W1 and about what exists in another possible world W2, we always have to precise which is the world we are talking about, to avoid confusion. For if one says, for instance, "Cyrano exists" without saying in which world it is that he exists (suppose he does in W1 but not in W2), we could likewise say "Cyrano doesn't exist" – a seeming contradiction. But if we possess a clear device to refer to a certain possible world (using restricted quantifiers, like ∃w1, ∃w2, …), we can then say "Cyrano exists in W1" and "Cyrano doesn't exist in W2", which is consistent. It seems clear that this is exactly what Lewis proposes for ∃@, and nothing more. His restricted quantifier is simply an abbreviation for an expression like "∃x_(Actual(x) ∧ …)". Of course, instead of saying "Cyrano exists in the actual world", we can often simply say "Cyrano exists", knowing that without other precisions we are speaking about the actual world – we are implicitly using a restricted quantifier. And of course, since the term "actual" was given an indexical analysis, the inhabitants of other worlds can do the same : if I say "Cyrano exists", my statement is true (if the actual world contains Cyrano), but if an inhabitant of W2 makes the claim "Cyrano doesn't exist", his statement will also be true (supposing, Cyrano does not exist in W2). I think that Lewis' reply to the objection is adequate. Nevertheless, I bear in mind Alvin Plantinga's denial (see Plantinga (1976)) that we have two distinct notions of existential quantifiers as those proposed by Lewis (or a plurality of them, as just sketched, one per world (or one per fridge)). Plantinga claims that we have only one concept of existence, and that it is

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the concept of actual existence. But here we have to be careful : if Plantinga's claim were to be taken as an objection to the adequacy of Lewis' reply here, then I think it would be wrong. If modal realism is accepted, the idea of having several existential quantifiers is not only a legitimate and justified one, but clearly inescapable. But if what we want to say by claiming that we have but one concept of existence is taken to mean that modal realism in toto must be rejected because it goes against our ordinary concept of existence, then there is an objection. Four accounts of persistence across possible worlds

§4. So here we are in a world that is just one among many. Here is also Cyrano, and his nose. And here is a de re modal claim about him : "Cyrano has a big nose but he could have a small one". How are we to understand such a claim under the modal realist hypothesis ? Modal realism can be combined logically with both trans-world identity and world-bound individuals theories. But there are more than only two possibilities to articulate those views. There are, I think, four, some of them analogous to the possibilities we have examined in the case of persistence through time. I am now going to examine those possibilities in the following order : (i) Straightforward trans-world identity (analogous to genuine endurantism) (ii) Modal counterpart theory (analogous to the four-dimensionalist stage view) (iii) Partial trans-world identity (iv) The theory of modal perdurants (analogous to the four-dimensionalist worm view)

Chapter 3, Straightforward trans-world identity §1. Genuine and straightforward trans-world identity is really the most immediate and obvious solution. The general analysis given for evaluating de re modal statements in terms of possible worlds, that we saw in II.1 was

Straightforward trans-world identity

(i) (X is possibly F) ↔ (There is at least one world where X exists and X is F) (ii) (X is necessarily F) ↔ (In all worlds where X exists X is F) Thus, if I say that Cyrano has a big nose but could have a small one, my statement is true iff Cyrano exists in the actual world and has a big nose here and Cyrano exists in another possible world and has a small nose there. The difficulty now is to understand the notion of Cyrano's existing in the actual world and also existing in another world. A theory of straightforward trans-world identity could immediately be thought of as the following picture shows 21.

Cyrano

Cyrano

W1

W2

Cyrano exists wholly in W1 (say this is the actual world), he has a big nose, he also exists wholly in another world W2, and has there a small nose. 21

Van Inwagen draws essentially the same picture (and rejects it) in Van Inwagen (1985, p. 196).

Fig. 16

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What is wrong with this picture ? Everything. The problem is just that it is plain false – no one individual can exist as two. If we look at the picture, it becomes obvious that Cyrano-in-W1 denotes one individual and Cyrano-inW2 denotes another, so how could it ever be true that they are numerically identical ? How could Cyrano live here and some other place as well ? How could two different objects inhabiting two disjoint space-times ever be identical ? Of course, they could not. My claim parallels what I have said in I.4.§16 about endurantism under the eternalist hypothesis. Eternalism, remember, is temporal realism, and so is analogous to modal realism. Endurantism is the thesis of genuine trans-time identity : one and the same numerically identical object can wholly exist at different times; likewise, the trans-world identity picture on the figure above claims that one and the same numerically identical individual can exist at different worlds. In the case of persistence through time I came to the conclusion that endurantism under the eternalist's hypothesis is simply intenable. Indeed, it seemed clear that the only viable option for the endurantist is to adopt presentism and not genuine temporal realism. The modal case with straightforward trans-world identity yields the same unacceptable picture. Furthermore, the modal case's picture could seem even worse for it claims numerical identity between spatio-temporally and causally unrelated objects. Transworld identity with overlap

§2. I know of no metaphysician who would defend the preceding picture of trans-world identity. But there is another picture of trans-world identity, discussed (and rejected) by David Lewis in Lewis (1986a, p. 198-). Cyrano

Fig. 17

?

W1

W2

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This picture shows how a single individual, one and the same numerically identical individual, could exist in two worlds at once, without drawing a picture as repugnant as the preceding one. The ontology of modal realism must be accommodated to render this picture acceptable, though. Possible worlds must be able to overlap. If two worlds overlap, they share a common part – for instance, Cyrano – and this is how Cyrano, being one, can be said to exist in two possible worlds. Trans-world identity then amounts to part-sharing of worlds. Let us accept (not for long) such a modification of the modal realist's ontology. The obvious difficulty with such a picture appears when one wants to draw it : indeed, if you have a close look at figure 17 above, you'll see that I did not draw Cyrano's nose. Why ? Because I did not know what to draw. Should I have pictured Cyrano as having two different noses, one of them big and the other small ? Should I have pictured him with one nose only ? (But which one ?) Or, should I have pictured him with no nose at all ? Surely, all of the solutions are unacceptable. The problem hidden here is a problem with accidental intrinsics that parallels the problem with temporary intrinsics discussed in I.4 that was also developed, not surprisingly, by David Lewis. If Cyrano from our world is numerically identical to the Cyrano from another world (and I have supposed that this is possible, according to the picture provided by figure 17, because there is only one Cyrano), then, being one and the same individual, he should obey the principle of Indiscernibility of Individuals – but he doesn't. In W1, he is supposed to have a big nose, and in W2 he is supposed to have a small nose. But he is only one individual, being a part of two worlds, and so he has the two incompatible properties. As far as the analogous problem with temporary intrinsics is concerned, the endurantist had several strategies at hand to face this problem (especially, indexicalism and adverbialism). But analogous strategies could not be developed in this modal case. As we have seen in §1 above, the endurantist-eternalist works with a picture analogous to figure 16, not to figure 17. In figure 16, a parallel problem with the different noses is at a first approach a semantical one, and this is why semantical solutions like indexicalism and adverbialism were given in the temporal case – if there were a defender of trans-world identity in the sense of figure 16, he could use such strategies (and they would be rejected for very similar reasons

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than in the temporal case); but not a defender of trans-world identity in the sense of figure 17. For here, the problem is obviously metaphysical and no semantic solution could help to render it less problematic.

Chapter 4, Modal counterpart theory §1. So it seems that trans-world identity leads to trouble. What about the other possibility ? What if one claims, intuitively enough I think, that one individual cannot live in more than one world ? Such a view would claim that all individuals are world-bound. We have already seen in II.1.§1 that a straightforward claim of this kind is unpalatable. The problem was that if we say that individuals are world-bound, and if we want to stick to the standard analysis of de re modal statements (i) (X is possibly F) ↔ (There is at least one world where X exists and X is F) (ii) (X is necessarily F) ↔ (In all worlds where X exists X is F) then we'll get the very counter-intuitive and unacceptable result that nothing could be any different than it actually is. If Cyrano has a big nose, it turns out, under this analysis, to be a necessary property of him because the right-hand part of (ii) is always satisfied (because he exists in one world only). David Lewis proposed a strategy that avoids this problem – modal counterpart theory. Modal counterpart theory claims that all individuals are world-bound but provides a different analysis of de re modal statements. According to this view, (i)' (X is possibly F) ↔ (X is F or at least one counterpart of X is F)22 (ii)' (X is necessarily F) ↔ (X is F and all of X's counterparts are F) The picture such an analysis provides is the following.

22

According to Lewis, it would be enough to say that (ii)'' (X is possibly F) ↔ (at least one counterpart of X is F) because of the postulate P6 he introduces in Lewis (1968, p. 111) : "Anything in a world is a counterpart of itself" (the counterpart relation is reflexive). My (i)' is only more explicit about this. Similarly for (ii)'.

Modal counterpart theory

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counterpart

Fig. 18

Cyrano

Cyrano*

W1

W2

Cyrano exists in a world W1 (say, the actual world), where he has a big nose. He does not exist in any other world, but has counterparts in other worlds. Because one of his counterparts, the one from W2, has a small nose it is true then that Cyrano could have a small nose. The problem with world-bound individuals and their contingent properties is avoided : having a big nose does not turn out to be a necessary property of Cyrano because not all of his counterparts have big noses. And, as the figure above shows, there is no problem with denotation, as there was in the first trans-world identity case, because Cyrano and Cyrano* are different people – so, "Cyrano-at-W1" denotes Cyrano and "Cyrano-at-W2" denotes Cyrano* who is a different person. What is a counterpart ? The counterpart relation is based on similarity. In short, something is an other-worldly counterpart of Cyrano if it is an individual inhabiting a different possible world who resembles him in his important features and who resembles him more closely than any other object in that world; it is important that those individuals, his counterparts, are not (numerically) identical to him : they all exist in their own worlds and he is the only one inhabiting the actual world. There are neither causal nor spatiotemporal relations between Cyrano and his counterparts – what there is, is a relation of similarity and that's how we can say that they are what he would be, would the world be different.

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This view solves nicely the problem with accidental intrinsic properties, and the solution parallels the one a four-dimensionalist gives to the problem of temporary intrinsics. Indeed, modal counterpart theory is closely analogous to the stage view defended by Sider (see I.7). Cyrano at a certain time t1 has a big nose, and he can be said to have a small nose at a later time t2 (after some plastic surgery, perhaps) in virtue of there having a temporal counterpart that has a small nose – but the two incompatible properties are had by two different things, different temporal stages, or temporal counterparts. This is why there is no threat of contradiction for the four-dimensionalist as far as the having of two incompatible intrinsic temporary properties at different times is concerned. The modal case raises just the same problem, and just the same solution : Cyrano has a big nose in W1, but he can be said to have the modal property of having possibly a small nose in virtue of having at W2 an other-worldly counterpart that has a small nose. But since the two incompatible properties are had by different things – different modal counterparts – no contradiction threatens to arise. §2. So we have seen that modal counterpart theory seems to be able to answer all objections arising against trans-world identity and world-bound individuals, or at least those we have seen until now. This is surely a great advantage of the view. But one must be ready to pay the cost of it. For counterpart theory leads to difficulties precisely because, to do the job it promises, it must be a world-bound individuals theory, which permits individuals to inhabit just one single world and no more. It is this feature of Lewis' theory that yields objections showing that it misses the target : counterpart theory does not permit to give a proper account of what may happen to us, because what are to be our counterparts are folks that are not related to us in any way, except by the fact that they resemble us. So, what might happen to me is not about me at all, it is a story about someone else, living in some other world which has neither causal nor spatiotemporal relations with mine. This is Saul Kripke's famous point (Kripke (1972, p. 45)) : we have a strong commonsensical belief that we have many properties only contingently and that there are many different ways for us to be different. If, for instance, I just avoided a deadly fall while trying to climb up Mont-Blanc, it is then fundamental, in order to justify my

Objection

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sensation of relief, that I have the belief that it was me who could have fallen and died. But according to counterpart theory, my idea that I could have died is not really about me : if I say this, I'm speaking about someone else – someone who resembles me and who is my counterpart but who is not me in any way. Following the counterpart theory, we then get a concept of de re modality that is quite different from our commonsensical beliefs about what might happen. Alvin Plantinga (1973, p. 164) makes the same point in an analogous fashion : if I say I'm able to perform a certain action A ("It is possible for me to do A.") then, according to counterpart theory, I'm speaking about someone who does A but who is not me – and of what importance and interest could this possibly be to me ? How can actions done by someone else in some other world be of any help to me to know what I can do or not ? Indeed, it seems that, according to counterpart theory, I (I myself) cannot perform A, for when I say "It is possible for me to do A" I'm not speaking about myself but about some other individual. Lewis' reply

§3. In defence to Kripke's worry and Plantinga's argument, Lewis claims (see Lewis (1986a, p. 196)) that what matters is that I have a certain modal property in virtue of my having an A-doing (falling down Mont-Blanc) counterpart and this allows me to truly say that I (I myself) could have Adone, fallen and died. It is quite enough that there is a world according to which I (I myself) die in the accident even if I (I myself) am not part of this world. This world represents me as slipping and falling and that is what we mean when we say that I could have fallen. The trouble here is that it is very hard to see how someone else, some other concrete individual, could possibly represent me ; and to say, as counterpart theory does, that this is simply done by a relation of similarity doesn't help much, I fear. There are many entities which resemble me, in our own world and in the others, and it seems very difficult to see how any one of those individuals could represent me. Under modal counterpart theory, I have my modal properties because of the way somebody else is, and this is just too strange. The next chapter presents an attempt to modify Lewis' counterpart theory to avoid this worry.

Chapter 5, Partial trans-world identity §1. The partial trans-world identity view is maybe a better way than counterpart theory to meet Kripke's claim, Plantinga's objection, and to give a good account of representation de re, while keeping its advantages. This view – a view that Lewis himself discusses and rejects in Lewis (1986a, p. 206-209) – requires a different, but still a genuinely realist, structure of possible worlds (this shall be the job of §2-§6 below) and another definition of the counterpart relation (§7 below).

Partial trans-world identity

§2. Lewis' structure of possible worlds is a static one and I mean by this more or less what Lewis himself means when he speaks about divergence (Lewis (1986a, p. 206)). According to his modal realism, possible worlds are causally and spatio-temporally disconnected. They don't overlap : no part of a world is part of another. There are worlds with duplicate initial segments : they are exact reproductions of each other and stay as simple copies up to a point from which only they will diverge and differ. Up to the day I decided to climb on Mont-Blanc, or the day when Cyrano decided to undergo plastic surgery, there were many worlds, infinitely many maybe, existing independently but being exactly alike, and diverging only afterwards (in some of them I fell and died, in others I survived; in some of them Cyrano has a small nose, but not in others). Sometimes, Lewis was accused of defending a 'crazy ontology' theory because it postulates that there is much more than what we usually believe there to be ; there are many counterparts of Mont-Blanc instead of the only one we believe in, there are many more climbers, and so on. I do not believe that Lewis' theory is more or less 'crazy' than any other of the abstractionist (actualist) alternatives (see II.8) : Lewis multiplies entities of one and the same kind beyond what we usually believe there to be, while others multiply kinds of entities there are, since possible worlds are said to be abstract objects like sets of propositions or abstract states of affairs. Choosing between multiplicity of things of the same kind (of a kind we commonsensically already believe in anyway) and multiplicity of ontological categories, I prefer the first. Besides, any abstractionist postulates as many entities that play the role of possible worlds as there are Lewisian worlds, so I really don't think abstractionism is any less costly

Lewis' modal realism is a static structure of possible worlds

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(on this, see also II.8.§1). However, Lewis' theory is, I would say, unparsimonious and unrespectful of Ockham's Razor in another sense : as mentioned, it postulates that there is a great number (an infinity, probably) of possible worlds which, for a very long time (seconds, hours, days, billions of years or more), do not differ in any way and are simple copies or duplicates – if there is waste in Lewis' ontology, then I think it's this. A dynamic structure of possible worlds. Branching.

§3. A dynamic structure of possible worlds I shall now examine will precisely set this point right : possible worlds will be said to exist only when their existence is required to give an account of what is possible ; no copies or duplicates will be allowed and entities will not be multiplied beyond necessity - no waste of entities will be permitted here. How can this be done ? The answer is : branching. Let us suppose that the world has a beginning and that all possible worlds share it – they all have the same origin. From that moment, and at every moment of time since then, it was possible for the world to evolve in many different ways : a certain particle could have interacted with others in a different way than it actually did and later on, consequently, the Milky Way could have been completely different, maybe Mont-Blanc could have measured 8850m and Mount Everest 4807m or there could have been no Mont-Blanc at all. What is important here is that at any moment of time of the evolution of the world different possibilities were open ahead of it – and those possibilities, those alternative evolutions of the world, determine the existence of possible worlds, for in a branching structure of possible worlds, at any moment, at any crossroads where alternative ways are to be chosen, the world will be said to undergo a fission and this will generate as many possible worlds as there were possibilities of evolution at the considered moment. Thus, according to this theory, when I nearly slipped and fell down the mountain, the world split into (at least) two : one where I died and one where I survived. So those are the two needed primitives for a dynamic structure of possible worlds: a common origin for all possible worlds and genuine fissions of them. Of course, those fissions will generate at every moment of time a great number – an infinity presumably – of possible worlds, but all those worlds will be said to come into existence only at a moment when their existence is required and useful to give an account of certain possibilities :

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there is no need here to postulate the same great number of 'parallel' static possible worlds which do not differ (up to a certain moment of time). It is in this sense that the branching structure of possible worlds is a dynamic one, for, at any time, it does not postulate more entities than necessary and is then more parsimonious. In a static structure of possible worlds, as the one defended by Lewis, there is always the same number of worlds, while the dynamic structure provides us with a number of worlds which increases over time. Schematically, it is possible to represent this structure as follows. Fig. 19

W3 W1

W4 W2

In this figure, each entire branch of the structure that begins at the origin represents a possible world, each single arrow represents a part of one or more possible worlds (a world-stage) – which is a state of a world at a given moment of time, each node of the tree represents a fission, and the direction of the arrows indicates the flow of time. A possible world is thus defined as an ordered aggregate of world-stages (temporal parts of worlds) that forms a complete branch and that has the common origin as its starting point. An example of such a world is represented here by "W3". Labels "W1" and "W2" don't denote a 'complete' world but only a world-stage, a world in a state at a given moment of time (world-at-t). W1 is thus a shared part of W3 and W4 while W2 is not. Terminological ambiguity will be avoided by underlining "W3".

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Direct and indirect generation

§4. Precision : if Wi split into two worlds Wj and Wk, I will say that Wi generated directly Wj and Wk – and I will say that Wi generated indirectly a world Wn, if Wn was generated directly by a world which was itself generated by Wi. In the figure below, for instance, Wn will be said to be indirectly generated by W1 because it is the result of a split of a world which itself is the result of a split of a world which is the result of a split of W1.

Fig. 20

W1

W2

W…

Wn-1

Wn

Indexicality of actuality

§5. All possibilities thus realised at any moment when a world splits will be said to have the same ontological status – all have the same reality as we claim for the actual world; they are of the same kind. How are we then to distinguish between the actual world and the others ? How does the actual world gain what seems to be an ontological privilege ? And how do we know that we inhabit the actual world ? To those questions, we know how Lewis replies (see II.2.§1) : "actual" is an indexical term, like "present", "here" or "I", which expresses simply the fact that I, who am writing here at this moment, am speaking about the world I inhabit – likewise, inhabitants of other worlds can use the word "actual" to speak about their own world, the one they inhabit. This conception of actuality is quite compatible with the branching structure of possible worlds : I inhabit one single world and no more (I am part of one of the 'branches' of the structure of possible worlds) and, whenever I use the word "actual" it denotes this world, exactly as the word "I" denotes me.

A multiverse ?

§6. One could be tempted to speak here about one big multiverse instead of speaking about a multiplicity of possible worlds : a multiverse could be

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seen as a set or aggregate of all 'branches' (see figure 19), which would then contain all universes, and all possible worlds. In short, the theory could seem to be an actualist one : a single big (actual) world containing all other 'possible' worlds. This must be avoided because there would be no more sense then to speak about "other" or "possible" worlds since there would be nothing but one huge world. But the splits, as I propose to consider them, guarantee a multiplicity of worlds : all possible worlds generated by those splits are, after a split occurred, entirely causally and spatiotemporally disconnected and isolated, and are all equally real. If Wi split and generated Wj and Wk then, from that moment, Wj and Wk are parts of different worlds, totally inaccessible one from each other. What one might call a "multiverse" could thus, at best, be a shortcut to speak about the set of all possible worlds. Let us now see how this structure can be used to give an account of de re modality. §7. I called the view I am now considering "partial trans-world identity". This could seem a bit confusing, for according to this view, all individuals are world-bound : I inhabit one single world and no more. It will now become clear why I chose such a label. Let us remember that the account of de re modality provided by Lewis, which also claims that all individuals are world-bound, appeals to his counterpart theory and gives the following paraphrase for de re modal statements. (i)' (X is possibly F) ↔ (X is F or at least one counterpart of X is F) (ii)' (X is necessarily F) ↔ (X is F and all of X's counterparts are F) In II.4.§2 and II.5.§2-§3, I exhibited reasons to believe that Lewis' counterpart theory is inadequate. However, its core idea, the existence of individuals inhabiting other possible worlds who are not identical with individuals of the actual world but who are related (who correspond) to them in a certain way, is a good one, I believe. The difficulties that Lewis' counterpart theory yields are rooted in the fact that those counterparts are causally and spatiotemporally totally disconnected from us (this is a direct consequence of his ontology of possible worlds) and, consequently, those

De re modality and Bcounterpart theory

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individuals have, we could say, nothing to do with us. But the basic idea of the existence of some kind of counterparts can perhaps be adapted to the branching ontology of possible worlds in such a way that problems yielded by Lewis' theory which bother Kripke and Plantinga so much can be avoided, while preserving its utility in the paraphrases (i)' and (ii)'. The new definition of a counterpart relation that I propose is the following (from now on, I will use the term "L-counterpart" to speak about Lewisian counterparts and the term "B-counterpart" when I will speak about the counterpart relation in a branching structure of possible worlds) : (B-CT)

An individual I1 existing in a world Wi is a B-counterpart of an individual I2 existing in a world Wk (Wi ≠ Wk) iff I1 and I2 have been a numerically identical individual in a world Wm which directly or indirectly generated the worlds Wi and Wk.

The following example illustrates this definition.

Fig. 21

…

1

W2 2

W1

4 5

W4

W5

3 W3

A circle represents an individual existing in the world represented by the arrow on which the circle is situated – for instance, the individual I1 inhabits the world W1. Let I1 be me and let W1 be the actual world on the 11th of July 2000 (the state of the actual world) just before I started the second half of the route to the summit of Mont-Blanc. W1 then split into (at least) two different worlds : W2 where I reached the summit and W3 where I did not. The individual I1 (I myself in W1) also split into (at least) two individuals I2 and I3 ; I3 is thus a B-counterpart of I2 and vice versa in virtue of B-CT, for

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even if they are, after the split, two distinct individuals inhabiting different worlds and are from that moment causally and spatiotemporally completely isolated from one each other, they have been numerically identical (they have been the very same individual I1) in a world that (directly) generated the two worlds they inhabit at present (W2 and W3). The same holds for worlds W4 and W5 which are, for instance, two worlds generated by a split of W2, where in W4 the individual I4 dies in an unavoided fall and is a counterpart of I5 in W5 who survives and safely returns home. §8. Let us turn now to some questions concerning identity and the Bcounterpart relation. On the figure below, let I1 be the individual I was just before the accident (before a split occurred), I2 the individual I am now and I3 my unlucky B-counterpart.

Identity and Bcounterpart relation. 4D.

Fig. 22

W2 …

1

W1

Wa 2

3 W3 Wb

One could object here that this conception leads to the assertion that I1 = I2, and I1 = I3, but I2 ≠ I3, and thus implies that identity is not transitive. Of course, this is not so because it is neither the case that I1 = I2 nor I1 = I3. For I1, I2 and I3 are not individuals, they are not people, tables, bottles of beer or whatever we usually consider – they are temporal parts of people, temporal parts of tables, temporal parts of bottles of beer, and so on, exactly as W1, W2 and W3 are temporal parts of worlds and are not worlds. I1, I2 and I3 must thus be regarded as individual-stages, which can be parts of one and the same individual but, being different stages, they are not (numerically) identical. According to this four-dimensionalist account, there is an individual Ia (I use the same convention as before by underlining Ia and not I1) which has as parts the individual-stages I1 and I2,

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and an individual Ib which has as parts the individual-stages I1 and I3 ; likewise Wa is a world which has as parts W1 and W2. The individuals Ia and Ib share one of their parts in common (namely, I1) but that does not make them identical, and the two worlds Wa and Wb also share one part in common (namely, W1) but are not identical either ; we'll say here that they overlap. Partial trans-world identity and fourdimensionalism

"The actual world"

§9. It is now clear, I think, why I chose the label "partial trans-world identity" for the present view : some distinct individuals (whole fourdimensional space-time worms) inhabiting different possible worlds share parts – they are 'partially identical', exactly as we have seen in the fission case in I.5.§5. It is not that identity (trans-world identity) is replaced by identity-at-a-time, for there is no genuine trans-world identity involved in this view; it is the B-counterpart relation that is grounded in identity-at-atime, in the idea of shared temporal parts, defended by fourdimensionalism. It is maybe a disadvantage of this view that it requires four-dimensionalism to be true. It would, one could say, be better neutral on this point. I think that in general this is right – it is always better for any theory to leave other controversial thesis open. But in this case it just seems inevitable and indeed justified, for there is a theory about persistence and it is not so surprising that it accounts for persistence through time and persistence across possible worlds in a connected way, since time plays a decisive role in the coming in existence of possible worlds. Besides, for those who believe four-dimensionalism to be true for independent reasons, the fact that it is a consequence or a requisite of the present view could even be seen as an advantage of it. The four-dimensionalist strategy will also help the B-counterpart theory to deal with the following problem. §10. Look at figure 22 again. When, in W1, I say "I" what is the denotation of this term ? Am I speaking about the individual Ia (= I1 + I2 + ...) or the individual Ib (= I1 + I3 + ...) ? Or if, in W1, I use the expression "the actual world", am I speaking about Wa or Wb ? I already noted that, due to occurrences of splits, a world-stage can be part of more than one world ; the world-stage W1 is part of the world Wa as much as it is part of

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the world Wb. Further, I proposed in §5 above that the B-counterpart theorist should endorse Lewis' indexical analysis of actuality : if, in W1, I use the expression "the actual world" I am speaking about "this world" – the world I happen to inhabit. But which one of the two worlds Wa and Wb is "this world" ? The problem here, of course, parallels the discussion of the case of fission from I.5.§5. The important point to remember here is that the two worlds Wa and Wb were, at the time of utterance of "the actual world" (in W1), just one single world : when I pronounced those words, I was part of two overlapping worlds at once (but only at the time when they were one) and, consequently, if by those words, I denote the world I inhabit, I am denoting all of the worlds that contain W1 as a part. But keep this in mind : I am a world-bound individual and I cannot be said to inhabit more than one world – it is I1, which is a temporal part of me (my individual-stage "at the time of utterance"), who pronounced those words and who can be said to be part of more than one world (as far as those worlds are one, before a split occurs) and who is ambiguously speaking about two worlds Wa and Wb. One could find genuinely absurd to conceive that by a singular term such as "the actual world" one can refer to more than one thing at once : but the strangeness is only rooted here in the fact that we usually never take into account the existence of genuine splits of worlds. The same holds in the case where I say "I" or "this bottle of beer on the table" in W1 – all those singular terms denote a plurality of things which have a common part exactly as Ia and Ib share I1. Hence, the word "I" uttered in W1 by I1 refers to two (or more) different individuals but only at a time when those individuals are one (before a split occurred). (This parallels, of course, the discussion of the case of Jean-Luc Picard's fission from I.5.§7.)

146 A pseudocase of trans-world identity

§11. Let us consider a last case that could seem problematic :

Wa Fig. 23

W1

W2

Wb

W3 Wc

Cyrano existed in W1 and W2 where he died. Isn't it the case then that he really existed in more than one world (namely, Wa, Wb and Wc) and was, after all, a trans-world individual despite the fact that the partial transworld identity view claims that individuals can only be world-bound ? The case is not the same here as in §10, as here we are speaking about Cyranothe-individual (the whole Cyrano) and not an individual-stage of him like Cyrano-in-W1 : we are considering here the entire collection of Cyrano's stages until the moment when, in W2, he died. Yes : he existed as part of more than one world but only at a time when all those worlds were one and so, he can be part of several worlds but stay a genuine world-bound individual (he could not, for instance, exist in W3 – only a B-counterpart of him could) and this, again, is a simple consequence of genuine splits. Advantage of Bcounterpart theory over Lcounterpart theory

§12. The partial trans-world identity view does not suffer from objections against the first straightforward trans-world identity view (see II.3.§1) and it also avoids the problem with accidental intrinsic properties raised against the second straightforward trans-world identity view (see II.3.§2), because the incompatible properties are simply had by different non-identical things. The partial trans-world identity view also seems to have an advantage over L-counterpart theory : it seems that the story of my avoided fall is really about me and not someone else in another and isolated world, and that I have good reasons to worry, or to be relieved. Remember Kripke's claim : if I say that it is possible for me to reach the summit of Mont-Blanc or to fall and die or whatever, then I say that I myself can die

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or appreciate the view, and not some L-counterpart of me who maybe resembles me but is not me in any way and is a different individual. Bcounterpart theory seems to give a better account of Kripke's claim – for there has been just one person who, for instance, could have had an accident and this person is me ; at the critical moment when I nearly fell down, the world split into (at least) two possible worlds – in one of them I survived but not in the other. The relief I'm experiencing is therefore entirely justified because I rightly feel that it was me who could have fallen and who could have been engaged in a different 'branch', in a different world where I would die. Of course my B-counterpart who wasn't as lucky is, after the accident, a completely different person but he was identical to me before the split occurred. The word "me" when I use it after the avoided accident denotes me (the individual who is writing now) and "me" pronounced by my unlucky B-counterpart just before his death denotes him (and so, denotes another individual) but I am identical to the person I was before the accident, in the sense of trans-time identity within a single world provided by four-dimensionalism, and so is my B-counterpart. So, there is an advantage of B-counterpart theory over L-counterpart theory. But perhaps not all worries have been dissipated : because, after all, B-counterpart theory, as well as L-counterpart theory, is a theory of worldbound individuals. Surely, B-counterparts share parts, and this is why they have good reasons to care for each other, whilst L-counterparts have no such reason at all. But it is also true that, after the accident, after the fission occurred, I have no reason any more to care for my B-counterpart resulting from this fission, since from now on, he is just someone else, and our common past does not change anything to it. Maybe the B-counterpart theorist could defend himself against this I-do-not-care claim by claiming that it is all right not to care about my B-counterpart after the accident : I enjoy a relief, because I was engaged in a branch where I had no accident, and I don't have to feel sad because someone else wasn't as lucky. As for claims like "If I did not go to high-school, I would have been happier", I think the B-counterpart theorist could, intuitively enough, claim that when I make such a claim I am imagining myself at a certain time before going to high-school, I am considering the possibilities open ahead of me, and I am concerned about them, in accordance with B-counterpart theory. So, even if some worries could perhaps persist, there really seems to be an

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advantage of B-counterpart theory over L-counterpart theory as far as the problem with caring and relief is concerned. Necessity of origin

Why I cannot be a monk from the 12th century

§13. Perhaps there is a problem rooted in the fact that all B-counterparts have the same origin. For wouldn't it sound sensible to say that it is possible that I could have been a monk living in the 12th century ? Or, simply, that I could have been born two years before I actually was ? It seems that there is an objection against B-counterpart theory, for there is no way for an individual of the 12th century to be my B-counterpart according to B-CT : if the monk existed between 1115 and 1174, then I (I myself) can by no means share any individual-stage with him – there is no world-stage in which we can be numerically identical. So, according to Bcounterpart theory, it is not possible for me to be a monk who lived before I did. In short, it seems that my origin and the moment of my origin must be necessary to me (the same holds for the origin of all possible worlds). §14. On one point, I think, B-counterpart theory is right – I believe that it is not possible for me to live in the 12th century. Let us consider the two following sentences : (i) (ii)

It is possible for me to climb Mont-Blanc. It is possible for me to be a monk living in the 12th century.

Those two cases are fundamentally different : (i) speaks about what I, the individual who is now writing, can really do or be whilst (ii) does not – it seems quite impossible to me that I could possibly be a 12th-century monk (I disregard here the possibility of being a time-traveller or the possibility of being a reincarnated monk). Of course, it is possible that there was a monk living some 850 years ago who resembled me a lot, but it simply wouldn't be me. What Lcounterpart theory says about it

§15. Is L-counterpart theory in a better position to give an account of the possibility of my being born two years before I actually was or my living in the 12th century ? I don't think so : Lewis' possible worlds are spatiotemporally disconnected so it seems impossible to make comparisons such as "this event in W1 happened before that event in W2" for there is no

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reference point. The same problem arises in the case of comparative statements about places : is it possible that I could stand two meters from the place I actually occupy ? It seems that such a statement doesn't make any sense if we accept Lewis' ontology – his worlds are distinct isolated space-times, and so to say that something in W1 is elsewhere than something in W2 is nonsensical; there is no way to speak about a reciprocal position between two individuals inhabiting two different worlds (this objection appears in Kolář (1999, p. 142-143)). So, if an account of such comparative statements (both, temporal and spatial) is wanted, Lewis is committed to accept L-counterparts of places and moments; but the Lcounterpart relation is a relation of similarity and it seems to me hard to see how a moment can resemble another – how a space-time point can resemble another. (Compare : B-counterparts of moments and places seem unproblematic, for it is easy to see that a certain place is a B-counterpart of another iff the two places have been one before a split occurred.) §16. Still, even if we agreed that the consequence of B-counterpart theory that it is not possible for me to be a monk living in the 12th century is maybe not a non-grata one, the fact remains that the B-counterpart theorist's claim of necessity of origin is a very strong one – not only could I not be a monk in the 12th century, but it is also impossible for me to be born just one year, or even one hour before I actually was, and this, I think, is really a counter-intuitive claim. So maybe the assumption should be dropped. Maybe the branching structure of possible worlds should be regarded as infinitely branching to the 'left' (backwards in time) as it is to the 'right' (towards the future). But there was a reason why I postulated a common origin for all possible worlds : to grant that they all are B-counterparts of each other (and so they are alternative ways things might have been). If the assumption of a common origin is dropped, some possible worlds would turn out to be entirely spatio-temporally and causally disconnected from others and that would simply amount to the Lewisian structure of possible worlds, and the definition of B-counterpart relation would have to be dropped, too.

On the common origin of all worlds

§17. Lewis himself rejects genuine branching because, according to him, such a view is contrary to the common sense idea that we have one single

Lewis' objection to branching

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future (see Lewis (1986a, p. 206-208)). If I wonder about what tomorrow will bring to me, then, if there is branching, this wondering seems to be nonsense; for if there are thirty-four alternative futures for me then all of them are equally mine, all of them will happen and all of them will happen to me (in the case of his static structure of possible worlds, this is not so : I have but one single future, the rest of them belong to my L-counterparts only). Reply

§18. I think the B-counterpart theorist could reply thus : I am an individual and not only an individual-stage. When I use the word "I" it denotes a complete four-dimensional person – but, in the case of the branching structure of possible worlds, ambiguously (see §10 above). But still, even if there is an individual-stage of me who is involved in the constitution of individuals having different futures, there is, for each individual, no more than one future; I stressed this point before when I insisted on the fact that an individual, as a whole four-dimensional being, cannot exist in more than one world (is a world-bound individual). So, since an individual-stage does not have a future at all (for it is just a stage which does not last for long), and since an individual exists in only one world and no more, there is no place for a plurality of futures for anyone. What there is room for in the theory, and this is, of course, highly wanted, is a plurality of possible futures. I (I myself, an individual) have many possible futures, for I have many B-counterparts which will evolve differently from me and will live a different future from mine; Lcounterpart theory with a static structure of possible worlds gives the same account : there are also many possible futures, lived by L-counterparts of actual individuals who, themselves, have one and one only.

Conclusion

§19. I think there is an advantage of the dynamical branching structure of possible worlds with B-counterpart theory over Lewis' static structure of possible worlds with an ontology of totally disconnected worlds and Lcounterpart theory based on relation of similarity. For B-counterpart theory provides us with a better account of de re modality in harmony with the commonsensical belief that if something is possible for me, then I (I myself) am involved and I have good reasons to care about it – it really is to me that things could have happened otherwise. We have seen that this

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advantage still seems to be subject to some worries and so one could say that it turns out not to be an entirely satisfactory view in the end, but I think it is better than L-counterpart theory. But there are the branching theorist's premises, and those are heavy to carry. For we have seen that the claim of necessity of a common origin for all possible worlds, and for individuals inhabiting them, is problematic; besides, it is controversial whether possible worlds (and, to start with, our world) must have a beginning instead of existing eternally and forever, in the first place. Also, it is counterintuitive to accept genuine splits of worlds and individuals 23. Further, as Lewis points out (Lewis (1986a, p. 209), the branching ontology of possible worlds seems less palatable than Lewisian modal realism, because it complicates the account of how possible worlds are unified by spatio-temporal interrelation. For Lewisian possible worlds are quite simply defined in terms of spatio-temporal relations of their parts (any x that is spatio-temporally related to any y is part of the same world as y). In the case of branching, the account is more complicated because there are spatio-temporal relations even between parts from different worlds : on figure 22, I2 and I3 have maybe a complex spatio-temporal relation because both are spatio-temporally related to I1. The branching theorist would maybe disagree, for he claims that his possible worlds are, after a fission occurred, spatio-temporally unrelated, and so, I agree with Lewis that the objection here is not deadly and consists mainly in the claim that Lewisian modal realism provides a simpler criterion for the unification of worlds. I think there are some genuine benefits of the partial trans-world identity view, but they are outweighed by the view's heavy ontological commitments.

23

It would be interesting to examine how Wheeler-Everett's interpretation of quantum mechanics could corroborate this premise. (See Everett (1957), Wheeler (1957), De Witt (1970), and De Witt (1971)).

Chapter 6, Modal perdurants §1. The last account of persistence under modal realism I am going to explore now is the theory of modal perdurants. The theory is analogous to the four-dimensionalist worm view : exactly as the four-dimensionalist claims that objects (sandglasses, Cyrano, …) are extended in time and that they exist at different times by having different temporal parts, the friend of modal perdurants claims that such objects are also extended across possible worlds and exist at different worlds by having different parts there – different modal parts or world-stages. In a bit of an exaggerated way24, such a theory could thus be called five-dimensionalism, since it takes objects to be extended across the three dimensions of space, the one dimension of time, and to also have extension across possible worlds – objects are said to be aggregates of spatial, temporal, and modal parts. Objects like Cyrano thus genuinely persist across possible worlds, as on the following figure :

A fivedimensionalist view

Cyrano Fig. 24

W1

W2

As the figure shows, there really is only one Cyrano (instead of two individuals as a counterpart theorist would say) that stretches across two different possible worlds, or, less metaphorically, that has parts in two 24

Because it is not very clear whether possible worlds could play the role of a "dimension".

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different worlds, and thus exists at two different worlds. In one of them, W1, he has a big nose, and in the other, W2, he has a small one – to speak more clearly, he has in W1 a world-stage that has a big nose and he has in W2 a world-stage that has a small one, and this is how he manages to have different modal (accidental intrinsic) properties, analogously to the way the four-dimensionalist claims that he has his temporary intrinsic properties. And as in the temporal case, no contradiction can arise here from the fact that those properties (having a big nose, and having a small nose) are incompatible, since they are had by different things – the different modal parts of Cyrano. The theory thus elegantly avoids any difficulties that led to the rejection of the straightforward trans-world identity view. Note that this theory is, in a sense, a theory of genuine trans-world identity, since the modal worm Cyrano is always, as all objects are, identical to himself. And so there is an object, Cyrano, that exists at a world W1 and that is the same object, Cyrano, that exists at a world W2 – but one must carefully take notice that the object that exists in W1, namely the W1-stage of Cyrano(-the-whole), is not identical to the object that exists in W2, namely the W2-stage of Cyrano(-the-whole). This is why, while not denying their existence, Lewis calls such trans-world objects impossible individuals, for they do not exist wholly in any possible world (Lewis (1986a, p. 211)). But this critique is not really one and is only a matter of terminology : one must simply make here a distinction between "existing at a world" and "existing (wholly) in a world" where for an object to exist at a world it is enough for it to exist only partly there. Again, such a distinction is analogous to the four-dimensionalist's claim that objects do not exist wholly at a certain time 25 but are said to exist at that time by having a temporal part there. (Of course, the analogy works only if one is a fourdimensionalist that endorses the worm view – the stage view being analogous to modal counterpart theory. Note : it seems likely that no nonfour-dimensionalist would ever endorse this five-dimensionalist theory, because the structural analogy is close and the arguments are similar – but I do not see any a priori reason that one could not be a temporal endurantist while endorsing the modal perdurants view (but then, of

25

Except instantaneous objects, like instantaneous temporal parts (if there are any).

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course, he could not call it a five-dimensionalist one, since he would lack the fourth dimension of time).) The theory of modal perdurants is less widely present in the literature than trans-world identity theories, or counterpart theory. Among others, it is discussed and rejected by Quine (1976), Lewis 26 (1968 (postscript B), 1986a), Van Inwagen (1985), Stalnaker (1994), and discussed, without being clearly endorsed or rejected, by Varzi (2001a). §2. Maybe the most obvious motivation to endorse five-dimensionalism, as unfamiliar as the view can be, is that while preserving the theoretical advantages of modal counterpart theory 27, it answers the problem that leads to its rejection. The problem with counterparts appeared because when analyzing a de re modal statement like "I could have had an accident" it turned out that such a statement was not really about me since its counterpart-theoretic paraphrase is "In W, there is a counterpart of me that has an accident" – but any counterpart of me is simply not me, and is only someone that resembles me, so I could not care less, the objection goes, for what happens to this individual in another possible world. There are many people even in our own world that resemble me, but I do not care for them having an accident in the same way I care about my having one or my possibly having one. And this just shows that counterpart theory does things wrong when explaining why I have such and such modal properties in terms of other people's having those properties. The five-dimensionalist's simple proposal here is that I am an aggregate not only of my spatial and temporal this-worldly parts but also of my other-worldly counterparts. And so it is clear that any modal de re claim about me is really, genuinely, about me – if I say that I could have had an accident then it is really a part of me, a world-stage of me the modal perdurant, that has it. Once more, this parallels what the fourdimensionalist who endorses the worm view claims about my having of 26

In Lewis (1983h), David Lewis prefers the term "modal continuant", and Achille Varzi, in Varzi (2001), chooses the terminology "modal occurrent" since entities that perdure through time are sometimes called "occurrents". I will prefer the term "modal perdurant" because it parallels the most standard terminology in the temporal case. 27 When speaking about modal counterpart theory, it is always L-counterpart theory I will have in mind from now on.

Advantage over counterpart theory

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temporary properties : I have had an accident because a past temporal part of me has it (in an atemporal sense of the verb), and I will have an accident iff one of my future temporal parts has one. And similarly, five-dimensionalism nicely answers Alvin Plantinga's worry that when I say "It is possible for me to do A" then, according to counterpart theory, I'm speaking about someone who does A but who is not me – and that's just not what I wanted to say. But if I am a modal perdurant, the sentence is about me since it speaks about what some part of me does. Thus, unlike under counterpart theory, nobody else enters in the story about my having modal properties. But perhaps not all worries have been dissipated. If one cares about caring, there seems to remain another worry for there seems to be a difference between the temporal case and the modal case as far as our self-interest is concerned – we care more about our temporal parts than we care about our modal parts, from which we are causally isolated. As Lewis puts it in (1986a, p. 219) when speaking about modal perdurants, "My this-worldly self has no tendency to make the purposes of its other-worldly counterparts 28 its own. […] There is no common purpose. The supposed trans-world person […] is not the sort of integrated self that is capable of self-interest." This is right. But it is also right in the temporal case, if one is a fourdimensionalist who endorses the worm view : for instance, unless I spend my entire life permanently desiring something, it is never the whole of me that can be said to have such and such common desire, purpose, or interest. The baby I once was and the man I am now (which are both parts of a single space-time worm – the whole of my this-worldly me) don't really have more common purposes and interests than my this-worldly self and my other-worldly parts (if I am a modal perdurant). So, at least the fourdimensionalist who wishes to embrace five-dimensionalism should not be troubled too much by this objection, I think. Certainly, there is a difference in degree : we care more about our present spatial parts than about our past or future temporal parts, and even more than about our other-worldly modal parts – but I don't see how this could 28

Lewis speaks about "counterparts" because he takes it for granted that modal perdurants are unified by the counterpart relation. On this, see II.7.§11.

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be an objection in principle to the modal perdurants view. This simply accounts for the fact that we care more about what happens now than about what is going to happen in 10 years time or about what could possibly happen – or at least, we do not care about it in the same way. But what Kripke's point shows is that we do care about what could possibly happen to us and that modal counterpart theory does not account for this properly – caring about what could possibly happen to me is not the same as caring for what happens to someone who resembles me. The modal perdurants view provides a better account of these modal concerns, in terms of what happens to me in other possible worlds. §3. Another motivation for the five-dimensionalist view is that it nicely solves a family of puzzles we have already encountered in Part I where it was showed how four-dimensionalism solves them better than the competing views. The modalized version of the puzzle from undetached parts given by Van Inwagen (see I.9) had as its target the theory of temporal parts, and so the present section could be seen as a motivation for four-dimensionalists to endorse five-dimensionalism since it helps their own business in the temporal case. The objection was the following :

The objection from undetached temporal parts

Jean-Luc Fig. 15

Jean-Luc-8

t0

t8

t10

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(i) (ii)

(iii) (iv)

(v) (vi) (vii) (viii)

Jean-Luc actually lived for 10 years. There was an 'undetached' temporal part of Jean-Luc that existed from t0 to t8 (see the figure above) – it lived for 8 years only. Let us call it Jean-Luc-8. Jean-Luc could have lived only 8 years. (There is a possible world, W, where Jean-Luc was killed at the age of 8.) So, Jean-Luc could have had the same temporal extent as Jean-Luc-8 has. (In the possible world W, Jean-Luc has the same temporal extent as Jean-Luc-8 has in the actual world.) Jean-Luc-8 could exist in W with the same temporal extent it actually has (even if Jean-Luc does not exist for more than 8 years in W). Jean-Luc and Jean-Luc-8 would occupy exactly the same space-time region in W. (In W, Jean-Luc and Jean-Luc-8 would coincide.) But coincident entities are impossible. So, there is no such thing as Jean-Luc-8 (a temporal part of JeanLuc).

The argument succeeds because it presupposes genuine straightforward trans-world identity. It is first assumed that (a)

and

Jean-Luc-W@ (Jean-Luc from the actual world) is identical to JeanLuc-W

and, similarly, that (b)

Jean-Luc-8-W@ is identical to Jean-Luc-8-W

when it is said that the actual Jean-Luc could have a shorter life and that Jean-Luc-8 could have the same length of life in another possible world (W). It is then claimed that, obviously, in the actual world (and so in W as well) (c)

Jean-Luc and Jean-Luc-8 are distinct

and, therefore, in W, there are two different things occupying the same spatio-temporal region, which is unacceptable.

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The implicit assumption of straightforward trans-world identity can easily be seen in an alternative formulation of this argument which makes explicit use of it, while not making explicit (but implicit) use of the premise that coincident entities are involved (and unpalatable), in step (vi)' below. Here is the reformulated argument : (i)' Jean-Luc actually lived for 10 years (from t0 to t10). (ii)' There is an 'undetached' temporal part of Jean-Luc that existed from t0 to t8 – it lived for 8 years only. Let us call it Jean-Luc-8. (iii)' Jean-Luc could have lived only 8 years. (There is a possible world, W, where Jean-Luc is killed at the age of 8.) (iv)' Jean-Luc-8 could exist in W with the same temporal extent it actually has. (v)' So, in the possible world W, Jean-Luc has the same temporal extent as Jean-Luc-8 (as well as the same spatial extent, material constitution, shape, colour, …). (vi)' So, in W, Jean-Luc is numerically identical to Jean-Luc-8. (vii)' Jean-Luc from the actual world is numerically identical to Jean-Luc from W. (viii)' Jean-Luc-8 from the actual world is numerically identical to JeanLuc-8 from W. (ix)' But then, by transitivity of identity, Jean-Luc from the actual world is numerically identical to Jean-Luc-8 from the actual world – which is false. (x)' So, there is no such thing as Jean-Luc-8 (a temporal part of JeanLuc). This modified formulation of the argument clearly indicates the way one can answer it (the modified objection, as well as the original one) – by rejecting the straightforward trans-world identity claim. This can be done, of course, in two ways : by embracing modal counterpart theory or the theory of modal perdurants. Provided one is willing to endorse modal counterpart theory, one could follow Sider's reply to the objection from I.9.§3. This reply is grounded in the fact that one can accept that there are different counterpart relations relativized to sortal terms holding between objects qua temporal parts and

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objects qua lizards, for instance (so there would be a lizard-counterpart relation and a temporal-part-counterpart relation). I shall now show how the five-dimensionalist can face this puzzle and it will be no surprise that the solution parallels the one given by the four-dimensionalist (see I.5.§89) while answering the non-modal version of the argument from undetached parts. The fivedimensionalist solution

§4. The picture five-dimensionalism provides of this case is the following :

Fig. 25

Jean-Luc

W@

Jean-Luc-8

t8

t0

t10 WormSMALL

WormBIG Jean-Luc

W

Jean-Luc-8

t0

t8

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In this figure, two modal perdurants are represented. They are (modal) worms stretched across two possible worlds. WormSMALL is the modal perdurant that includes Jean-Luc-8 in the actual world and Jean-Luc-8 in W – in this case, it is quite clear that those two entities are distinct objects (so (b) above is rejected) : Jean-Luc-8 in the actual world is nothing but a world-stage of WormSMALL and Jean-Luc-8 in W is just another worldstage of WormSMALL, so they are different parts of the same modal perdurant. Similarly for Jean-Luc : there is WormBIG the modal perdurant that has as two different parts Jean-Luc in the actual world and Jean-Luc in W. And again, those two parts are, quite obviously, distinct (so (a) above is rejected). And since (a) and (b) are rejected, there is no obstacle to claim that, in W, there is only one (and not two coincident) entity that is a part (a world-stage) of two non-identical modal perdurants – WormSMALL and WormBIG. In W, Jean-Luc and Jean-Luc-8 are simply one and the same object, and not two that coincide. Indeed, WormBIG includes the whole of WormSMALL as a part. So, what looked like a puzzle with coincident entities dissolves as a mere case of part-sharing 'modal worms', exactly as temporal worms can share temporal parts, as we have already seen. (And, as far as the modified version of the argument is concerned, the objection is avoided even more quickly since, if claims (a) and (b) are rejected, the premises (vii)' and (viii)' are rejected, and so the conclusion (ix)' cannot be drawn.) The objection from undetached spatial parts

§5. And of course, this solution is not only available to dissolve the puzzle concerning temporal parts (and so the solution would only be appealing for four-dimensionalists) but also for the parallel argument from I.9.§2 that concerns everybody. The argument was the following : (i)'' Jean-Luc actually has its tail. (ii)'' There is an 'undetached' spatial part of Jean-Luc that consists of all of it except its tail. Let us call it "Jean". (iii)'' Jean-Luc could lose its tail. (There is a possible world, W, where Jean-Luc is grabbed by a predator and loses its tail.) (iv)'' So, Jean-Luc could have had the same spatial extent as Jean has. (In the possible world W, Jean-Luc has the same spatial extent as Jean has in the actual world.)

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(v)'' Jean could exist in W with the same spatial extent it actually has (even if Jean-Luc does not have its tail in W). (vi)'' In W, Jean-Luc and Jean would coincide. Similarly as above, in the five-dimensionalist's picture, there would be two non-identical modal perdurants, one of them having as world-stages JeanLuc in the actual world and Jean-Luc in W, and the other having as worldstages Jean in the actual world and Jean in W. And again, it is obvious that according to such a picture the two following claims are false : (a)' (b)'

Jean-Luc-W@ (Jean-Luc from the actual world) is identical to JeanLuc-W Jean-W@ is identical to Jean-W

and so, the objection does not go through, for in W there will just be one object shared as a part by two modal perdurants instead of two different coincident entities. §6. In I.5.§2-4, I discussed the problem involving coincident entities with the case of the statue and the lump of clay it is made of. The fourdimensionalist had a nice reply to the puzzle, but there is another 'modalized' version of it that could cause him trouble – but not if he goes one step further and endorses five-dimensionalism. The puzzle appeared when one imagines that at t1 there is a lump of clay that, at t2, an artist forms into a statue. Let us say that the statue persists until some later time t3 and is then destroyed (squashed). At a time after its destruction, at t4, the statue, of course, does not exist anymore but the lump of clay still does. The lump persists from t1 to t4 : it existed at t1 in a certain (let's say cubic) form, then it was shaped into a form of a statue and, after the destruction, it was shaped again into some other form. The puzzle arises here because it seems that in the interval of time from t2 to t3, the lump of clay and the statue are one and the same object : they have the same form, the same location, they are made up of the same particles. But, if they were the same object, they should, according to the principle of Indiscernibility of Identicals, share all of their properties. But this is not the case : the lump of clay has, for instance, the property of being cubical at t1

The statue and the lump case

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that the statue has not. So, after all, the statue and the lump of clay are different objects. But then, it seems we have there two different objects that, from t2 to t3, coincide, which is to be avoided. The four-dimensionalist solution from I.5.§3 simply exploited the fact that all of the temporal parts of the two objects between t2 and t3 are numerically identical and do share all of their properties. The t2-part of the statue and the t2-part of the lump, for instance, do not have any properties like "being cubic at t1" and "not being cubic at t1" since none of these objects exists at any other time than t2. And so, the solution goes, between t2 and t3, there is only one object (that is shared as a part by two space-time worms). But such a solution is probably not entirely satisfactory because even if we accept that the statue and the lump between t2 and t3 do not have any different historical properties, they do have different modal properties. For instance, at any time in the interval from t2 to t3, the lump could have survived squashing, but the statue could not. So, after all, there is a reason to believe that, even in the crucial interval of time, there are two different objects (because they have different modal properties), and that would lead us back again to coincident entities. It is good enough that fourdimensionalism dissolves the puzzle as far as historical (temporal) properties are concerned, but it does not help if modal properties are involved. But it is no trouble for the five-dimensionalist to make his way out of this puzzle, using the same strategy as for the puzzles above. For there really is not more than one object between t2 and t3. And how can this allegedly one object manage to have different modal properties ? Simply because it is part of two (or even more) modal perdurants, simply because it is a part of several objects extended across possible worlds and that one of those objects, a statue-worm, does not survive squashing in some possible world, while the other, a lump-worm, does. Again, one could use the fourdimensionalist strategy to claim by analogy that the W@-part of the modal perdurant that is the statue and the W@-part of the modal perdurant that is the lump of clay do have all of their intrinsic properties in common – it is only one object. The two modal perdurants simply share it as one of their this-worldly parts.

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§7. It is worth noticing that one can also deal with this puzzle by the means of modal counterpart theory (as with the two previous puzzles as well, as I have mentioned (see above and I.9.§3)). As Lewis (2003) claims, there is a multiplicity of counterpart relations that hold between the one and only one object that is there in the actual world between t2 and t3, namely the statue-lump, and other-worldly objects, its counterparts. So the this-worldly statue-lump has a counterpart in some possible world that is something that survives squashing "under the counterpart relation that is called to mind when we describe [statue-lump] as a lump, but not under the different counterpart relation that is called to mind when we describe the very same thing as a statue" (Lewis (2003)). (Note that such a view makes thus the counterpart relation to be relative to some sortal terms.) It is no surprise that when five-dimensionalism can help, counterpart theory is also of good use, for remember that as I have introduced them, modal perdurants are just aggregates of modal counterparts. What the counterpart theorist takes to be different objects existing in different possible worlds, the friend of modal perdurants sees as one big object stretched out across different possible worlds, by having modal parts there. Indeed, Lewis himself claims that the theory of modal perdurants is just an equivalent reformulation of counterpart theory (see below §10). But first, let us examine an objection David Lewis raises against modal perdurants with respect to the puzzles I have just discussed.

Counterpart theory and this puzzle

§8. In Lewis (1986a, p. 218-219) and Lewis (1968 (postscript B), p. 41), he raises an objection to modal perdurants based on the discussion of some problem cases, like the case of fission (see I.5.§5-7 and I.7.§3). Remember there was a problem about counting : if Jean-Luc Piccard undergoes a fission that makes two of him, how many people were there before the fission occurred ? According to Lewis, anything we say here will sound awkward and counter-intuitive. I was inclined to say (see I.7.§3) that, following four-dimensionalism, in such a case, there is metaphysically only one pre-fission individual Jean-Luc, but of course, he as the prefission temporal part we're talking about is part of two space-time worms that share this part. So even before the fission, and even if there is only one individual, it makes sense to speak about two individuals here. It is awkward, perhaps (not that much, as I have argued), but this is perfectly

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understandable – after all, none of us usually takes into account such rare and bizarre phenomena as fissions of people. So a bit of counterintuitiveness is to be expected. But here comes Lewis' objection, in the case of modality, where we'll have to say pretty similar things if we want to endorse modal perdurants, those 'pathological' cases are everywhere – they are much more numerous than the rare or fictional cases involved in thought experiments like the one above. Take simply the case of Jean-Luc and Jean-Luc-8 from §4 above. It is a modal analogue of the temporal case of fission since there also are two modal perdurants that share one W-part. And so we'll have to ask the same question as before : how many lizards are there in W ? And presumably we'll give the same reply as before : there is, of course, metaphysically only one, but it makes sense to speak of it sometimes as two because it is part of two or more modal perdurants – indeed, it is likely that it is part of an infinity of those. But even if this is perhaps a semantically and metaphysically satisfactory view, it is very awkward and counter-intuitive : I, the person who is writing now, am present here, in my office, but at the same time, I am part of many modal perdurants who are also present here, in a derivative way. There is nothing to object here really, but it is certainly a strange view – and that's why Lewis recommends to accept the existence of such modal perdurants but to reject that we, ordinary people and ordinary objects, are such things. In the temporal case, he claims, we'll be able to defend such views, even though they are quite bizarre, because the puzzles involved are only fictions of philosophers or rare phenomena. But because modality involves such cases everywhere, the view is unbearable in the modal case. Reply

§9. In response, I have two things to say. First a remark about intuitiveness : as I have argued in the temporal case, things are not as counter-intuitive as Lewis puts it (see I.7.§3). Besides, in everyday life, we are mostly interested by what actually happens to us and to actual objects, and so we can happily ignore all the modal perdurants we are part of (thus, usually, "a is F" means "the actual world-stage of a is F", just like if one is a four-dimensionalist, it often means "the present temporal part of the actual world-stage of a is F").

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Second, as Sider also points out (Sider (1996, p. 14-15)), there is no reason why frequency of puzzle cases would matter in their resolution. If one is happy with a solution of a puzzle case, be it fictional or rare, then why wouldn't one be happy with the same solution even in actual and frequent cases ? If a method works, then it works no matter how frequently we must use it. §10. There is another critique that Lewis addresses to the theory of modal perdurants. The critique is that it just does not provide us with anything new and compelling. In Lewis (1968 (postscript B), p. 41), he says : "I have no objection to the theory of modal [perdurants]. It is an equivalent reformulation of counterpart theory, so it is just as right as counterpart theory itself. It does not offend against Postulate 2, which merely prohibited individuals from being wholly in more than one world 29 ." Remember that as they were introduced, modal perdurants are aggregates of modal counterparts, and so this is why, I think, Lewis claims that this is no new theory but just another reformulation of counterpart theory. But this is not true. As we have seen, ordinary individuals have parts in several worlds according to the theory of modal perdurants, but not so according to counterpart theory. Also, ordinary names like "Cyrano" refer on this view to modal perdurants, but not so according to counterpart theory where they refer to entirely actual individuals – for instance, to what the friend of modal perdurants calls the actual part of the modal perdurant "Cyrano". Later, in Lewis (1986a, p. 217), he weakens his equivalence claim between the two theories, and acknowledges that, while there is no metaphysical difference between the two theories (there is no disagreement on what there is in reality's stock), there is an important semantic disagreement, mainly as to what entities are properly called "Cyrano", "lizard", and so on. But there also is another difference that was brought out by Achille Varzi (2001a). The difference concerns the way the two theories handle indeterminacy. Let us think of modal sentences like the following : (i) Cyrano could have been a green pet lizard.

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For the Postulate 2, see Lewis (1968, p. 111) : Nothing is in two worlds.

Is the theory of modal perdurants equivalent to counterpart theory ?

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Maybe we are not sure whether this sentence is true or not – or simply just suppose that its truth-value is indeterminate. Counterpart theory will handle the indeterminacy of such statements as a semantic or pragmatic one since the counterpart relation is a relation of similarity, and similarity is vague, so it can be a vague matter whether such and such thing is similar enough to Cyrano to be his counterpart or not (is the other-worldly lizard similar enough to Cyrano ? similar in what respects ?). Certainly, there is no ontological vagueness here, which speaks in favour of counterpart theory. But still, a worry remains. As Varzi says, the counterpart relation is a primitive of the theory, and it is no good for any theory to have a vague primitive – it means that the theory itself is vague ("a theory built around a vague predicate" (Varzi (2001a, p. 14))), and this can be seen as a serious objection. But if we take the name "Cyrano" to denote the trans-world modal worm instead of the actual part (counterpart) of him, things turn out differently. Statements like (i) will turn out to be indeterminate simply because the singular term "Cyrano" is indeterminate – it is indeterminate which modal perdurant is referred to by it. Cyrano-in-the-actual-world is a part of many modal perdurants, and if (i) is indeterminate, it is just because some of the candidates to be the referents of "Cyrano" contain other-worldly parts that are green pet lizards and some do not. As Varzi puts it, "a term is indeterminate insofar as there appear to be many ways of assigning it a referent, all of them compatible with the way the term is used" (Varzi (2001a, p. 14-15)). So, depending on the referent of "Cyrano", (i) will turn out to be true or false, and it is indeterminate because in our case some admissible referents of "Cyrano" have as part a green lizard, and others do not. This is not always the case, of course, since in some cases the statement turns out to be true under all admissible disambiguations of "Cyrano", like in the non-modal claim (ii) Cyrano has a big nose. So, in the case of the theory of modal perdurants, indeterminacy is also dealt with as semantic, and not ontological, vagueness but furthermore, it does not make the theory vague – it is a simple case of semantic vagueness like many others. The source of vagueness in the theory of modal

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perdurants is not the same as in counterpart theory for the former case is just a case of semantic indecision, while the latter is a case of a theory that contains a vague concept as a primitive. As Varzi points out, "Cyrano" is, under the theory of modal perdurants, modally vague, exactly as "MontBlanc" is spatially (and temporally) vague – because which candidate with such and such spatial and temporal boundaries is to be taken as the referent of "Mont-Blanc" was never defined precisely enough by our linguistic practices. If one wanted, according to Varzi, to 'precisify' the name "Cyrano", under the theory of modal perdurants, one would simply have to make a semantic decision – but not so under counterpart theory, since here it would be necessary to clarify the concept of a counterpart. So, if this is right, it is not true that counterpart theory and the theory of modal perdurants are equivalent. (Besides, the theory of modal perdurants has perhaps an advantage here over counterpart theory, if one prefers semantic indecision to theoretical vagueness). §11. The preceding discussion clearly suggests the problem of how the different world-stages, or modal parts, of a single modal perdurant are unified to make up a whole. The question is : what's the 'glue' that makes them stick together ? Traditionally, in the case of four-dimensionalism there are three 'glues' that make the space-time worms stick together : (a) causality (b) resemblance (c) spatio-temporal contiguity I say these are the traditional glues but in fact many four-dimensionalists would probably not endorse at least one of its components. This is the case of four-dimensionalists who endorse the principle of unrestricted mereological composition and who claim, in short, that any mereological sum of anything is a space-time worm. For instance, there is a space-time worm made up of my sandglass today, Cyrano's nose on the 9th of February 2003, and all of the tropical fish of the 19th century – and nothing forbids that we name such a worm "Bernard" and refer to it by this name, and quantify over it, like we quantify over 'ordinary' individuals like Cyrano, my computer or any particular fish. If we accept such individuals in our

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ontology, then it is clear that they do not seem to satisfy any of the three components of the traditional glue, or only partially. So this could lead to a first strategy for the five-dimensionalist : he could accept the very same principle of unrestricted composition, and simply claim that there is no specific glue – any individual composed of any components is as good as any other (as real and existent as any other). The internal glue that unifies a modal perdurant simply needs not have any ontological force. But while such a view is probably the best a five-dimensionalist can hold, it is likely that it would not sound very satisfactory to many philosophers – for such individuals, even if they exist, are not the interesting ones. The interesting individuals are computers, fish, lizards, Cyrano, David Lewis, and so on – and the reason they are interesting is precisely because they seem to stick together and stand out from their environment. We have seen in I.8.§7 that the problem of how the space-time worms from the actual world are unified is a genuine one, but is not only the four-dimensionalist's – whatever trans-time identity and individuation conditions the endurantist chooses, it will also be available to the four-dimensionalist as the 'glue' that makes the successive temporal parts of familiar objects stick together – but those conditions are not easy to determine. For instance, condition (c) seems to be a reasonable one, until one notices that on the atomic level all of the 'ordinary' individuals that 'stick together' are fairly scattered and are nothing but a huge amount of particles with a lot of space in between (if this simplified picture motivated by physics is right). And in the case of modality, it is clear that (a) is not available either. So it seems that we only have (b) to unify the modal perdurants, if we want them to be the 'interesting' ones. But (b) alone just turns out to be the counterpart relation – and this is why modal perdurants were from the beginning introduced as aggregates of modal counterparts. Maybe this really is satisfactory – after all it serves counterpart theory well, while, as we have seen, it does not make the theory of modal perdurants equivalent to it, and there are some genuine advantages to the modal perdurant's view. But is there not some better glue one could find ? Haecceitism

§12. One way to glue together the modal parts of a single 'interesting' modal perdurant could be to embrace haecceitism. This notion was introduced and defined by David Kaplan as follows : "The doctrine that

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holds that it makes sense to ask – without reference to common attributes and behaviour – whether this is the same individual in another possible world, that individuals can be extended in logical space (i.e., through possible worlds) in much the way we commonly regard them as being extended in physical space and time, and that a common 'thisness' may underlie extreme dissimilarity or distinct thisnesses may underline great resemblance, I call haecceitism" (Kaplan (1975, p. 217)). In this excerpt, I take it so that Kaplan means by "thisness" more or less what Alvin Plantinga means by the notion of individual essence. An individual essence, for Plantinga, is a property that an individual has, that is an essential property of him, and that he is the only one to have (quantifiers unrestricted). And a property is said to be an essential one to an individual if and only if it is not possible for him to exist and not exemplify this property. So here we are with a notion of a property, and of individual essence, or thisness, that makes one individual to be this individual and not some other. And, most importantly, this property is neither equivalent nor supervenient on any qualitative or other properties of the individual that has it – in particular a thisness is not supervenient on similarity. And so, here we have a simple solution to our trouble : a thisness of a modal perdurant that is extended across possible worlds just is the glue that makes him stick together – this allows us to say that in different possible worlds this individual and that individual are just modal parts of the very same trans-world worm. Cyrano from W@ will then be said to be part of the same modal perdurant than Cyrano from W1 is, if and only if they both possess the haecceitist property that we could call "Cyraneity". And the reason why a pink fire-breathing dragon from W2 is not admissible as a modal part of the same modal perdurant is simply that it does not possess "Cyraneity". Now, this solution to the 'glue problem' sounds very nice, but unfortunately I think it does not help us at all. Our original worry was : what makes the different modal parts of a single modal perdurant stick together ? Their thisness, is the answer. But now we have a new worry : in virtue of what do the different modal parts of a single modal perdurant possess this thisness (and not some other) ? In virtue of nothing, the answer would go (I guess), you are asking a silly question – any individual has the thisness he has simply because he is the individual he is; remember that it was clearly

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said that having such and such thisness does not supervene on the having of any other properties, so when you ask in virtue of what a thisness is exemplified by some individual, you are in fact asking in virtue of what his other properties, he has the thisness – but that's not the way thisnesses are distributed among individuals, you did not pay attention to what was said. The main problem with such a position is that it is a genuinely magical one. Why is this and that the same individual (the modal parts of a single individual) ? Because it is, period – says the friend of haecceities. I do not take this to be a bad solution to the problem, I just take it to be an absence of solution that creates an unnecessary mystery and posits obscure properties such as thisnesses. Our original problem was how to discriminate the 'interesting' modal perdurants from all the others, but I just don't see at all how haecceitism could be of any help here. An unrestricted glue again

§13. So perhaps, the best glue available to the five-dimensionalist really is the principle of unrestricted composition, already mentioned above in §11. The glue that makes stick together different world-stages of a modal perdurant is just a relation that makes only some stuff in other worlds 'accessible' for an individual from a given world30. And what this stuff is, is just determined by the constraints one chooses to apply to this relation : for instance, it is not possible for Cyrano to be a pink fire-breathing dragon under some definable constraints (perhaps, biological ones), but it is logically possible – so there are different modal perdurants that correspond to different constraints. David Lewis (see Lewis (1986a, p. 234)) uses a very similar strategy to relativize his counterpart relation, which was of good use while answering the modal objection against four-dimensionalism (see I.9.§3 and II.6.§3). According to this view, there is not only one counterpart relation but a plurality of relations – but, according to Lewis, all of them are relations of

30

In his respect, this strategy is similar to accessibility relations that hold between possible worlds. In short, an accessibility relation is a relation that holds between a world and a set of other worlds that are said to be accessible from it, i.e. that are possible alternatives of the way the world could be under some restrictive conditions – for instance physical laws, logical laws, biological laws, and so on – and this is how one gets a notion of logical, nomic, and biological possibility.

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comparative similarity, it's just that some are under such and such additional constraints, and others are under different additional constraints. But why not to say that comparative similarity is just one of the many constraints we have at hand, and so, that the counterpart relation doesn't always need to be a relation of similarity ? In search for a glue for modal perdurants, such a proposal simply amounts here to claim that first, there is an entirely unqualified relation that has no ontological force at all that unifies modal perdurants, and second, that this relation can be qualified and can be given any constraints we want it to have to pick out the 'interesting' modal perdurants and discriminate them from the unrestrictedly composed Bernard-like entities. Granted, such qualifications and constraints are strongly human-dependent and have no ontological force at all, but this is only for the good since four-dimensionalists and five-dimensionalists will typically claim that Bernard-like entities are ontologically on a par with, and are every bit as real as 'ordinary' objects like Cyrano (that seem to stick together and stand out from their environment). Besides, I do not find the idea that the way we see the world as being cut up into people, lizards, sandglasses, clouds, and so on, is a genuinely human-dependent way, and I can easily imagine there being different intelligent beings in our world that would not cut up the world (the spacetime regions filled with matter) in the same way we do, maybe because their sensorial apparatus would not be similar to ours, or for other reasons.

Chapter 7, Genuine actualism – modal fictionalism §1. In the preceding chapters, we have seen a review of different positions that are available to the modal realist as far as persistence across possible worlds is concerned. The different views provide different analysis of modal de re statements, using some kind of trans-world identity or counterpart relations. Some of those accounts fail, while others, namely the theory of modal perdurants, seem to give satisfaction. But still, very few philosophers are willing to endorse it. Why_? There are two main reasons : first, the heavy and counter-intuitive ontological commitment of the modal realist to the existence of an infinity of genuine possible worlds, and second, a persisting problem with epistemology. According to modal realism, possible worlds are spatio-temporally and causally isolated from ours, and so there is no way for us to have an epistemic access to them. And so it makes it hard, perhaps impossible, to see how we manage to have modal knowledge at all. §2. The only theory of modality that intuitively provides a good account of our modal knowledge is what can be called "genuine actualism" – the fictionalist theory. It is a genuinely actualist theory since it claims that there are no possible worlds at all, and that only the actual world and its inhabitants exist. Fictionalism about possible worlds is then designed for philosophers that acknowledge many theoretical advantages to the framework of possible worlds, but are not willing to endorse the modal realist's ontological commitment – as it is sometimes said, fictionalism is the hope to keep all the advantages without paying the cost. The basic idea is really quite simple : just take your favourite realist theory of possible worlds 31 and do as if it were true, while keeping in mind that it is false. Such a strategy was primarily proposed by Gideon Rosen (1990) – he suggests that Lewis' modal realism with counterpart theory is the most satisfactory view on the market for its explanatory power and theoretical advantages, and proposes that we should take it as the best fiction of possible worlds. The core idea is that talk about possible worlds is to be

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Realist alternatives to Lewis' modal realism will be discussed later (see II.8-11).

Modal realism, epistemology, and ontological commitment

Modal fictionalism

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treated analogously to the talk about fictional entities. For instance, the sentence (i) There is a 111 years old hobbit in Bag-End. is, of course, a false existential statement, but it is one that expresses a truth if uttered in a context of a particular fiction. More explicitly, (i) simply means (ii) In the Tolkien stories, there is a 111 years old hobbit in Bag-End. The important thing then, as Rosen proposes, is that one can rationally assert (i) or (ii) as true without being committed to believe that there really are hobbits, since they are only fictions, as well as Bag-End is. And he proposes to treat possible worlds the very same way. For instance, the sentence (iii) Cyrano32 could have a small nose. is to be understood as an elliptical expression for (iv) According to the hypothesis of the plurality of worlds, there is a possible world where Cyrano has a small nose. where the prefix "According to the hypothesis of the plurality of worlds,…" is taken to work similarly to the prefix "In the Tolkien stories,…". One can meaningfully assert what follows the prefix, without being committed to assert it outside its scope as well. In general, Rosen's proposal is that for any modal proposition P there is a non-modal paraphrase P* in the language of possible worlds such that the modal realist endorses the schema (v) 32

P ↔ P*.

Please keep in mind that I am talking here about my neighbour Cyrano, not about Edmond Rostand's fictional hero.

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This, Rosen claims, is false. But what can be accepted is the fictionalist's paraphrase (vi)

P ↔ According to the hypothesis of the plurality of worlds, P*.

More explicitly, we'll have the following biconditionals, (vii) ◊P ↔ According to the fiction of possible worlds, there is at least one world at which P is true. (viii) □P ↔ According to the fiction of possible worlds, P is true at all worlds. where the fiction of possible worlds consists of seven postulates that capture Lewis' theory of possible worlds 33 together with a list of nonmodal truths about the intrinsic character of our world. (see Rosen (1990, p. 335)).

33

The seven postulates given by Rosen (1990, p. 333) are : (1) Reality consists in a plurality of universes or 'worlds'. (2) One of these is what we ordinarily call the universe : the largest connected spatiotemporal system of which we are parts. (3) The others are things of roughly the same kind : systems of objects, many of them concrete, connected by a network of external relations like the spatio-temporal distances that connect objects in our universe. (Lewis (1986a, p. 2, 74-76)). (4) Each universe is isolated from the others; that is, particulars in distinct universes are not spatio-temporally related. (It follows that universes do not overlap; no particular inhabits two universes.) (Lewis (1986a, p. 78)). (5) The totality of universes is closed under a principle of recombination. Roughly : for any collection of objects from any number of universes, there is a single universe containing any number of duplicates of each, provided there is a spacetime large enough to hold them. (Lewis (1986a, p. 87-90)). (6) There are no arbitrary limits on the plenitude of universes. (Lewis (1986a, p. 103)). (7) Our universe is not special. That is, there is nothing remarkable about it from the point of view of the system of universes.

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The hypothesis of the plurality of worlds is thus taken as a useful fiction that one is recommended to use for many philosophical and logical purposes without endorsing it literally. Of course, there are as many varieties of modal fictionalism as there are varieties of realist theories of modality. Any such variety will inherit its realist model's advantages and drawbacks, and will be subject to the objections that apply to the chosen realist view – and will have many of its replies at hand as well. This is why it will not be necessary in this chapter to discuss all of the alternative accounts of the problem of persistence across possible worlds (trans-world identity, L-counterparts, Bcounterparts, modal perdurants, …) – for this is something that has been done in the preceding chapters – it will be quite enough to pick the best modal realist account we have encountered so far, and take it to be our favourite fiction. Rosen chose Lewis' modal realism and counterpart theory to be his fiction. But since I think that the preceding discussions showed that the theory of modal perdurants is more satisfactory than counterpart theory, I shall suppose from now on that the fiction of possible worlds that the modal fictionalist uses is the hypothesis of the plurality of worlds with modal perdurants. The purpose of this chapter is then to see what is gained, and what is lost, if one were to treat this hypothesis as a fiction and not as a literal truth. Thus, most of the objections to the modal fictionalist view will turn out to be quite general, and not specific to the theory of modal perdurants, and will easily be applied across the board of all varieties of modal fictionalism. Advantages of modal fictionalism

§3. Probably the most immediate advantage of modal fictionalism is that almost nobody would give it the 'incredulous stare' that is almost everybody's reaction when one reads Lewis' "On the plurality of worlds". But really, one often says, he cannot be serious when he wants me to believe that there is an infinity of genuine possible worlds out there ! And often I have even heard in conversation doubts about Lewis himself – does he really believe in his plurality of possible worlds ? He does. For no philosopher, as he says, should put forward a philosophical theory that he cannot himself believe in his least philosophical and most commonsensical moments (Lewis, (1986a, p. 135)). And I think that this is one of the most important reasons modal realism is so widely rejected despite its

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theoretical advantages and explanatory power. It is perhaps a very strange phenomenon that one of the most weighty reasons to reject a philosophical theory is not justified by any philosophical argument, but rather by an intuition – but still one has to deal with it. And this is exactly what modal fictionalism was designed for. At the beginning of Rosen (1990), he supposes that all of the philosophical objections to modal realism were successfully answered by David Lewis – all but one : the incredulous stare. And of course, this objection is one that modal fictionalism has no difficulties to meet successfully – there is no counter-intuitiveness in the claim that there is a fiction according to which there is a plurality of possible worlds à la Lewis. There are maybe many philosophical problems with such a theory, as we shall see below, but it certainly is the most intuitive of all theories of modality. This certainly is a weighty advantage of the view, since one of the purposes of a theory of possible worlds and an account of persistence of ordinary individuals across those worlds is to provide an analysis of ordinary de re modal statements 34 that we use in everyday language – thus, it is nice if the theory does not take us too far from what we seem to believe in everyday life. There is another, philosophical, and also quite strong argument, in favour of modal fictionalism : it seems that it is the easiest way to provide an account of modal epistemology. I have already mentioned above that genuine modal realism has a problem here since it is impossible for us to have any epistemic access to the causally and spatio-temporally isolated possible worlds. And, as we shall see later, an abstractionist strategy will not be of much help either. But there doesn't seem to be any problem as to 34

I take it to be one of the purposes of any theory of possible worlds and persistence across possible worlds discussed in this book to provide with such an analysis. If less is wanted, one could endorse a weaker, so-called "timid", version of modal fictionalism instead of a "strong" modal fictionalism I will be discussing here. Timid modal fictionalism accepts that claims about possible worlds are explained in modal terms, and thus does not provide an analysis of modality and of modal claims (which, in turn, are analysed in talk of possible worlds). Strong modal fictionalism seeks an analysis of modal discourse, and tries to provide with a reduction of modal claims to non-modal possible worlds talk (or, alternatively, to reduce all modal notions to only one (see II.7.§4)), and thus provide truth-makers for modal claims in terms of possible worlds. (For more on this distinction, see Nolan (2002), and Nolan (1997)).

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how we can have epistemic access to a fiction, since a fiction is, typically, a creation of the mind (unless one prefers an account of fictions as abstract entities here – in that case, the epistemological advantage is lost, and similar problems to the problems with abstractionism appear). This is obviously the case in situations where two people disagree on some modal issues – for instance if someone claims that my neighbour Cyrano could have been a pink fire-breathing dragon, and someone else claims that he could not; how are they going to settle their dispute ? They're certainly not going to take a telescope to see what happens in some other possible world. What they're most likely to do is to use their imagination, their reasoning capacities, and so on – in short, they're going to imagine Cyrano as a pink dragon, and see whether this is acceptable or not, and try to give some reasons. It is no surprise that imagination is a good lead to fiction, and if that's what possible worlds are, we got the goods we were looking for. Primitive modality

§4. As appealing as modal fictionalism is, it faces many serious philosophical objections. The first of them shows that it seems to miss its target, since it takes in the end modality as a primitive, and so does not provide an analysis of modal statements. Maybe some philosophers would be happy to find other useful purposes for modal fictionalism, but if an analysis of modal statements is wanted, it seems that the theory fails. The objection, raised by Rosen (1990, p. 344-349), and discussed by Nolan (2002), goes as follows. Remember the general paraphrasing schema in §2 above that the modal fictionalist gives for sentences like "Cyrano could have a small nose" : (vii) ◊P ↔ According to the fiction of possible worlds, there is at least one world at which P is true. The problem appears when one asks the modal fictionalist to say something more about the operator "According to the fiction of possible worlds, …". As Rosen points out (see Rosen (1990, p. 344)), one could broadly explain its function in (vii) by something like the following : "If the fiction of possible worlds were true, there would be a world at which P is true" or "If we suppose the fiction of possible worlds, it follows that there is a world at which P is true" or "It would be impossible for the

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fiction of possible worlds to be true without there being a world at which P is true as well". The problem is that all this makes the modal fictionalist's most fundamental operator to be a modal one. As mentioned, this would not be a problem for philosophers who do not want to use modal fictionalism to provide an analysis of modality. Also, it could satisfy those that would be happy with a reduction of all modal notions and locutions to this one only. But still, at least, one must agree that modal fictionalism loses here an important advantage that its realist model has, and that was perhaps one of the most important motivations for it. And further, one might feel, as Rosen himself does, that if one takes this operator as primitive, such a primitive is a very unpalatable and obscure one – as he puts it : "[…] this primitive just does not feel primitive. Truth relative to a story sounds like the sort of thing one ought to be able to explain, in stark contrast to more plausible primitives like negation." (Rosen (1990, p. 347)). If a reductive analysis of modality is wanted, modal fictionalism just seems to be a non-starter. §5. Another problem for modal fictionalism was also raised by Rosen himself (Rosen (1990, p. 341-344)). The weaker objection is that modal fictionalism loses, here again, an advantage that modal realism has; the stronger one claims that modal fictionalism is in deep trouble : it does not yield all of the modal truths it should. Rosen takes as an example a modal claim about the maximum size of any possible world, a claim that Lewis' modal realism contains but of which we are ignorant – according to Lewis, there is such an upper limit to the size of possible worlds, but we do not know what the size is, we only know there is one (see Lewis (1986a, p. 101-104)). Furthermore, this ignorance is not due to our ignorance of the empirical data about the actual world, so it is genuine modal ignorance. The claim is the following : (i) There might have been k non-overlapping physical objects. The modal fictionalist's paraphrase of this claim is the following. (i)' According to the fiction of possible worlds, there is at least one world containing k non-overlapping physical objects.

The incomplete -ness problem I

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The problem here is that even if we have the fictionalist's fiction of possible worlds as complete as possible – so that we have all of the postulates from the hypothesis of the plurality of worlds (see II.7.§2, footnote), and a full specification of non-modal intrinsic truths about the actual world as well – we could not specify the truth-value of (i)', and thus neither that of (i). As Rosen says, the fictionalist's fiction "is simply silent on this point" (Rosen (1990, p. 342)). So, modal fictionalism seems to lose one of the welcomed features of its realist model for in the modal realist's case, one can simply claim to be ignorant about the truth-value of (i) and (i)', but unlike in the modal fictionalist's case, this simply means that there is a truth-value we don't know. For the modal fictionalist, there are then two options : either (i) and (i)' turn out to be false, or they turn out to be truth-valueless. But unfortunately both alternatives are unpalatable. If one takes the first option, then, following the very same considerations as above, one will be forced to conclude that not only (i) (and (i)' as well) is false, but also it's negation ¬(i) It is not the case that there might have been k non-overlapping physical objects. But then, one is forced into a contradiction : ¬(i) and ¬(¬(i)). If one takes the second option, one could claim that (i) lacks truth-value, that there is a truth-value gap. And the same would hold for ¬(i). But certainly, the disjunction "(i) or ¬(i)" is true, so one must accept that a disjunction of two truth-valueless propositions is true, which is a departure from our standard understanding of such logical connectives as truthfunctional. The incomplete -ness problem II and primitive modality.

§6. Nolan (1997, p. 266-268) and Nolan (2002) show that there is another problem with incompleteness for modal fictionalism. There is presumably an infinity of possible words. There is also an infinity of modal claims that one must account for in terms of those possible words. But of course, because of our finitude, the modal fictionalist will not be able to list explicitly all of them when introducing his fiction – thus his fiction will be strongly incomplete, and will be silent on many more issues than the preceding section showed.

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Of course, the modal fictionalist has a remedy at hand : he will include in his specification of the fiction some general principles, like, for instance, the principle of recombination, that will permit him to avoid the obligation to specify explicitly all of the modal truths. The seven postulates of modal realism, the list of all non-modal intrinsic truths about the actual world, and some general principles should permit to imply every modal truth we need. But, as before, there is a problem with this remedy for the philosopher who seeks an analysis of modality, and of modal statements, for the notion of implication is a modal one, and so the modal fictionalist account would turn out to be circular. Such a philosopher would have the painful choice between abandoning his demands and expectations and embracing primitive modality, or endorsing a modal fictionalist theory that is fairly incomplete and that does not provide with all of the modal truths we were seeking. (Modal realism, by contrast, would give him entire satisfaction on those points.) §7. Another worry about incompleteness one might have if modal fictionalism were to be true concerns the so-called 'alien' properties and entities – properties and entities that are not contained in the actual world and that are not built by recombination of actual properties and actual entities. I know of no example of any such property or entity because I cannot imagine it, and this is perhaps one of their natural features, but it still seems plausible that there might be such properties or entities. However, this turns out not to be possible under the modal fictionalist's hypothesis, for the modal fictionalist's fiction contains only non-modal truths about the actual world, and the seven postulates of the plurality of worlds that include the principle of recombination (see II.7.§2, footnote, postulate 5), and so the fiction will only, at most, contain actual properties and entities and possible recombinations of those. And, maybe even this is not satisfactory, as suggested by Sider (2002, p. 42-43). Let us consider the sentence (i)

According to the fiction of possible worlds, there is a world containing pink chimpanzees.

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The fictionalist's account of the truth of (i) is precisely that it is true because of some non-modal truths that hold in the actual world and some recombination of them. Thus we have, in the actual world, some things that are chimpanzees and some things that are pink. But, as Sider suggests, none of this implies logically the existence of a world containing pink chimpanzees since it seems difficult to combine together duplicates of chimpanzees and pink things (pink t-shirts, pink lipstick, …) to generate a pink chimpanzee. (Sider then goes on suggesting that the modal fictionalist's way out of this is to patch together duplicates of things like atoms to yield pink chimpanzees, and shows that this would also lead modal fictionalism to trouble (see Sider (2002, p. 42-43)). But why is this a problem ? Why should anyone be tempted to combine lipstick and chimpanzees ? Surely, this would be a difficult matter but it does not seem at all necessary to do so, I believe. One could simply combine a duplicate of an actual chimpanzee with the property of being pink, and not with some pink object – and this would permit to generate the pink chimpanzee we were seeking. Such an account would raise the problem of the ontological status of properties, of course, but there is no a priori reason for this to be more problematic for the fictionalist than it is for the modal realist or any other theory of modality. Still, the aforementioned problem with alien entities remains genuine. Fictionalism and persistence

§8. Modal fictionalism is supposed to keep all the relevant theoretical advantages of its modal realist model used as the fiction of possible worlds, while gaining some new – lower ontological cost, and better account of modal epistemology. We have already seen that, unfortunately, this does not appear to be true – there are points of departure from modal realism, and even some new drawbacks of modal fictionalism that the original realist view did not possess. And, as mentioned earlier, modal fictionalism of course also inherits some problems raised against modal realism – the one I am going to discuss now is the famous problem about persistence of objects across possible worlds. Rosen himself embraces Lewis' modal realism and counterpart theory. Counterpart theory, as we have seen, suffers from Saul Kripke's famous objection about concern (see II.4.§2-3) – in short, our counterparts are just other people in distant and inaccessible possible worlds, so why would we care about what happens to

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them, or, to put it a bit differently, why would we care about facts about those people in the same way we care about modal facts that concern us ? For the counterpart theorist the modal fact that Cyrano might have a small nose just is the very same fact that some man in some possible world that resembles Cyrano has a small nose. And this, the objector says, is unacceptable, because it is far too revisionary about our normal concerns, about the way we feel about what might happen to us, or about some other important feelings like, as Rosen points out, regret – because regret is, broadly, the idea that had we done something differently, things would have been otherwise (better). So, such a revision would go too deep into our normal psychological patterns, our normal concerns, and our understanding of notions such as that of regret, to be acceptable. Now, the heritage : modal fictionalism à la Rosen inherits the problems of counterpart theory in a slightly different way that is unpalatable for similar reasons because "just as modal realism [with counterpart theory] strains credulity by identifying facts of vital concern with apparently indifferent facts about distant simulacra, so fictionalism may be thought to strain credulity by identifying these same facts with facts about the content of an arcane story" (Rosen (1990, p. 351)). Just as Cyrano, before his rendezvous galant, could not care less about someone else's nose in some other possible world, so he could not care less either about a fictional story about someone else's nose. Furthermore, besides the inherited problem, there is an additional worry of modal fictionalism alone : why and how would Cyrano be able to discriminate his caring, or not caring, about someone's nose in the Rosen fictional story, and someone's nose in the Tolkien fictional story_? It seems difficult to give here a non ad hoc reply (see also §9 below). One could think that the choice that I have proposed for the modal fictionalist to reject counterpart theory in favour of modal perdurants might be able to save him from trouble, exactly as it provided help for the modal realist. Unfortunately, I think it does not. The obvious reason is that the theory of modal perdurants just does not seem to be an available option for the modal fictionalist. Remember : modal perdurants are individuals that are stretched across several possible worlds, and that are composed of parts existing in each of those possible worlds, as the following figure shows.

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Cyrano Fig. 24

W2

W1

But if the possible worlds are fictional, and only the actual world is real, then there would have to be individuals that have parts that don't really exist, parts that are only fictional. The picture would then turn out to be something like the following (suppose W1 is the actual world). Cyrano Fig. 26

W1

Such a proposal parallels the (rejected) proposal from I.3.§6 that there are perduring things that have past and future temporal parts under the presentist hypothesis – so there also are objects, the temporally extended space-time worms, that have parts that don't exist. And it is no surprise to encounter this analogy here, since modal fictionalism is a genuinely actualist view (a view that claims that only the actual world exists and that

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no possible worlds really exist) that parallels the presentist view (a view that claims that only the present time exists and that no past nor future times do). I think that in the modal case objects that have non-existent parts are no more acceptable than in the temporal case, for reasons given in I.3.§6. §9. I have mentioned the problem for Cyrano that he does not seem to have a good reason to care more about some story told by Rosen rather than one by another story-teller like Tolkien. Maybe this is not quite accurate. As Nolan (2002) points out, it seems true that fictions, as creations of human beings, depend on them – what is true according to the fiction will then not be independent of human activity and, thus, will turn out to be arbitrary. And this certainly is not an acceptable position since the modal fiction is supposed to provide serious truth-makers for modal statements, at least if modal fictionalism wants to have any chances to compete with modal realism. However, the arbitrariness is perhaps not so deep : not all stories will do as candidates to the position of the fictionalist's fiction, for such a fiction has to meet some theoretical purposes and constraints (so clearly, any story like the one about Bilbo's life is out of the run), and will also be supplemented with a large list of non-modal truths about the actual world. But still, the constraints that the fiction should obey being difficult to state, many points will be left undetermined – so, there will always be some place for manoeuvres and the fiction will be arbitrary to a lesser degree, depending on what some philosopher story-teller says. Furthermore, as Nolan (1997, p. 264-265) points out, all stories are made by human beings (or any other 'intelligent' species), and so are contingent in the sense that had no philosophers existed, the stories about possible worlds would not have existed, and so, nothing would turn out to be possible or necessary – and, as Nolan nicely puts it, "however important one thinks philosophers might be, one should not think that philosophers are that important" (Nolan (1997, p. 265)). It seems then hard to see how modal fictionalism can provide objective mind-independent modal truths. (The one way he could take to achieve this result, namely by taking his fiction to be an abstract entity existing independently of human minds, is to be discussed in II.7.§12 below. It will be remarked that such a strategy

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would put the fictionalist in a position where he will have to face new competitors, namely the so-called abstractionist or actualist theories of modality, that would perhaps do better than modal fictionalism, if abstract possible worlds, or abstract stories about possible worlds, were accepted.) A plurality of worlds for the fictionalist ?

§10. There is a technical objection to modal fictionalism raised by Brock (1993) and, independently, by Rosen (1993) that, if successful, is a decisive one : it shows that modal fictionalism is self-refuting. It is the main motivation for the modal fictionalist view, and a central claim of it, that there is only one world. When speaking about possible worlds, the modal fictionalist uses his paraphrases where the assertion that there is more than one world lies within the scope of the operator (the "story prefix") "According to the fiction of possible worlds, …" that authorises the fictionalist to use the talk of possible worlds without endorsing their existence, like in the schema (i) □P ↔ According to the fiction of possible worlds, P is true at all worlds. Now, let the variable P be "There is a plurality of worlds". This, of course, is unacceptable for the modal fictionalist but it is true according to modal realism, indeed it is a central claim of the view – so, the right-hand side of (i) turns out to be true, because the fiction of possible worlds includes the hypothesis that there is a plurality of worlds. But if the right-hand side of (i) is true, and if the modal fictionalist uses this paraphrase, then it follows that the left-hand side of (i) is also true – and so, it turns out to be true that "Necessarily, there is a plurality of worlds". But then, using the axiom "□P → P", it follows that "There is a plurality of worlds". But this contradicts the modal fictionalist's claim that "There is only one world" and undermines modal fictionalism completely by showing that the view implies the existence of a plurality of worlds, and is thus self-refuting. Noonan (1994) and Rosen (1995) provide a reply to this objection. First, it must be noted that in some way modal fictionalism must be modified to face the challenge because as it stands, the conclusion of the objection seems unavoidable. Thus Noonan proposes, and Rosen endorses the proposal, that in defining the modal fictionalist's fiction one should not use

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as the modal realist's model the theory given by Lewis (1986a) but the one from Lewis (1968). What is the difference35 ? We have the sentence (ii) According to the fiction of possible worlds, at all worlds it is true that there is a plurality of worlds. If the fiction of possible worlds includes Lewis (1986a), the sentence turns out to be true because the existential quantifier is entirely unrestricted – at any world W it is true that there is a plurality of worlds because the quantifier "there is …" does not only range over things that exist in W but over all of the things there are, including things of other worlds, and all of the other worlds themselves. This was something Lewis had to introduce (that sometimes quantifiers are completely unrestricted) precisely to be able to grant his central claim – that there is a plurality of worlds. In Lewis (1968), this was not so because here the claim that at W there is a plurality of worlds meant that really in W, in one world, there are many worlds, which is false. This was so because in Lewis (1968) the existential quantifier "there is …" was restricted to things from W only. So, if the modal fictionalist chooses the older of the two Lewis' theories, (ii) will simply turn out to be false and so the claim "Necessarily, there is a plurality of worlds" will not be derivable, and, of course, the non-modal claim "There is a plurality of worlds" either, saving modal fictionalism from perdition. Thus saved, the modal fictionalist will still have to endorse the consequences of the amendment to his theory he just made. As Rosen (1995), and Divers (1999, p. 320-321) point out, the modal fictionalist who chooses to endorse Lewis (1968) as his favourite modal realist theory to construe his fiction will not only be able to deny that "There is a plurality of worlds" is true, but will also be forced to deny that "It is possible, that there is a plurality of worlds is true". Remember the paraphrase the modal fictionalist provides for possibility statements : 35

The reader is invited to consult Noonan (1994) for all technical details associated with the reply to the objection. I wish here, as Rosen also does, to give the spirit of it and simply point out how the reply goes.

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(iii) ◊P ↔ According to the fiction of possible worlds, there is at least one world at which P is true. The left-hand side of the equivalence is true if and only if the right-hand side is, of course. But the right-hand side turns out to be false, for the same reason the right-hand side of (i) is false – on the Lewis (1968) account, it is not true that at some world it is true that there is a plurality of worlds. Thus, not only the modal fictionalist claims that there is not a plurality of worlds, but he has to claim that it is an impossibility. As such, this consequence is not likely to be a problem for the modal fictionalist, but as we shall see in the next section, it will turn out to be quite important. Hale's objection

§11. So, we have seen that the modal fictionalist can escape the endorsement of his fiction as literally true, and is able to maintain that the claim that there is a plurality of worlds is false – this was, indeed, what he claimed from the beginning. Further, we have seen that the modal fictionalist has to accept that this is necessarily true. But then, Bob Hale (1995a) raises a simple, but quite compelling objection. Remember the broad explanation the modal fictionalist gives for the operator "According to the fiction of possible worlds, …" (II.7.§4) : (i) According to the fiction of possible worlds, there is at least one world at which P is true. was taken to mean something like (ii) If the fiction of possible worlds were true, there would be a world at which P is true. Take now any modal statement you want to evaluate by the means of the fictionalist's analysis, for instance, the claim (iii) Cyrano could have been the number 17.

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I take this to be an obviously false claim, if my reader does not share this conviction, he is invited to pick any modal claim that he takes to be false. The trouble is that under modal fictionalism, (iii) turns out to be true. This is so because the modal fictionalist possible worlds (ii)-like paraphrase of it is (iii)' If the fiction of possible worlds were true, there would be a world at which Cyrano is the number 17. and this claim is true simply because its antecedent is false (necessarily false), no matter what the truth-value of the consequent is, given the standard truth-table for material implication. And so, it turns out that any modal claim is, if one endorses the modal fictionalist's analysis of it, vacuously true. As a particular case, there is, I think, the further difficulty that even the claim "There could be a plurality of worlds" turns out to be true on this analysis, which generates a plain contradiction : the modal fictionalist asserted that "There is a plurality of worlds" is necessarily false, and then seems committed to the vacuous truth of its possibility 36 ! So one can push Hale's objection further and accuse modal fictionalism of being inconsistent. To face this objection, the modal fictionalist has two possibilities. The first is that he could reject the analysis of his "According to the fiction of possible worlds, …" as "If the fiction of possible worlds were true, …". Here again, he has two possibilities : he can claim that this is his primitive and that it is not to be analysed at all, or he can provide an alternative analysis. "Officially, the prefix is primitive", Rosen says (Rosen (1995, p. 70)). But it seems clear that a modal fictionalism that would employ such a primitive without giving at least an enlightenment of it, would very likely not appear compelling to most philosophers. This is why, I think, Rosen also argues for the second way to face the objection that is to reject the standard truth-table for material implication and provide another analysis

36

Let P be "There is a plurality of worlds". The modal fictionalist claims that □¬P and ◊P, but given the equivalence "◊P ↔ ¬□¬P", he then claims that □¬P & ¬□¬P.

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of counterfactual statements with false (necessarily false) antecedents. The argument is the following 37 : (a) We do in fact make pointful, discriminating uses of counterfactuals with necessarily false antecedents. (b) But we could not do so if (all) such conditionals were vacuously true, as on the standard semantical account. (c) Hence, the standard account is defective. The rationale given by Rosen (1995, p. 70) for premiss (a) is that in some cases, for instance when we use reductio ad absurdum arguments of the form "P → Q, but Q is absurd, then P must be false", we take the counterfactual statements as making sense, and we do use them meaningfully in an argument or when we try to explain some philosophical view. It is premise (b) of the argument that is a problem, according to Hale (1995b, p. 77). For why would the vacuous truth of conditionals forbid us to make pointful discriminating uses of them ? The case of the reductio, says Hale, is precisely a case where we have a counterfactual statement and we use it because we want to show that the antecedent is in fact necessarily false, but we do not do this by appealing to the fact that the counterfactual is vacuously true (because that would amount to appeal to the necessary falsehood of the antecedent, which is what we want to show). So we have a case of a counterfactual that is, on the standard semantics, vacuously true, but that we can pointfully use in our arguments. The debate here is probably not closed by these considerations. But still a conclusion can be drawn from Hale's objection : either modal fictionalism contains an unexplained and quite obscure primitive, or modal fictionalism must provide with a new semantics to replace the standard one of counterfactuals with necessarily false antecedents. Concluding remarks

§12. The purpose of this chapter devoted to modal fictionalism was to explore an alternative to modal realism – an alternative that is needed for those who'd subscribe to Rosen's claim that "the most powerful objection 37

This formulation of the argument is from Hale (1995b).

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to [modal realism] is that [it] is simply incredible. […] Now strangeness can never be a decisive objection. But I believe it must count for something. We have little use in the end for a philosophy we cannot seriously believe." (Rosen (1990, p. 337)) Certainly, Rosen is right, and his claim is in accordance with Lewis' meta-philosophical principle that no philosopher should put forward a philosophical theory that he cannot believe in his least philosophical and most commonsensical moments (see Lewis (1986a, p. 135)). The fact is just that one of them does believe in a plurality of genuine concrete possible worlds, and the other does not. And this is quite representative of the dialectical situation that one has to face here : it seems that the endorsement of modal realism with all of its theoretical advantages is just a matter of a particular philosopher's intuitions – will he be able to believe that modal realism is true or not ? While there is no decisive argument that would decide the matter, we can probably do better than simply rely on the willingness of our common sense to accept such and such metaphysical view in this case. What one has to do, I think, is to put things in a balance and see which side is heavier. (Armstrong calls this "an intellectual cost-benefit analysis" (Armstrong (1989b, p. 19).) In the balance concerning modal fictionalism, one has to put on the side of the drawbacks all of the technical and other objections mentioned in this chapter. Some of them look quite heavy like the considerations about arbitrariness from §9, the problems with incompleteness from §5-7, or accusations about primitive modality from §4, but perhaps none of them standing alone could be considered as objectively decisive. On the side of the advantages one has two important ones : a better understanding of modal epistemology, and a cheaper ontology (see §3). But what exactly does the so-called 'cheaper' fictionalist's modal ontology amount to ? This question is the one about the ontological status of the fictional objects used by modal fictionalism. It seems that there are several possibilities. Of course, the fictionalist's ontology should not include genuine concrete possible worlds. But it could still perhaps be a nominalistic view – as Nolan (2002) notes, the fictional objects could be conceived as ink-marks on pieces of paper, mental entities, states of human brains or some other concrete entities. But while such an ontology of fictions is perhaps not a priori impossible to defend, it raises immediately

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the worry that some of the objections from this chapter would perhaps simply knock it down, like the threat of incompleteness (§5-7) and arbitrariness (§9). (But note that this would not sound unpalatable to some. Nicholas Rescher (1973), for instance, holds the view that the realm of mere possibilia is mind-dependent.) The other alternative is the Platonist version of modal fictionalism – such a view claims that fictional entities are abstract objects, and that the fictionalist's possible worlds are just abstract constructions of those. This is the way Rosen takes, and claims that "a commitment to abstract objects is not nearly so weighty as the realist's commitment to possible worlds" (Rosen (1990, p. 338)). We will see in II.8.§1 that there is no obvious reason to say that this is so. For the time being, let us just note that not only would the modal fictionalist have to pay the price of abstract entities, presumably sets of abstract propositions, but he would also have to provide an account of what such abstract propositions are – an account that had better not to involve any modal notions, if one does not want to commit his theory to embrace primitive modality, or take it to be circular. (In Lewis' theory, which is what Rosen takes as part of his modal fiction, there is a non-modal account of what propositions are – they are sets of possible worlds – and so, it could seem that the modal fictionalist can happily use such an account to provide an account of what he needs. Unfortunately, as Nolan (1997, p. 269) pointed out, this will not do because possible worlds, according to modal fictionalism, do not really exist, and so propositions, if they are to be made up of them, don't exist either, and so, of course, are not available to do the job they were supposed to do.) There is also another worry for the modal fictionalist if he chooses to build his fiction with abstract entities – there are other, maybe better, theories in the run here that construe possible worlds as abstract entities, that are not fictionalist but realist about them. In fact, if the modal fictionalist chooses the Platonist strategy, it would then be hard to distinguish his theory from some of those competing views. Because defenders of such views also claim that the ontological cost of abstract entities is lower than the cost of concrete entities, and because they would reject modal fictionalism for its theoretical drawbacks, they will agree that it is not possible to have possible worlds gratuitously, as the (non-Platonist) modal fictionalist

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would maybe like, and will be ready to pay an ontological price for them, which is, according to those theorists, lower than the modal realist's. It is the purpose of the next chapter to explore this family of theories.

Chapter 8, Abstractionism-Ersatzism-Actualism §1. Ersatzism. Actualism. Moderate modal realism. Abstractionism. The theory goes by many names – in fact, there is a family of theories that provides different versions of a certain view on the ontology of possible worlds. What do these versions share ? What are the fundamental claims of such a view ? By answering these questions, I shall try to present a view of modality that should be the spokesman of the whole family, for it is not the purpose here to enter into detailed discussions and distinctions concerning this family, but rather to state its basic claims as clearly as possible in order to be able to evaluate and study in greater detail its role in the question of persistence across possible worlds. I shall not, of course, try to elaborate any new theory that would be the intersection of all the members of the family, rather I shall try to expose how the family, as a group, looks. Let us start by examining all of the labels the family was given by some authors. "Ersatz modal realism" is the label given to this family of theories by David Lewis (1986a, chap. 3). It deserves to be called a modal realist view since it does not take possible worlds and possibilia to be in any way minddependent. But it's an 'ersatz' modal realism for the simple reason that according to this view possible worlds are just not worlds. Instead of a plurality of 'genuine' concrete spatio-temporal worlds, the ersatzers postulate a plurality of abstract non-spatio-temporal entities that play the theoretical role of possible worlds. (And so, avoid the commitment to a plurality of possible worlds à la Lewis.) And this is why the view is also properly called "abstractionism" (see, for instance, Van Inwagen (1986)) since it makes extensive use of abstract (i.e. non-spatio-temporal) entities, and makes them to be a central piece of modal metaphysics. So, according to this view, there really is only one world (quantifying unrestrictedly), the actual world (that is absolutely, and not relatively, actual), that contains abstract entities that play the role of possible worlds. Thus, on this view, possible worlds really are actual entities – and that's why the view is also called "actualism" by many philosophers since it is claimed here that only what is actual exists, and merely possible non-actual things don't. This claim and the claim about absolute actuality, instead of relative (indexical) actuality, is important because it allows us to avoid the

Introduction

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claim that the actual and the possible are ontologically on a par, and this accommodates better our pre-philosophical commonsensical intuitions, telling us that there is a difference in kind between what actually is the case and what could have possibly happened. (For the modal realist that has in mind Lewis' framework of possible worlds, the claim that, in the end, possible worlds are said to be actual, really sounds like a plain contradiction – but don't forget that we are on other grounds here where "possible world" does not mean more than "such and such kind of abstract actual entity" that somehow represents the way the concrete actual world would be if things were otherwise, and only plays the possible worlds theoretical role.) And finally, the view is said to be a "moderate" version of modal realism because, unlike Lewis' hard-core possible worlds theory, it does not force us to believe in a plurality (an infinity) of genuine spatio-temporal worlds, but replaces them by less costly abstract entities. This is, indeed, a reason that is often put forward and that often strongly motivates the endorsement of this view. But here I must disagree : why would abstract entities be any 'cheaper' than concrete ones ? After all, as far as any non-philosopher's common sense is concerned, he or she never even thinks of abstract entities, but naturally believes in concrete spatio-temporal things that make up the actual world. Indeed, as far as common sense is concerned, abstract entities turn out to be quite counter-intuitive things – things that do not exist in space, nor in time, that are not psychological nor mind-dependent entities. Things that are such that it is difficult, if not entirely a piece of magic, to see how we could have epistemic access to them. Things that no one would ever believe in except philosophers that introduced them for their usefulness in some areas of research, especially philosophy of mathematics. Compare to Lewisian worlds : granted, he postulates much more of them than we usually believe in (that is, only one), but if he tells us his story about a plurality of worlds that are just of the kind our world is, everybody understands what notions and entities are involved, and can easily manifest his or her disagreement or agreement with such a view – some will take it as a crazy science-fiction story, some will accept it as the truth, but everyone will understand what is going on : there is no mystery. So it

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seems (to me) that if one wants to have common sense on his side, Lewis has a very hard job to do, but the abstractionists have lost in advance. And there is no philosophical reason either to prefer abstract worlds to concrete ones on this point : why would an ontology of abstract lizards be 'cheaper' or more 'moderate' than one that postulates concrete spatiotemporal animals ? In general, there will be as many abstract possible worlds as there are concrete Lewisian worlds, so there is no reason to see moderation here. But perhaps, it is not the number of entities that is in question, but their kind – abstract possible worlds would serve a more moderate theory because, precisely, they are abstract. This, I think, is also unacceptable for there really is no reason to take abstract entities as cheaper than concrete ones. Besides, it is true that modal realism multiplies entities of one and the same kind beyond what we usually believe there to be, but abstractionism-ersatzism-actualism not only multiplies the entities, but also the kinds of entities there are. Choosing between multiplicity of things of the same kind (of a kind we commonsensically already believe in anyway) and multiplicity of ontological categories, I would certainly prefer the first. At any rate, what I want to claim here is that the label "moderate modal realism" is not justified, and should be dropped. Since the most distinctive feature of this family of theories is its use of abstract entities, I shall from now on use the label "abstractionism", to make it shorter than "abstractionism-ersatzism-actualism". §2. So, here we have a theory-schema : instead of a plurality of concrete possible worlds, let's have a plurality of actual abstract entities that play the same theoretical role. The question that arises now is – how ? How do those entities manage to play the role they are intended for ? And, in the first place, what are they ? The answer here is not simple because many different versions of abstractionism have been put forward by different philosophers that often don't agree with each other, and so we do not face here a unified army but rather a difficult-to-localise philosophical guerrilla. Typically, abstract possible worlds are states of affairs, sets of propositions, or special properties – ways things might have been. Of course, not all states of affairs will do – the state of affairs that consists in Cyrano's having a big

Abstractionism

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nose, for instance, is certainly not a possible world, nor an abstract representation of it, because it is not inclusive enough, and similarly for the set of propositions {Cyrano has a big nose}. The states of affairs and sets that can properly play the theoretical role of possible worlds must not only be consistent (to avoid that impossibilia turn out to be possible) but also maximal (to avoid being silent on certain issues). Any such abstract entity will then represent a way a complete possible world is. One of these abstract representations represents correctly, the others falsely – or, in other words, one of them is actualised (or realized, or instantiated, or obtains, depending on the version of abstractionism), the actual world. As we have already seen above, unlike in David Lewis' modal realism, actuality here is not given an indexical analysis (i.e. the actual world is just the world we inhabit), but rather actuality is an absolute property of the abstract possible world that is the only one to be actualised38. The figure below illustrates this, and pictures the abstract possible worlds as sets of propositions (sometimes called "world-stories" since one can easily imagine them as maximal and consistent abstract books that describe possible worlds).

38

This makes me wonder how we can guarantee that only one world is actualised and not two, three, or all of them. But I suppose that one of the presuppositions of the abstractionist theory is that this is simply the case.

Fig. 27

{Cyrano has a small nose., …}

represents correctly is actualised

{Cyrano has no nose., …} represents falsely

represents falsely

{Cyrano has a big nose., …}

concrete actual world

abrstract possible worlds

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In this figure, only one of the world-stories is actualised, since it includes the proposition that Cyrano has a big nose, and thus represents correctly the actual world. The other world-stories fail to represent anything correctly, and so just play the role of merely possible worlds that would represent the actual world correctly, had the actual world been different. And so, this is how the abstractionist provides a paraphrase for de dicto modal statements : (i) ◊P ↔ There is a world-story according to which P. (ii) □P ↔ According to all world-stories, P. or, alternatively, if one is not a friend of world-stories but rather takes the abstract possible worlds to be states of affairs :

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(i)' ◊P ↔ There is a maximal and consistent state of affairs that includes the state of affairs that P. (ii)' □P ↔ All maximal and consistent states of affairs include the state of affairs that P. If we call the world-stories or states of affairs "possible worlds" (keeping in mind that they are not worlds and that "possible worlds" is here just a technical term), the paraphrase for de re modal statements is the one already familiar to us : (i)'' (X is possibly F) ↔ (There is at least one world where X exists and X is F) (ii)'' (X is necessarily F) ↔ (In all worlds where X exists X is F) And more explicitly, if one sticks, for instance, to the world-stories vocabulary the paraphrase turns out to be : (i)''' (X is possibly F) ↔ (There is at least one world-story according to which X exists and X is F) (ii)''' (X is necessarily F) ↔ (According to all world-stories where X is said to exist, X is F) (And similarly for the paraphrase in terms of states of affairs.) I like to stick to this last paraphrase, because when using paraphrases like (i)'' and (ii)'' one can easily forget that when one uses the technical term "possible world" one is really talking about some abstract structures, and not about any "worlds" at all (at least if one also wants to use the term "world" to describe the spatio-temporal world we live in). And this is important for the question of persistence, for it seems obvious that the persistence conditions for individuals that are said to exist across genuine concrete worlds will be quite different from the persistence conditions for individuals that exist in one concrete world only, but exist as abstract representations in different abstract structures that describe different ways the actual world might have been. But before we turn to this question of persistence, let us shortly examine two points concerning abstractionism to

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grasp better the theory's content in the first place, and also to point out some difficulties the view has, independently of the question of persistence. §3. First, the view exhibits difficulties in the account of our knowledge of modal truths, since our epistemic access to abstract entities in general, and thus abstract possible worlds, is traditionally problematic (can you look at them to see what's going on at other worlds ? can you causally interact with them ?). And so our modal knowledge seems to remain without satisfactory explanation, unless one postulates some power of our mind to enter in contact with them. It is not that abstractionism yields any additional difficulty, but it exhibits the well-known one that concerns our epistemic access to abstract entities in general, independently of modality. §4. Second, there is the fact that such a view cannot provide an analysis of modal notions, and so, in particular, cannot provide an analysis of de re modal statements. But first of all, let us note that this will not bother a large class of abstractionists, those who think that the concept of a possible world is part of a network of inter-related modal concepts (possibility, necessity, counterfactuals,_…) that are not to be analysed in a reductive way – rather, the concept of a framework of possible worlds is seen as a central piece of the network, that allows for a better understanding of modal notions. Primitive modality will then not be something that they would take as a knock-down objection, and some would even not take it as an objection at all. In my opinion, a theory that explains some modal notions like the one involved in "It is possible that P" in terms of other modal notions like the one involved in "There is at least one abstract maximal and consistent set of propositions that contains P" lacks any real appeal, since the explanans seems to me more puzzling than the explanandum. And I am inclined to take it as a genuine drawback of any view to have primitives that involve the notions we are trying to understand. The need for primitive modality arises quite obviously in the following way. Let us first consider the view that the abstract possible worlds are consistent and maximal sets of propositions (see Adams (1974)). Of course, as we have already seen, not any set of propositions will be a

Epistemology

Primitive modality

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possible world : for instance, the set that contains the proposition "Cyrano has a big nose" and also the proposition "Cyrano has a small nose" certainly is not a possible world. That's why it is required that possible worlds should be maximal and consistent (that is, possible) sets of propositions – here it just is obvious that the definition of a possible world includes the notion of possibility, which is in turn explained in terms of possible worlds (It is possible that P ↔ There is a possible world where P is true). The very same claim about primitive modality can also be raised in the case of the other variants of abstractionism. Take Plantinga's conception of possible worlds as abstract states of affairs (Plantinga (1976)), where only one among them obtains (is realised, is actualised, …) – the actual world. To see the point differently, let us see how Plantinga himself introduces his possible worlds (I am going to add some italics where the need for primitive modality arises (some of the italics are Plantinga's own)) : "Now a possible world is a possible state of affairs. But not just any possible state of affairs is a possible world; to achieve this distinction, a state of affairs must be complete and maximal. We may explain this as follows. Let us say that a state of affairs S includes a state of affairs S* if it is not possible that S obtains and S* fails to obtain; and let us say that S precludes S* if it is not possible that both obtain. A maximal state of affairs, then, is one that for every state of affairs S, either includes or precludes S. And a possible world is a state of affairs that is both possible and maximal." (Plantinga (1976, p. 258)) Here, both the notions of consistency and maximality are clearly defined in terms of the notion of possibility, and so it is obvious that the theory does not provide a reductive analysis of modal notions (of course, this is something Plantinga expects and he endorses the view that possibility (and necessity, and other modal notions) are to be left unanalysed). §5. I hope we have now a clear picture of the family of abstractionist theories – at least clear and complete enough to turn now to the question of persistence. As in the case of modal realism, I am first going to examine the theory of trans-world identity, then counterpart theory, and finally the theory of modal perdurants – all of them, of course, under the abstractionist hypothesis.

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I shall write these chapters in such a way that they parallel the discussion of the views we have seen in II.3, 4, and 6, where the question of persistence under modal realism was discussed. The point is to see whether the question of persistence is dependent or not on the ontology of possible worlds. As we will easily see, it is, and some of the views that deserved our attention under modal realism should not be taken very seriously here – but they're still worth mentioning, I think, because by reviewing them and discussing them we will get to the interesting and defendable views.

Chapter 9, Abstractionism and trans-world identity

represents falsely

{Cyrano has no nose., …}

represents correctly is actualised

{Cyrano has a big nose., …} represents falsely

Preliminaries

Fig. 27

{Cyrano has a small nose., …}

concrete actual world

abrstract possible worlds

§1. My concrete neighbour Cyrano inhabits a concrete apartment in a concrete building in a concrete spatio-temporal world. This much, I hope, is here uncontroversial enough. And it is important, for one might ask : what exactly is the actual world according to abstractionism ? Remember the abstractionist picture :

Possible worlds are easy – there is only one thing that can play their role, namely the abstract entities that represent the actual world falsely; here, they are sets of propositions (world-stories). But the case of the actual world is more complicated – there are two things that could be taken to play its role. First, there is the concrete spatio-temporal world inhabited by things like Cyrano, myself, my pet lizard Jean-Luc, and so on. Second,

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there is the abstract world-story that represents correctly this concrete world. Until now, I have implicitly assumed that what deserves the label "the actual world" is the concrete thing. This had as a consequence that possible worlds are really not worlds, since they are of a very different kind the actual world is, and so it could perhaps be tempting to claim that the actual world is not the concrete one but rather the world-story that represents it correctly – thus, all of the worlds, both possible and actual, would be of the same kind, and could properly be called worlds – and it's just that one of them would be actualised or instantiated, but not the others. And this would have a deep consequence for the question of persistence since the question would then be one about the persistence of abstract objects from one set of propositions to another, or from one state of affairs to another, not involving concrete individuals at all. I mention this as a possibility, but it seems quite obvious that such a line of argument would be completely mislead. For of course, what any theory of modality has to account for is the fact that we (humans, lizards, computers, …) inhabit the actual world. And certainly, if we look at the abstractionist's schema, we are located in the one concrete world. A theory of persistence of (material) objects across possible worlds has then to deal with the fact that some concrete entities are said to exist in other possible worlds that are abstract. Let us now see how this could be done. The naïve picture

§2. The most straightforward way to understand trans-world identity in the case of modal realism (II.3.§1) was the following.

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Cyrano

Cyrano Fig. 16

W1

W2

Let us call this "the naïve picture" since it really is the one that springs into one's mind the most immediately if one claims that one individual is said to exist in several possible worlds. On this figure, for instance, W1 is the actual world and Cyrano exists there and has a big nose, and W2 is just another possible world where he also exists but where he has a small nose. Of course, under the abstractionist hypothesis such a picture does not gain any more credibility than under modal realism – as argued before (see II.3.§1), it is just plain false : two distinct things can never be one. Further, the problem with this picture becomes even more acute under abstractionism, for the Cyrano from W1 is a concrete person, but the Cyrano from W2 is an abstract entity, a part of some abstract state of affairs, or a certain proposition (like "Cyrano has a small nose"), and it certainly is unacceptable that any concrete individual could be numerically identical to any abstract entity, be it a proposition, a property or a state of affairs. (Also, as a consequence, the sentence "I am concrete but I could be an abstract entity" would turn out to be true.) §3. A similar worry also arises for the "trans-world identity with overlap" view. Again, let us remember the picture from II.3.§2 that such a view suggests :

Transworld identity with overlap

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Cyrano Fig. 17

?

W1

W2

This avoids the main problem of the naïve picture because, obviously, there is only one Cyrano (that can, of course, be numerically identical with himself) – it's just that he is part of several possible worlds, since worlds are said here to be able to overlap. The reason that was given to reject such a picture was that it does not seem to be able to accommodate the fact that Cyrano can have some nonnecessary intrinsic properties in some worlds that he lacks in other worlds (he has a big nose in the actual world, and a small nose in W2). (On this point, see II.3.§2.) While this objection works under modal realism it could, perhaps, be avoided if one embraces the view that possible worlds are world-stories. Let us have the world-story WS1 that is a set of propositions among which there are propositions P1 "Cyrano exists" and P2 "Cyrano has a big nose". This is the world-story that represents correctly the actual world. Let us also have the world-story WS2 that is a set of propositions among which there also is the proposition P1 (the very same abstract proposition can be a member of several sets) but not the proposition P2, instead it contains the proposition P3 "Cyrano has a small nose". The following figure illustrates this view.

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Fig. 28

"Cyrano has a big nose."

"Cyrano has a small nose."

"Cyrano exists."

WS1

WS2

And so the problem with accidental intrinsic properties is avoided because it is never said in the intersection of WS1 and WS2 that Cyrano has a big and a small nose – in fact, it is silent on whether he has a nose at all – those precisions are only given outside the intersection. The trouble here is not with accidental intrinsic properties, but with Cyrano himself : we've lost here the concrete individual ! Indeed, it seems here that we forgot the preliminary from §1 above, where it was said that Cyrano is a concrete individual and we did as if Cyrano were the abstract proposition "Cyrano exists" – which is said here to exist in several possible worlds, while Cyrano himself doesn't. Such a view simply does not seem to be very appealing for the abstractionist. §4. No philosopher, as far as I know, defends any of the two positions I just briefly sketched here. The reason why such pictures are so obviously false, and even worse here than in the case of modal realism, is simply that the one who'd like to embrace them would still want to work under the modal realist's framework, and, being a prisoner of his pictures, he'd imagine different individuals genuinely existing inside different possible worlds – and this is simply not fair to the abstractionist view, which claims that there is only one world and some abstract entities that merely represent other ways this world might have been.

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I turn now to an account of trans-world identity that has been defended by some abstractionists. Plantinga's and Van Inwagen's picture

§5. The picture defending trans-world identity à la Alvin Plantinga drawn by Peter van Inwagen (van Inwagen (1985, p. 198-202)) is like the following.

Fig. 29

Cyrano

The thing that would be Cyrano (and would, incidentally, have a small nose) if W2 obtained.

The thing that would be Cyrano (and would, incidentally, have no nose) if W3 obtained.

The first important thing to note about this picture is that, as it should be, there is only one Cyrano, only one individual. This should of course be the case (we learned our lesson from the naïve picture from §2 above) because it is clear that the only case in which an individual I1 is numerically identical to I2 is when I1 and I2 are just one and the very same individual – numerical identity just holds only in the case of self-identity. The second important thing to note is that van Inwagen's picture, slightly modified and adapted to Cyrano's case, draws Cyrano with a big nose – the nose that he in fact has in the actual world. So Cyrano – the concrete spatio-temporal object – is the one portrayed on the picture, with all of his actual properties. Again, this really seems to be as it should be since the actual Cyrano really is the only concrete individual at hand for the abstractionist. But how does this solve the problem with his accidental intrinsic properties, like the one of having a big nose, that he can lack in

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other possible worlds ? Well, on Plantinga's and van Inwagen's proposal, the different properties are certainly had by one and the same individual but this yields no worries, and no contradiction, since those properties are not incompatible. Cyrano on the figure above is portrayed with two labels that specify his properties in two different possible worlds. There is the property involved in the label "The thing that would […] have a small nose […] if W2 obtained" and the property described by the label "The thing that would […] have no nose […] if W3 obtained". And since Plantinga (1973, p. 155) claims that "in general, when P is a property and W a world, to say that x has P-in-W is simply to say that x would have had P if W had been actual" (i.e. if W had obtained) the labels just amount to attributing to Cyrano the properties of having-a-small-nose-in-W2 and having-no-nosein-W3 which are perfectly compatible and can be had by one single individual (that has a big nose) without threat of contradiction. Those properties, then, are world-indexed properties, which should remind us of the discussion of time-indexed properties that are embraced by some eternalist endurantists (see I.4.§8 and following). But while I clearly think such a strategy is to be rejected in this latter case, I think it is more acceptable in the former (modal) case. Remember that what was conceded to the endurantist eternalist as a plausible semantic solution to the problem of temporary intrinsic properties, was not accepted because of a persisting metaphysical worry, because although one could perhaps be happy with time-indexed properties, and thus avoid Lewis' objection, one cannot, in my opinion, hold a theory that claims that different objects located at different times and having different temporary intrinsic properties are numerically identical – because, as said in this section above, the only acceptable case of numerical identity is the one of self-identity. This is different in the present modal case because while endurantism is analogous to the trans-world identity view, abstractionism is not analogous to eternalism, it is rather analogous to presentism (in some ways). So, if one is an abstractionist happy with world-indexed properties (and suffers that Cyrano cannot have a small nose simpliciter but can only have-asmall-nose-in-W2), one can possess here not only a semantic solution, but one can also provide a metaphysically acceptable view, since one does not embrace pictures like figure 16 in II.9.§2 above but rather pictures like

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figure 29 – such a picture does not yield the unacceptable view of a series of several objects with different properties that are numerically identical. Primitive modality again

§6. So, if one is ready to pay the price of world-indexed properties, one can be an abstractionist and hold the trans-world identity thesis, while avoiding the objection from incompatible accidental intrinsic properties. But as a drawback, one has to accept modality as primitive. We have already seen in II.8.§4 that the need for primitive modality arises in the abstractionist's account of the nature of possible worlds, but it is not this claim I want to make again now – here, the need for primitive modality arises from the present account of persistence (trans-world identity), which is independent of the account of the nature of possible worlds. Just look at the form of the labels attached to Cyrano on figure 29 above : "The thing that would be Cyrano (and would, incidentally, have a small nose) if W2 obtained". The italics show the manifest need for modality in the explanation (and, so, not an analysis) of what it is to say de re about Cyrano that he could have a small nose. And more generally, this need for primitive modality is also obvious when one asks what it means to say that an individual In exists in a possible world W – this amounts to say, according to van Inwagen (1980a, p. 171), that if W were actual, In would exist, i.e. that it is impossible for W to be actual without In's existing. Of course, as already discussed above, primitive modality would not bother Plantinga, nor van Inwagen, and other abstractionists. But I must keep asking myself : what do I learn when I am told that "Cyrano could have a small nose" is explained in terms of "If some world had obtained, Cyrano would have had a small nose" ? In the first place, I wanted the theory to enlighten me on the modal notions involved in the former sentence, but since, again, the explanans contains, at bottom, the very same notions I was interested in understanding in the explanandum, I do really have no need for the explanans at all. Of course, it can prove to be very useful, but it does not deliver a good understanding of modality. §7. But, if one is an abstractionist ready to embrace primitive modality and accept world-indexed properties, one can – unlike under modal realism – hold the trans-world identity view. Or so it seems. The following puzzle is designed to show the contrary. (The puzzle would also apply to trans-

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world identity under modal realism but it was unnecessary to bring it out at that time, since that view was to be rejected at any rate.) §8. There is a puzzle designed to show that the trans-world identity thesis is incompatible with the view that identity is transitive. I present here an adaptation of this puzzle that is originally from Roderick Chisholm (1967). Let us take Cyrano and Roxane (another neighbour of mine that Cyrano loves secretly) as they are in the actual world (W1). Cyrano has a big nose, whilst Roxane has a medium-size nose. Now, it is of course possible for Cyrano to have a medium-size nose, and for Roxane to have a big nose – so, we have a possible world W2 which is just like W1 except for the single fact that Cyrano and Roxane exchanged one of their properties, namely, the size of their noses. Cyrano-from-W1 is, following the trans-world identity view, numerically identical to Cyrano-from-W2; and, similarly, Roxane-from-W1 is identical to Roxane-from-W2. Now, let's move on in another possible world W3 where Cyrano and Roxane exchange a further property (say, the colour of their eyes). And, as before, this slight change does not prevent Cyrano-from-W2 to be identical to Cyrano-from-W3, and similarly for Roxane. The puzzle appears if we continue this game further and consider a long series of possible worlds from W1 to Wn, where we always make a very slight exchange of properties between Cyrano and Roxane that preserves their identity – but, in the end, we can imagine that bit by bit they end up with all of their original properties exchanged. Cyrano-from-Wn has then all and only the properties of Roxane-from-W1, and Roxane-from-Wn has all and only of the properties of Cyrano-from-W1 – which, following the principle of identity of indiscernibles, entails that they are numerically identical, but they cannot be if identity is transitive (since Cyrano and Roxane in the actual world would then be identical, which is absurd). So it seems that one has either to reject the transitivity of identity and/or the principle of identity of indiscernibles, which are not very palatable options, or to reject the trans-world identity view.

Cyrano and Roxane puzzle

§9. The standard way the trans-world identity theorist defends his view against this objection exploits a view we have already encountered in II.6.§12 : haecceitism. Remember what a haecceity is : a haecceity, or a

Solution to the puzzle

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thisness, or an individual essence is a property that an individual has, that is an essential property of him, and that he is the only one to have. And a property is said to be an essential one of an individual if and only if it is not possible for him to exist and not exemplify this property 39. So here we are with a notion of a haecceistic property, or thisness, that makes one individual to be this individual and not some other. And, most importantly, this property is not equivalent nor supervenient on any qualitative or other properties that the individual has. Now, the friend of trans-world identity and haecceitism will simply claim that there are properties that Cyrano and Roxane cannot exchange : their individual essences (such properties can be simply understood as the properties of 'being identical to Cyrano' or 'having Cyraneity' and 'being identical to Roxane' or 'having Roxaneity'). So, Cyrano-from-Wn is not identical to Roxane-from-W1 but is identical to Cyrano-from-W1. End of puzzle. When facing this solution to the puzzle, I feel frustrated. Certainly, the solution works all right, but at the price of a mystery – what are these properties like "Cyraneity" ? Is it the property of being identical to Cyrano? If this is the case, the solution works only because it stipulates the solution : Cyrano-from-Wn is identical to Cyrano-from-W1 just because he is. And if it is some other property, what is it ? And how can we know it ? I think that we are left with a solution that does not really explain anything. §10. Here we are : if an abstractionist wants to hold the trans-world identity view, he can – if he's ready to pay the price. For not only has he to embrace primitive modality and a solution to Lewis' objection that appeals to world-indexed properties, but he also has to endorse haecceitism. Perhaps it is now time to have a look at alternatives to the trans-world identity view and consider that individuals are world-bound.

39

The reader will no doubt note here the use of modality in the definition of the notion of a haecceity. So, the need for primitive modality arises again.

Chapter 10, Abstractionism and counterpart theory §1. Although it suffers from Kripke's objection discussed in II.4.§2-3, counterpart theory is a powerful and simple tool to solve puzzles like the one from the end of the preceding chapter (II.9.§8). This is so because the counterpart relation, being a relation of similarity, is not an equivalence relation and, in particular, is not transitive. So, in short, while Cyranofrom-W1 will have Cyrano-from-W2 as a counterpart, he will not automatically have, for instance, Cyrano-from-W356 as a counterpart – because small changes end up at a certain point to be big changes, too big for Cyrano-from-W1 and Cyrano-from-W356 to resemble each other closely enough to be counterparts. So, like the modal realist, the abstractionist could be tempted to endorse counterpart theory, or a modified version of it, instead of trans-world identity. Let us see in this chapter how such a move would look like.

Counterpart theory, and the Cyrano and Roxane puzzle

§2. Since abstractionism provides a different ontology of possible worlds, only one being concrete and the other abstract, it seems to follow that it is likewise for the individuals that inhabit them – there is only one world-bound concrete Cyrano and other world-bound abstract Cyrano's counterparts. The first picture that is suggested here is the following.

The first picture

{Cyrano has a small nose., …}

represents correctly is actualised

{Cyrano has no nose., …} represents falsely

represents falsely

{Cyrano has a big nose., …}

concrete actual world

Fig. 30

abrstract possible worlds

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The dashed line represents the counterpart relation. So, there is the concrete actual world that contains our concrete Cyrano with a big nose. There is also the abstract representation of this world (on the figure above it is a world-story, but it could be a maximal state of affairs, or some other suitable abstract entity) that represents it correctly – but this is not the actual world; as before, it is agreed here that the actual world is the concrete thing, and not the abstract representation of it. So, here we have Cyrano. Now, as the semantics of counterpart theory goes, Cyrano has a big nose but could have a small one in virtue of having in another possible world a counterpart that has a small nose. The paraphrases for de re modal statements simply are the same as under Lewis' counterpart theory :

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(i) (X is possibly F) ↔ (X is F or at least one counterpart of X is F)40 (ii) (X is necessarily F) ↔ (X is F and all of X's counterparts are F) So, we have to find in other possible worlds things that could play the role of Cyrano's counterparts. Of course, those will not be concrete individuals with small or big noses, but some abstract entities that represent (falsely) such individuals. In the case of the world-story version of abstractionism, the suitable entities here are most likely abstract propositions like "Cyrano exists" or "Cyrano has a small nose". So, this is why the dashed line on the figure above goes, for instance, from Cyrano to the proposition "Cyrano has a small nose". And so, the counterpart relation holds between the concrete individual and an abstract proposition, or alternatively, between different abstract propositions, for of course the counterpart relation holds not only between an actual entity and some possible entities, but also between solely possible entities. Thus, the proposition "Cyrano has a small nose" in some world-story turns out to be the counterpart of the proposition "Cyrano has no nose" in some other world-story. I guess the idea is clear by now. I also guess it is clear that it is an obviously false picture. Remember what the counterpart relation is : it is a relation of similarity. But how could any concrete entity resemble any abstract entity ? This just seems absurd. Abstract entities just cannot bear the counterpart relation to concrete entities. Further, given this account, it would also turn out to be true that our fleshand-blood Cyrano could be the proposition "Cyrano has a small nose" or, perhaps, the proposition "Cyrano exists", or a set of those, from some world-story, which is certainly at least very unwelcome. §3. But the abstractionist counterpart theorist does not have to draw such a repugnant picture. Here is an attempt to propose a perhaps more sensible account of counterpart theory under abstractionism :

40

According to Lewis, it would be enough to say that (X is possibly F) ↔ (at least one counterpart of X is F) because of the postulate P6 he introduces in Lewis (1968, p. 111) : "Anything in a world is a counterpart of itself" (the counterpart relation is reflexive). My (i) is only more explicit about this. Similarly for (ii).

The second picture

{Cyrano has a small nose., …}

The thing that would be Cyrano (and would have a small nose) if this world obtained.

represents

{Cyrano has no nose., …}

represents correctly is actualised

{Cyrano has a big nose., …} represents

Fig. 31

abrstract possible worlds

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The thing that would be Cyrano (and would have no nose) if this world obtained.

On this view, the concrete Cyrano is not a counterpart of any abstract entities, rather, he is a counterpart of the things that would be him if some other world-story were actualised. (This strategy would follow, roughly, the line of Van Inwagen's defence of trans-world identity in II.9.§5 above, using explicitly modal notions (but this should not bother the abstractionist who does embrace primitive modality anyway)). Here we do not have the same problem as in the first picture. We have Cyrano with a big nose, and we have his counterpart that is the thing that would be him, and would have a small nose, if some other abstract possible world were actualised. And if this other possible world were actualised, Cyrano's counterpart would be a concrete entity – something that Cyrano could resemble,

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exactly as he can resemble other-worldly individuals in Lewis' counterpart theory under modal realism. And so, this view avoids the problem with trans-categorical similarity of entities of different ontological kinds – and also it does not yield the unwelcome conclusion that Cyrano could be an abstract entity. But, while less repugnant than the first picture, this view is also to be rejected for the simple reason that it can never be true. Take the example of the de re claim that Cyrano could have a small nose. Certainly, this modal claim is true. The counterpart theorist's paraphrase of it is "Cyrano has a small nose, or at least one counterpart of Cyrano has a small nose". But this claim is false. The first disjunct is false empirically, and the second is false 41 because there simply is no such counterpart. Of course, one could say, modally, that there would be such a counterpart if such and such possible world were actualised, but the problem is that it is impossible that both relata of any counterpart relation exist 42 – because, according to abstractionism, only one world 'at once' is actualised. David Lewis makes the same point when he proposes that perhaps we could say here, modally again, that "two ersatz [i.e. abstract] individuals are counterparts iff, necessarily, if they were both actualised, then they would describe genuine individuals which would be counterparts" (Lewis (1986a, p. 238)). But it is not possible for both of those individuals to be actualised, and so, as Lewis notes, the conditional would be vacuous. §4. So far, we have learned two lessons : first, the counterpart relation cannot be trans-categorical, and second, there simply are no entities that could be counterparts of the concrete actual Cyrano, if the first lesson is learned and abstractionism is true. So, the last picture that emerges from these considerations is the following :

41

Perhaps, some would say that it just is not true, not committing themselves by this to the claim's falsity. In that case, the objection would still be applicable since "Cyrano could have a small nose" has to turn out to be true. 42 Except in the case where an individual is a counterpart of himself, the counterpart relation being reflexive.

The third picture

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{Cyrano has a small nose., …}

represents correctly is actualised

{Cyrano has no nose., …} represents falsely

represents falsely

{Cyrano has a big nose., …}

concrete actual world

abrstract possible worlds

Fig. 32

According to this view, the counterpart relation holds between the different abstract representatives of individuals from different possible worlds. As before, they are here pictured as world-stories made up of propositions, but they could be made of states of affairs, or other abstract structures. Further, one can at least suppose that it makes sense to claim that some abstract entity can resemble some other abstract entity. This seems perhaps difficult, but it certainly is more acceptable than the claim that a concrete entity can resemble an abstract one. The explanation of how it is that two abstract entities can resemble each other will depend on what kind of abstract entities one chooses to make up possible worlds. Perhaps abstract entities can have similar internal structures. For instance, in Heller (1998), Mark Heller proposes that worlds are Quine-inspired sets of ordered pairs

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where the first member of the pair specifies a point in four-dimensional space-time and the second member specifies a property being instantiated at this point. Counterart relations are then relations between the properties, and since these are represented in Heller's view as sets of numbers, the relevant similarity involved in the counterpart relation is between these sets (which is roughly the question of how many members they have in common (see Heller (1998,p. 301-) for more details)). My aim here is not to discuss the details of Heller's view, rather I would just like here simply to suppose as charitably as possible that talking about similarity between the abstractionist's representations is plausible, and thus suppose that it should be possible (in Heller's way or other) to avoid the worry from the first picture (II.10.§2 above). Further, this third view also avoids the problem from the second picture since all of the abstract possible worlds exist ('at once') in the actual world and so both of the counterpart relation's relata exist all right (for instance, if worlds are world-stories, both the propositions "Cyrano has a big nose" and "Cyrano has a small nose" are included in two different world-stories that both actually exist). The immediate problem with this third view is that Cyrano, my concrete flesh-and-blood neighbour, who was our concern in the first place, just seems to be left forgotten. It is all very nice if, for instance, the proposition "Cyrano has a big nose" has different counterparts in different possible worlds, or if the state of affairs that represents Cyrano as having a big nose has other states of affairs as counterparts, but we do not want that things could have been otherwise for propositions or states of affairs but for individuals, namely for Cyrano. Remember that the paraphrase for the de re modal statement "Cyrano could have a small nose" is "Cyrano has a small nose or at least one counterpart of Cyrano has a small nose", but for this paraphrase to be true it is needed that Cyrano has at least one counterpart – which he has not on the present view, since only the abstract structures that represent him have counterparts, but not Cyrano himself. So what is needed in order to face this immediate worry is to modify the initial counterpart-theoretic analysis of de re modal statements in order to include Cyrano in the picture, which can be done as follows43. 43

As suggested by Mark Heller in conversation. He of course does not construct worlds as world-stories, but the general strategy is the same.

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(i)' (X is possibly F) ↔ (X is F or X is represented by a world-story and that world-story has a counterpart that represents X as being F)44 (ii)' (X is necessarily F) ↔ (X is F and X is represented by a world-story and all counterparts of that world-story represent X as being F) So, the initial worry is avoided – but only to re-arise in another form. For it's simply incredible (even much more obviously incredible than the wellknown Kripke objection to Lewisian counterpart theory !) that Cyrano's possibly having a small nose just is the existence of some abstract structure (a world-story, a set in Heller's case, or some other structure…). The initial worry was that if counterpart relations hold between abstract structures, then Cyrano, the concrete individual, was just left forgotten. The present worry is that even if the amended analysis includes now Cyrano in the game, it does so in such a way that one does not see what the abstract structures really have to do with his (modal) properties – so, he is in the game, but the abstractionist doesn't really let him really play it. Speaking specifically about Heller's account, Trenton Merricks makes the same point : "My being possibly 40 feet tall is not the same thing as there being a particular set of ordered pairs of ordered quadruples of numbers and sets of numbers" (Merricks (2003, p. 536, my italics)). Scounterpart theory

§5. So it seems that counterpart theory simply is not available for the abstractionist, if one does not want weird results to show up, and so it seems that the counterpart-theoretic move lacks, for the abstractionist, any real motivation. In fact, this is perhaps not a big surprise since counterpart theory was created by David Lewis, and was supposed to work under the modal realist's hypothesis where there can be genuine similarity between individuals from different worlds, since they are all of the same ontological kind. But one does not have to take the counterpart relation to be a relation of similarity – at least, this is what was suggested by Robert Stalnaker (1986). He takes it that the abstractionist can make use of a different counterpart relation that would not be transitive which is required in order to face 44

The first disjunct is/seems here redundant – see the footnote in §2 above.

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puzzles like the one we have seen above (Stalnaker provides four puzzles as well, see his (1986, p. 124-126)), but that would not be based on any considerations of similarity; rather his counterpart relation would have to represent our concept of trans-world identity. The latter is important because Stalnaker wants his counterpart relation to be able to face Kripke's objection – if the counterpart relation can be said to represent our concept of identity across possible worlds, then the worry that one should not care about one's other-worldly counterparts is avoided, simply because the theory will claim, for instance, that what happens to Cyrano in another non-actual possible world is really about him. Let us see how the theory works. (From now on, I will use in this section the term "L-counterpart theory" again to speak about Lewis' counterpart theory, and the term "Scounterpart theory" to speak about Stalnaker's. It must be kept in mind that the two counterpart relations involved are two different things that do not have much in common.) Like in the third picture we have seen above, the S-counterpart relation holds not between objects from the concrete actual world and something else, but rather between their abstract representatives. The picture Scounterpart theory provides is the following.

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abrstract possible worlds

Fig. 33

essence2 of Cyrano

essence3 of Cyrano

essence1 of Cyrano

W1 W2

concrete actual world

W3

In this picture, there is my concrete neighbour Cyrano who has a big nose, and who is correctly represented, for instance, by an abstract representative included in the domain of the world W1 (thus W1 is the abstract world that is actualised). This representative is an essence of Cyrano, and it is this essence that is actualised in the concrete actual world. The other essences (essence2 from W2 and essence3 from W3) are abstract representatives that also represent Cyrano (the one from the concrete actual world) but they represent him as having different properties – essence2, say, represents him as having a small nose, and essence3 as having no nose at all. This is what Stalnaker means when he claims that if another world were actualised Cyrano himself would still be there, he would still be the very same individual, but he would have instantiated a different essence.

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(It is clear that here the concept of essence is not the same as the one used by Alvin Plantinga (1973, p. 154) who uses the term "essence" thus : an essence of x is an essential (necessary) property of x and it is a property that x is the only individual to have (quantifying over all possible worlds). Stalnaker's essences are not essential properties of the individuals that have them (since they can instantiate different essences according to different possible worlds). I think that it is a very badly chosen label then, but this is only a question of terminology.) This is why Kripke's objection does not apply here : Cyrano is justified to care about what happens to him in other possible worlds because, unlike in the case of L-counterpart theory, he himself would still exist if things were otherwise (that is, if another possible world were actualised), for instance, he would have a small nose if W2 obtained because he would instantiate the essence2. The S-counterpart relation that holds between different essences, and that is represented on the figure above by the dashed line, is defined as follows: (i) x is an S-counterpart of y iff x and y represent the same (concrete) individual Thus, the S-counterpart relation is based on identity, and this is why it can be said to represent our concept of trans-world identity. But wait, we saw at the beginning that we wanted the S-counterpart relation to be more flexible than identity –namely, that we wanted to avoid the puzzles that arise from the fact that identity is transitive. But this does not seem to be the case here. As Stalnaker himself shows, the S-counterpart relation seems to inherit the transitiveness of identity : it is clear that if an essence x is an S-counterpart of an essence y, then they both represent the very same individual. And if the essence y is an S-counterpart of some other essence z, then they both represent the very same individual. But then, via transitivity of identity, x and z represent both the very same individual – and are S-counterparts. So, at this point, as Stalnaker notes, it just seems that the S-counterpart strategy has no real point. To see why S-counterpart theory can be of good use, there is an objection against trans-world identity he raises that uses precisely the transitiveness of identity : suppose it is possible for an object to be in fact two objects –

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in Cyrano's case, let's suppose that it is possible for him to be twins in another possible world. W1, let us say, is the actualised world that represents Cyrano as we know him. A world W2 would then be a world where there would be two individuals C-twin1 and C-twin2 that would both be identical to Cyrano. So the trans-world identity view claims that both Cyrano = C-twin1 and Cyrano = C-twin2 would be true. But then, via transitivity, it would turn out just as true that C-twin1 = C-twin2, which is clearly false. And so trans-world identity is in trouble, and so is the Scounterpart relation, if it works the same way, as it seems it does. We would reach the conclusion that C-twin1 is an S-counterpart of C-twin2, but we don't want that since the S-counterpart relation is supposed to represent our concept of identity. The way out of trouble is to claim, as Stalnaker does, that identity is not world-independent : "[…] all statements, including those made by possible worlds theorists when they are talking in their semantical metalanguages, are made in and from the perspective of a possible world. The idea that there is a perspective outside all possible worlds from which we can talk about them is a possibilist [modal realist] myth. […] Identity statements are not special in this regard : true identity statements are identity statements that are true at the actual world. […] Truth, from the perspective of the actual world, is absolute truth, the only real truth there is. Truth in or at other possible worlds is just what would be true if things were different. 45" (Stalnaker (1986, p. 131)) Thus, we should always remember that when we make trans-world identity statements, we always do it from the perspective of some possible world. And with such a conception of identity as world-dependent, one can answer the objection from above under S-counterpart theory as follows. First, let us see how things look from the perspective of W1.

45

"Of course, some things that an actual or possible person might say are necessary truths, and for these statements, it makes no difference whether they are evaluated from the perspective of the actual world or from the perspective of some other possible world." (Stalnaker (1986, p. 131)).

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essence of C-twin1

W2

essence of C-twin2

essence of Cyrano

W1

concrete actual world

abrstract possible worlds

Fig. 34

W1 is actualised, so we have our concrete Cyrano that is correctly represented by his essence, and that is also represented by the essences of C-twin1 and C-twin2 in W2. Those can perhaps represent him as having different properties, like having a smaller nose, but this is not important here. What is important is that in virtue of representing one and the very same individual, all of the three essences are S-counterparts. So it seems that we reached the conclusion we wanted to avoid because the Scounterpart relation is supposed to represent our concept of identity and so we would get the conclusion that the essence of C-twin1 = the essence of C-twin2. But if we recognize that the concept of identity is worlddependent, we will see that, from the point of view of W1, this is no problem : it is true that the individual that exists according to W1 (the

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concrete Cyrano) is identical to the individual that exists according to the C-twin1's essence from W2 (that is, the concrete Cyrano !), and it is also true that the individual that exists according to W1 (the concrete Cyrano) is identical to the individual that exists according to the C-twin2's essence from W2 (that is, the concrete Cyrano !). But what about the controversial claim that C-twin1 = C-twin2 ? Well, from W1's point of view, this just means that the individual that exists according to the C-twin1's essence (that is, the concrete Cyrano) is identical to the individual that exists according to the C-twin2's essence (that is, the concrete Cyrano). And, certainly, there is no problem with the statement that Cyrano = Cyrano, and so the transitivity of identity is not violated here and does not yield any unacceptable conclusion. Let us now see how things look from the perspective of W2.

abrstract possible worlds

?

essence of Cyrano

essence of C-twin2

essence of C-twin1

W2

W1 ?

concrete actual world

Fig. 35

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As the figure shows, if we take the point of view of W2 – that is, if W2 were actualised – there would be, of course, two concrete individuals instead of one, namely, the two twins. Each of them is represented by his own essence, and those two essences are not S-counterparts since they do not represent the same individual. What about the essence of Cyrano from W1 ? Well, the point is that the description "the individual that exists according to the essence of Cyrano from W1" is not really a definite description from W2's point of view, since there are two candidates to be the referents of it. The description, as Stalnaker says, is then either ambiguous, false, or truth-valueless. The argument that Cyrano = C-twin1, and Cyrano = C-twin2, therefore C-twin1 = C-twin2 then does not succeed, because, as Stalnaker notes, the fallacy here is the same as in the argument : "Russell is the author of 'Principia Mathematica', the author of 'Principia Mathematica' is Whitehead, therefore Russell is Whitehead" (Stalnaker (1986, p. 132)). So, to generalize, Stalnaker claims that if we keep in mind that identity is world-dependent, the S-counterpart relation doesn't need to be an equivalence relation (and, especially, doesn't need to be transitive). §6. We have seen that if S-counterpart theory is to be of any good use, one has to endorse the view that identity is world-dependent – absolute identity would then simply be identity at (or 'from the point of view of') the actual world. But this is perhaps not really objectionable since if one is an abstractionist there is only one world that is absolutely actual (unlike under the modal realist's account where "actual" is an indexical term). What is objectionable is, first, that there appear to be primitives that are quite puzzling : (a) the nature of the S-counterpart relation which is supposed to represent our concept of identity, but which is not identity, is not given any real explanation (it is "a primitive relation, irreducible to qualitative similarities and differences" (Stalnaker (1986, p. 131))), and (b), more importantly, there are Stalnaker's essences that are not given any definition at all46 (while they are doing a big part of the job !).

46

Stalnaker only says that his proposal "may require a non-standard theory of essences". (Stalnaker (1986, p. 130)).

Comments on Scounterpart theory

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Second, it does not seem clear to me at all how, in the general picture (see fig. 33 above), essence2 from W2, for instance, can be said to represent the concrete actual Cyrano since it really misrepresents him ! Not only is the relation of representation unexplained47, but here we have a representation that is supposed to represent an individual that has different properties than those that the representation attributes to him. In virtue of what then does any representation represent the individual that it represents and not some other individual ? Suppose that in the concrete actual world we have not only Cyrano but also Sam who is just like Cyrano except that he has a small nose. In virtue of what essence2 can it then be said to represent Cyrano and not Sam (or even some other completely different person from the actual world since difference in properties does not matter) ? There just seems to be an unappealing lack of explanation.

47

Troubles with representation ('In virtue of what and how do abstract representatives represent what they represent ?') are a general feature of abstractionism, and unexplained representation is a feature of several abstractionist theories. (see Lewis (1986a, chapter 3))

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Chapter 11, Abstractionism and modal perdurants §1. Under modal realism, as we have seen in chapter 6, it seems that the theory of modal perdurants can do better than competing views and has genuine advantages over counterpart theory and trans-world identity. Especially, it is highly efficient at answering puzzles like the one from the objection from undetached temporal and spatial parts (II.6.§3-4 and II.6.§5), or the statue and lump case (II.6.§6). It is no surprise that it can also answer our Cyrano and Roxane puzzle from II.9.§8 since the 'glue' that unifies the different world-stages of the modal perdurants will not be an equivalence relation, and so the puzzle will not appear. Indeed, for those who'd like to take the counterpart relation (that is, the L-counterpart relation) as the glue, the solution will be exactly the same as for the counterpart theorist from II.10.§1. And as far as the glue is not identity, or some other relation that is transitive and symmetric, puzzles like this one will in general be avoided. So perhaps an abstractionist could be tempted to endorse modal perdurants. No philosopher, as far as I know, goes this way – but let's see how it could work.

Modal perdurants

§2. In fact, there is no surprise. All of the pictures one can draw here will parallel the pictures from the preceding chapter on counterpart theory under abstractionism. The first, then, will go as follows (where the dashed line shows the extension of the modal perdurant).

The first picture

Cyrano {Cyrano has a small nose., …}

represents correctly is actualised

{Cyrano has no nose., …} represents falsely

represents falsely

{Cyrano has a big nose., …}

concrete actual world

Fig. 36

abrstract possible worlds

234

Remember what kind of individuals modal perdurants are : they are individuals stretched across different possible worlds, they do not exist entirely in one possible world, rather they exist at different worlds by having parts (world-stages, modal parts) there. So, as the figure above shows, Cyrano is such a 'modal worm' – the name "Cyrano" applies to the whole that has one part in the actual world and another part in another world. Also, Cyrano manages to have the property of having a big nose in the actual world in virtue of having a this-worldly part that has a big nose, and he is said, without contradiction, to have a small nose in some other possible world W in virtue of having a W-part that has a small nose.

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Now, under abstractionism, this first picture of what modal perdurants are turns out to be highly bizarre : the modal worm has some concrete parts and some abstract parts. Indeed, only those parts of modal perdurants that are located within the actual world are concrete, all others are abstract. So, modal perdurants that do not have actual parts have only abstract parts, and are wholly abstract individuals. There are two immediate problems with this picture. First, the general problem for the theory of modal perdurants, namely the problem of how to unify the different modal parts of a single modal perdurant, becomes even more acute and difficult here. For what could possibly unify ('glue together') my concrete neighbour (the actual part of Cyrano) with some abstract propositions or states of affairs to make a single individual from them ? It is clear that relations such as causality or spatio-temporal contiguity are not applicable here. And using the counterpart relation as the glue would be very unwise since we have seen in the previous chapter that counterpart theory yields here an unacceptable picture. Second, the claim that Cyrano could be an abstract individual would also turn out to be true here, which is unacceptable. Cyrano surely could be different in many ways, but I would say it is reasonable to think of him as essentially concrete. Third, some will perhaps share my intuition that creatures that are partly concrete and partly abstract (partly flesh-and-blood, and partly propositions, for instance) are of a very suspicious kind and that this is perhaps enough to reject this picture immediately. §3. The second picture that portraits modal perdurants under abstractionism and that parallels the picture from II.10.§3 is the following.

The second picture

{Cyrano has a small nose., …}

{Cyrano has no nose., …} represents

The thing that would be Cyrano (and would have a small nose) if this world obtained.

represents correctly is actualised

{Cyrano has a big nose., …} represents

Fig. 37

abrstract possible worlds

236

The thing that would be Cyrano (and would have no nose) if this world obtained.

Cyrano

Here, the problem with the first picture is avoided since Cyrano-the-modalperdurant does not have any abstract parts. Rather, he is made up here, as the figure shows, of his concrete actual part and of the thing that would be Cyrano if some other possible world obtained. And this thing, if this other possible world obtained, would be a concrete individual. (Note, however, that modal notions are required here to define what individuals are.) Analogously to the case of counterpart theory in II.10.§3, it appears here that different modal parts of a single modal perdurant can never exist 'at once' since only one world is ever actualised. Twice already, we have encountered theories that postulate individuals that have parts that do not exist. Twice, I have argued that such views should be rejected. For the first time, it was in I.3.§6 when I discussed the combination of presentism and

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perdurantism, and for the second time in II.7.§8 when I discussed the combination of fictionalism and modal perdurants. As before, I would ask : how can Cyrano have parts that do not exist ? I am convinced that the answer is : he cannot. But it is worth noting that for those who would not share my intuition and who would not be moved by the arguments given in I.3.§6, the combination of abstractionism and modal perdurants as portrayed here could seem plausible, and could be a serious option – an option that would inherit some interesting advantages, like the efficiency to solve puzzles that are very difficult to deal with if one embraces transworld identity. Such an option would also require to embrace primitive modality, but this is something an abstractionist would be ready to do anyway; and such an option would also yield even more acutely than ever before the difficult problem of how to 'glue together' the different worldstages of a modal perdurant because it really is far from obvious how, for instance, a concrete world-stage of Cyrano (the one with the big nose) can be unified into a whole with some other-worldly part that does not exist – how an existing and non-existing thing could be related, and could both be parts of Cyrano. The 'glue' would then have to stick together one existing and one non-existing thing (and, also, two non-existing things, in the case of a modal perdurant that has no parts in the actual world, for instance). §4. The third picture of modal perdurants under abstractionism that parallels the one from II.10.§4 looks like the following.

The third picture

Cyrano {Cyrano has a small nose., …}

represents correctly is actualised

{Cyrano has no nose., …} represents falsely

represents falsely

{Cyrano has a big nose., …}

concrete actual world

Fig. 38

abrstract possible worlds

238

According to this picture, modal perdurants are composed not of individuals but rather of their abstract representatives. If one takes, for instance, possible worlds to be world-stories, like on the figure above, modal perdurants would then turn out very likely to be sets of propositions from different world-stories. Thus, the problems with individuals that would be partly concrete and partly abstract are avoided since here the modal perdurants are always wholly abstract. Also, all of the abstract representatives of actual and possible individuals exist, so the problem with objects that allegedly have parts that do not exist does not arise. The problem with this view, of course, is that, as in the counterpart theory case in II.10.§4 (where I discussed this in more details), Cyrano, my flesh-

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and-blood neighbour, is simply left aside here, and since it is not him that is part of any modal perdurant, nothing could have been otherwise for him – and it is no good that one could perhaps claim that things could have been otherwise for the proposition that Cyrano actually exists and has a big nose. The theory just does not provide the goods we asked for.

Chapter 12, Bundle-bundle-bundle theory §1. In the last chapters, we have seen attempts to reconcile abstractionism with counterpart theory and the theory of modal perdurants, and we have seen that, ultimately, those attempts do not turn out to be very appealing. To sum up, take the case of modal perdurants first : it was first argued, in II.11.§2, that entities composed of actual concrete (spatio-temporal) parts and modal abstract (non-spatio-temporal) parts are highly bizarre, and that, further, while Cyrano actually is a concrete individual, it would turn out, according to this view, that he could have been an abstract individual. Then, the alternative view where modal perdurants have parts that don't exist was considered, in II.11.§3, and rejected. Finally, it was mentioned as a possibility that modal perdurants should not be made up of concrete entities from the actual world but rather solely of the abstract entities that compose the abstract representations of possible worlds – at the unacceptable cost that we can make no de re modal claims at all about the concrete individuals that interested us in the first place. In the case of modal counterpart theory, things turned out to be quite similarly unappealing : it was argued, in II.10.§2, to be a real puzzle how a concrete person could resemble an abstract representation (a set of propositions, for instance); and also that, according to this view, Cyrano, the concrete inhabitant of the actual world, could have been such an abstract entity. In II.10.§3, the view that Cyrano stands in a counterpart relation with entities that don't exist was also rejected. And, finally, the proposal that the counterpart relation holds between the abstract representations of possible worlds, but not between things from the concrete actual world and things from other possible worlds was rejected – for on such a view only the abstract representations that represent Cyrano have counterparts, but not Cyrano himself; and so, nothing could have been otherwise for him. The last solution, namely S-counterpart theory, seemed to work better – but at a price that perhaps some philosophers would not be willing to pay : identity as world-dependent, the primitiveness of the S-counterpart relation, an under-explained ontology of essences, and problems with representation (in virtue of what does any of the abstract representations

Problems with a twocategory ontology

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represent the concrete individual it represents and not some other individual ?) (see II.10.§6). What I would like to suggest now is that most of these problems come from a common source : the fact that the abstractionist's ontology is a twocategory ontology. Indeed, the view holds that there is the actual concrete world that is spatio-temporal, material, and that there are other possible worlds which are abstract non-spatio-temporal actual entities that play the possible world's theoretical role. Problems then come from the multiplicity of ontological categories and relationships between those. To make my claim clear, consider, for instance, why modal counterpart theory works much better under modal realism (which is a one-category ontology) than under abstractionism. Well, very simply, because the counterpart relation is a relation of similarity, and it is not difficult to see how a certain concrete individual can resemble another concrete individual, even if they are both located in different, but concrete, possible worlds – while it really seems prima facie bizarre to speak about similarity between a concrete Cyrano, for instance, and an abstract proposition, or set of propositions. Briefly, similarity can only hold between entities from one and the same ontological category. So, if an abstractionist is not satisfied with trans-world identity (for reasons given in II.9, and summarized in II.9.§10), which is the only option left, perhaps he should try to elaborate his theory as a one-category ontology. Look again at the abstractionist's theory-schema :

Fig. 27

{Cyrano has a small nose., …}

represents correctly is actualised

{Cyrano has no nose., …} represents falsely

represents falsely

{Cyrano has a big nose., …}

concrete actual world

abrstract possible worlds

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Let's put it quite simply : what causes trouble if one wants to use counterpart theory or modal perdurants here, is the fact that some of the counterparts, or some parts of the modal perdurants, are concrete, while some are abstract. The modal realist à la Lewis says : so, get rid of the abstract worlds. What I propose that the abstractionist could say : so, get rid of the one concrete world. This really may sound very bizarre, but in fact, similar claims have been made by some philosophers – those who hold a certain version of the bundle theory of substance, a version where individuals are said to be bundles of properties, and where properties are given an account in terms of abstract (non-spatio-temporal) universals (repeatable entities), instead of concrete tropes. Before going further, let us now examine in some more detail what the bundle theory is.

244 The bundle theory of substance

§2. The bundle theory of substance is easily understood as a reaction to its main competitor : the substance-attribute view of substance. This latter view can be put as a claim about what the relationship between an individual (a concrete particular) and its properties is : exemplification, or instantiation. On this view, there are individuals and there are their properties that are exemplified, instantiated, or simply had by the individuals who are conceived of as being the bearers of those properties. Such a bearer of properties, which has its identity independently of the properties which it bears, is often called "an underlying subject", a "substratum", or a "bare particular". This view comes in many versions, depending on what account properties and their relations to the bare particulars are given – the one that I am concerned with now is the metaphysical realist's, who claims that properties are universals (that is, repeatable entities which are capable of being entirely multiply instantiated) which are abstract (that is, non-spatio-temporal) entities. Now, it is easy to see why such a view can be taken as unpalatable by many philosophers : the substratum, the bare particular, is a quite mysterious thing. We cannot see it, nor know it in any direct way (because when we experience any individual, we always experience its properties, and not the bare individual itself) – this is the epistemological problem. Besides, we cannot give any positive characteristics of it – since, in itself, it does not have any, and so, it may seem hard to see what makes it different from other bare particulars. (How many particulars are there ? If indiscernibility is a good guide to identity, the answer seems to be : only one.) And finally, such a view seems to be ontologically uneconomical since it postulates entities that can be done without – and this is where bundle theory comes into the picture. According to bundle theorists, all the theoretical work that is done by the substance-attribute view can be done with less : no bare particulars, just the properties. Take Cyrano : he is of a certain age, he has such and such a nose, he has such and such a height, and so on. And this is all there is to know, and all there is to be Cyrano – his properties. On this view, Cyrano

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is then taken to be a bundle (a cluster, a bunch, … 48) of its properties. And the same story goes for all individuals_: they are bundles of properties which are, then, the ultimate constituents of reality. Now, I finally come to the point : the bundle theory is a one-category ontology, and, combined with the view that properties are abstract universals, it is something that could be called an extreme abstractionist theory – for if individuals are made up solely of their properties, and if properties are abstract universals, individuals turn out to be abstract as well. (I will have something to say about the counter-intuitiveness of this claim later in II.12.§14. For the time being, I dare suggest to my reader to put this particular worry aside.) So, to summarize the view : our actual world is ultimately a world of properties, individuals that inhabit the world are smaller bundles of properties, and properties are abstract universals. To understand this view better, let us now consider some traditional objections to it – and replies that can be made to them. Those replies will permit to develop and enrich the view by bringing out the question of persistence through time and possible worlds, which is indeed the purpose of the present chapter. §3. The first objection can be found, for instance, in Van Cleve (1985, p. 122) : "If a thing were a set of properties, it would be incapable of change. For a thing could change its properties only if the set identical with it could change its members, but that is impossible; no set can change its members." Taking an example of an individual that is supposed to change one of its properties over time, he adds : "[…] what we have is replacement of one individual by another, not change in the properties of one and the same individual." (Van Cleve (1985, p. 124)). The idea here is simple, and quite compelling : if an individual is identified with a bundle of properties, then if one of the properties changes, the bundle is not the same, and so, the individual who is the bundle is not the same – it simply ceased to exist, while another individual has taken its place. So, nothing can undergo change in properties. 48

I am not claiming here that all of these labels mean the same (this depends very much on the authors who used them), I just don't want to commit to either way for the time being.

The problem of change

246

This objection should sound familiar : it is exactly analogous to the objection that was raised against the four-dimensionalist in I.4.§2-4. And so, of course, it is very easy to adapt the four-dimensionalist's reply to save the case of the bundle theory49. The reply goes as follows. Granted, if one property of a bundle of properties is taken away and replaced by another, then the resulting bundle is not numerically identical to the original bundle, and so, the original bundle did not change, but was replaced by a new one. But ordinary individuals, like Cyrano or a particular sandglass, are not such bundles – they are bundles of bundles50. That is : ordinary individuals are four-dimensional entities that are extended in time, as well as they are extended in space, by having temporal parts at different times. In the bundle theorist's vocabulary : they are bundles that are made up by bundles of properties, which are the temporal parts that make up the whole four-dimensional individual (the bundle of bundles). Now it is easy to see how the bundle theorist can give an account of change in intrinsic properties. Cyrano Fig. 39

"having a big nose" "being a man" "having blue eyes" …

"having a small nose" "being a man" "having blue eyes" …

"having a small nose" "being a man" "having blue eyes" …

t1

t2

t3

Take Cyrano : at t1 he has a big nose, then he undergoes a plastic surgery operation and so, at t2, he has a small nose. There was a bundle at t1 that contained the property of having a big nose, and lost it – and so ceased to exist. And there is a bundle at t2 that contains the property of having a small nose. None of those two bundles of properties changed. But Cyrano did. Cyrano is the bundle of those two (and, probably, much more) bundles 49

Such a strategy was also taken by Casullo (1988) and Hawthorne and Cover (1998, p. 208). 50 Castaneda (1977, p. 322) uses the label "bundle-bundle theory" (but his theory is different in several respects from the one I am considering).

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of properties and he, the four-dimensional individual, can be said to change from t1 to t2, in virtue of having different temporal parts at those two different times. (This solution is developed in more detail in I.4.§4.) It takes then no more (and no less) than adopting the four-dimensionalist's strategy to answer this objection against bundle theory. §4. The next traditional objection to bundle theory is structurally very similar to the first 51 . Take Cyrano, who is a bundle of bundles of properties. Now, the objector remarks, as before, that the identity of bundles depends on their constituents – a bundle must have the constituents it has, otherwise it would not be the same bundle. So, it seems that the components of a bundle are essential to it. But then, the bundle theorist faces the unwelcome consequence of his theory that any property of any individual turns out to be a necessary property of it. Take, again, Cyrano who has a big nose. In the bundle theorist's vocabulary, what we have is a bundle of bundles of properties, among which is the property of having a big nose. But, since Cyrano is this bundle, and since bundles have their components essentially, it is impossible for Cyrano to have had any other properties than he actually has – even the most insignificant and contingent ones, like the size of his nose, or the amount of hair he had this morning at 7 A.M.. If this is true, bundle theory certainly does not look very appealing. Fortunately for the bundle theorist, this is not true, or at least, need not be. In II.6, I argued that the modal perdurants view was the best account of persistence across possible worlds under modal realism, and I recommended to the four-dimensionalist to adopt this view for its efficiency in solving puzzles that were otherwise quite tricky to deal with. What I propose now is that the bundle theorist can also make good use of modal perdurants to be saved from the unwelcome consequences just mentioned. What is being proposed, then, is that individuals, like Cyrano, are to be conceived of as bundles of bundles of bundles of properties. Not only is Cyrano spatially and temporally extended, but he is also 'modally 51

The objection can be found, for instance, in Van Cleve (1985, p. 122-) or Loux (1998, p. 105-106)

The problem with contingent properties

248

extended', that is, he is a modal perdurant. In the bundle theorist's vocabulary : not only is he a bundle of his temporal parts (the bundles of properties), but he is also a bundle of several (many) such bundles, each of them existing in some possible world. So, Cyrano is to be identified with a bundle of bundles (of bundles of properties) inhabiting different possible worlds, and those bundles can of course have different properties. For instance, one of them has the property of having blue eyes, and another has the property of having brown eyes – and this is how such properties turn out not to be necessary but only contingent properties of, for instance, the actual Cyrano. Schematically, Cyrano, the modal perdurant, looks then as the following figure shows. Cyrano Fig. 40

Wactual

W2

"having a big nose" "being a man" "having blue eyes" …

"having a small nose" "being a man" "having blue eyes" …

"having a small nose" "being a man" "having blue eyes" …

t1

t2

t3

"having a small nose" "being a man" "having brown eyes" …

"having a small nose" "being a man" "having brown eyes" …

"having a small nose" "being a man" "having brown eyes" …

t1

t2

t3

In the actual world, Cyrano (the actual modal part of Cyrano, the actual bundle of bundles of properties) starts his life with a big nose but later he undergoes plastic surgery in order to change its size, and so, at t2, he has a small nose. He also has, throughout his entire actual life, blue eyes (and does not undergo any operation to alter this feature), but this property can be said to be only a contingent one, since he is a part of a modal perdurant that has an other-worldly W2 modal part which has the property of having brown eyes. But all of the modal parts of Cyrano, the modal perdurant (that

249

is, all of the bundles of bundles of properties that make up the bundle of bundles of bundles of properties, that is Cyrano, the modal perdurant) share the property of being a man, and this is why it is said to be one of the actual Cyrano’s essential, non-contingent, properties. (This is just an example to show how the theory works, and I do not claim that "being a man" is an essential property of Cyrano. If you don't like this example, just pick any other property you take to be essential to Cyrano.) In short, the actual Cyrano manages to have the contingent properties he has in virtue of being a part of a modal perdurant that has modal parts that have them – similarly, the actual Cyrano manages to have intrinsic temporary properties by having different temporal parts at different times that have those properties simpliciter. §5. This is the four-dimensionalist's strategy, and the fivedimensionalist's, that we have already seen when discussing the problem of persistence under modal realism. But wait – we are now working under an abstractionist hypothesis, and, in II.11, when I examined the theory of modal perdurants under abstractionism, I concluded that it was highly unpalatable. What is, then, the reason that it can work perfectly well here ? Well, it's quite simple and obvious : because the abstractionism we have under consideration here is, unlike the abstractionist theories from preceding chapters, a one-category ontology. What we have here, is an equivalent of David Lewis' claim that possible worlds are of the same ontological kind (category) as the actual world. According to Lewis, all those worlds are concrete material entities; according to the present abstractionist theory, they are complex bundles made up of properties, which are abstract universals. But both theories recognize only one ontological category – the concrete or the abstract, but not both. So, it is no big surprise that the problems we had with the two-category abstractionist ontologies when introducing modal perdurants do not arise here. For instance, there was first the worry of how it would be possible to conceive of an individual, like Cyrano, as being a concrete individual, but as being possibly abstract, or in other terms, as being partly concrete and partly abstract (see II.11.§2). And the problem did not come from the abstract components of Cyrano, the modal perdurant, but from the fact that it would be hard to accept that he is a trans-categorical individual.

Modal perdurants under abstractionism ?

250

Second, there was, in II.11.§4, the worry that if we tried to construe modal perdurants solely out of the abstract representations, rather than out of the concrete individuals and the abstract representations (to avoid them to be trans-categorical entities), we would yield a weird picture where nothing could really be possible to be otherwise for my neighbour Cyrano (a concrete individual) but only for the abstract representations that represent or misrepresent him. Cyrano, so to speak, was simply left out of the picture, and forgotten. But, quite obviously, such a worry does not arise in the present one-category abstractionism – Cyrano is not left out of the picture because he is an abstract individual. §6. (This has the further important advantage over the two-category version(s) of abstractionism that we avoid here any problems with representation. Remember_: one of the genuine worries we had was to understand how such and such abstract representation represents such and such concrete individual, and why it represents this individual and not another 52. Here, the individuals are not represented by anything, because they are identified with abstract bundles of bundles of bundles of properties – and that is all there is.) The identity of indiscernibles objection

§7. Now, fortified with the theory of modal perdurants, let us see how the bundle theory can face what is often taken to be a deadly objection to it 53. For this, let's take two steps back, and consider again the original bundle theory, and leave the bundle-bundle-bundle theory aside, for just a moment. The objection then goes as follows54. The bundle theory is committed to the principle known as the principle of Identity of Indiscernibles. But this principle is false. So, bundle theory is false.

52

For more on this problem, see Lewis (1986a, chap. 3). Note that this objection only works against the version of bundle theory we have under examination here. Other versions, that take individuals to be bundles of tropes, are immune to it. 54 The objection can be found, for instance, in Van Cleve (1985), Allaire (1963), Armstrong (1997, p. 98), Armstrong (1989b, p. 64-), Loux (1998, p. 106-111). See also Black (1952), Casullo (1988), Zimmerman (1997), Hawthorne (1995). 53

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The principle of Identity of Indiscernibles states that if an individual shares all of its properties with another individual, they are numerically identical – same properties entail numerical identity. More formally : (Id.Ind.)

(∀x) (∀y) ((∀F) (Fx ↔ Fy) → (x = y)) For any objects x and y, if, for any property F, F is a property of x iff F is a property of y, then x is numerically identical with y.

It is easy to see why bundle theory is committed to this principle. Material objects, according to this theory, are bundles of properties. Now, take two objects that have the same properties, for instance two perfect spheres of the same size, same mass, same composition, same colour, and so on. Both spheres are bundles of the same properties – and so, according to bundle theory, are the same bundles, for a bundle is given its identity through its components, as we have already seen before; indeed, if two bundles have exactly the same components, they are numerically identical. But then the bundle theorist must accept that the two spheres, being bundles of the same properties, are numerically identical – that is, that there is only one sphere. And this is exactly what the principle of Identity of Indiscernibles claims. Now, the objector argues, this principle is false, for it is quite possible for there to be two numerically distinct objects that have exactly the same properties. Our example of two spheres exactly alike in all of their properties is possible. But wait, one could reply here, this is not possible – for, if we really have two spheres, they cannot share all of their properties. For instance, let us name the first sphere "Jean" and the other "Luc". Jean then has the property of being identical to Jean, which Luc lacks, and Luc has the property of being identical to Luc, which Jean lacks. So, the example is not one where two objects share all of their properties, but only some (perhaps many, but not all). Further, if there are two spheres, they have different spatio-temporal locations, they do not occupy the same place, and they are at a certain distance from each other – and so, have different properties in virtue of having different locations; one of them, for instance, has the property of being on the left of Cyrano, and the other has the property of being on the right of Cyrano. So, our example of two spheres exactly alike

252

in all of their properties is not possible, after all. (And this is well accounted for by the bundle theory.) But the objector will not admit that the bundle theorist can make use of properties such as "being identical to Jean", or "being on the left of Cyrano", and similar. Firstly, using properties such as "being identical to Jean" and "being identical to Luc" to distinguish between the two spheres will most likely not be a very useful strategy, for to appeal to such properties seems here to be ad hoc and to simply beg the question : we want to distinguish between two spheres and so we furnish them with properties that do just that, and nothing more. Secondly, and most importantly, properties such as "being on the left of Cyrano" should not be allowed to enter into the account of what a particular like Jean or Luc is. The reason we don't want such extrinsic properties (that is, 'external' properties that a particular does not have solely in virtue of the way it is, but that involve other particulars as well) involved here is that we don't want to say that to make it possible for something to exist, something else must also exist; more precisely, we don't want that while giving the conditions of existence of a certain particular we must mention and involve some other contingent particular (like Cyrano). For instance, it seems unwelcome that in the explanation of what I am some other particulars must be included – for my existence surely does not depend on them. So it seems that properties such as "being on the left of Cyrano" cannot be satisfactorily used here by the bundle theorist after all. So, to get back to the objection from Identity of Indiscernibles, what we now have is the claim that (Id.Ind.)'

If x and y share all of their properties, they are numerically identical.

is true, but that the principle (Id.Ind.)''

If x and y share all of their intrinsic properties, they are numerically identical.

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is false. And it is this second principle that is used by the objector against the bundle theorist, who is committed to its truth. To sum up : the bundle theorist cannot make use of extrinsic properties in his account of what Jean and Luc are, and so, he is committed to the claim that it is impossible for there to be such two numerically distinct objects ((Id.Ind.)''). But this is possible, and (Id.Ind.)'' is false. So, bundle theory is false. §8. A reply a bundle theorist could make to this objection would be to claim that (Id.Ind.)'' is true because Jean and Luc have not only actual properties like having the same size, or having the same colour, but also modal properties like having possibly a certain different size, or having possibly a certain different colour. And, since Jean and Luc, while sharing all of their actual properties, can have different modal properties (surely, there is a possible world where Jean has a certain colour and Luc has another one), they turn out not to be the same bundles of properties after all. The only counter-example to (Id.Ind.)'' that the objector would have to find to trouble the bundle theorist would be an example of two individuals that share necessarily all of their properties – and plausible cases may be very hard to find here. But now, everything depends on the account we give of modal properties. It will be argued that the account provided by bundle-bundle-bundle theory, the bundle theory fortified with modal perdurants, is the best solution – but let us first have a look at its main competitor : modal counterpart theory 55. For what is required to answer the objection is that Jean and Luc have modal as well as actual properties, and counterpart theory, of course, accommodates this claim. But there are two serious problems. First, if we use counterpart theory here, it sounds plausible to say that Jean and Luc could not have different modal properties, because since they both have, by hypothesis, the same non-modal properties, they cannot have different counterparts in any possible world – because the counterpart relation is a relation of similarity and Jean and Luc, being 55

Hawthorne and Cover (1998, p. 209-210) use modal counterpart theory already when answering the objection to the bundle theory from §4 above (the problem with contingent properties).

A reply with modal properties and counterpart theory

254

actually exactly alike, will bear the same degree of similarity or resemblance to exactly the same other-worldly things. What is a counterpart of one, is automatically a counterpart of the other – or so say the many supporters of the modal supervenience principle. The second problem with counterpart theory as used here lies in the account it provides of modal properties – for instance, of the property that Jean has of being possibly pink, while it is actually green. The counterpart theorist will claim that Jean has the property of being possibly pink in virtue of having an other-worldly counterpart that is pink. And so, it is clear that the counterpart theory makes modal properties to be extrinsic in a way we wanted to avoid since they are given an account in terms of other individuals from other possible worlds. This line of response to the objection would then not be a very compelling one here. Bundlebundlebundletheory's solution

§9. The bundle-bundle-bundle theorist can follow at least three lines of response to face the objection. First, he can try to show that under his account modal properties are intrinsic; second, he can show that even if they turned out to be extrinsic, this would not yield any difficulties for his account; and third, he can argue that the objection simply does not arise against his view at all. Let us start with the first strategy. Bundle-bundle-bundle theory provides an account of modal properties as being intrinsic, and so answers the objection. Take the sphere Jean : since it is a modal perdurant, it has as parts several four-dimensional individuals inhabiting different possible worlds, and some of them are pink, while others are green, for instance. So it is the one who really has one nonactual part that is pink and an actual part that is green. The modal property of being possibly pink is then a modal property had by the actual Jean-part, who has it in virtue of being a part of a modal perdurant which has a pink part. In the bundle theorist's vocabulary : there is an actual bundle of bundles of properties (containing the property of being green), which can be said to have the modal property of being possibly pink by being a constituent of a bundle of bundles of bundles of properties which contains the property of being pink. Schematically, this case looks as the following figure shows.

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Jean Fig. 41

Wactual

W2

"being green" "being possibly pink" "being spherical" …

"being green" "being possibly pink" "being spherical" …

"being green" "being possibly pink" "being spherical" …

t1

t2

t3

"being pink" "being possibly green" "being spherical" …

t1

"being pink" "being pink" "being possibly green" "being possibly green" "being spherical" "being spherical" … …

t2

t3

The modal property of being possibly pink, had by the actual Jean (the actual part of Jean, the bundle of bundles of properties that is the actual Jean (who has it in turn in virtue of having a temporal part that has it)) is an intrinsic property because it does not involve any other individual than Jean itself (unlike properties such as "being on the left of Cyrano"). And so, such a property can, and must, be used in the account of Jean's nature, and of Luc's nature – and this will then allow us to distinguish easily between the two actual allegedly indiscernible objects. What we have now is the principle (Id.Ind.)''' If x and y share all of their intrinsic, actual, and modal properties, they are numerically identical. which is true (unlike (Id.Ind.)''). It would take an example of two distinct individuals that share necessarily all of their properties to make this principle false – and such examples do not seem to be easily and intuitively available. If this is true, we can conclude that bundle-bundle-bundle theory answers satisfactorily the objection, but not only this – it is also easy to see that

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only bundle-bundle-bundle theory provides such a satisfactory answer. Indeed, we have seen in §8 above that modal counterpart theory fails here (because modal properties turn out to be clearly extrinsic), and the same would be true of any attempts to solve the problem with world-indexed properties had by actual individuals since such properties, involving worlds, would also be clearly extrinsic. Remaining worries about the extrinsicness of properties

§10. But perhaps, this is not really satisfactory. Granted, it is true that the having of modal properties of the actual part of Jean does not involve any other individual than Jean itself (unlike under modal counterpart theory) but still, the having of modal properties involves relations between the different modal parts of Jean – and perhaps this is enough to make these properties extrinsic. But now, the bundle-bundle-bundle theorist can argue, why is this an objection to my view ? Remember the motivation we had to rule out extrinsic properties : we didn't want them in the account of what a particular individual is because we didn't want to say that other individuals must be involved in the account of what this individual is. Under modal counterpart theory, particular individuals are world-bound and the analysis of their having of modal properties appeals to other-worldly distinct individuals and so this account is unappealing here – but compare to the case of bundle-bundle-bundle theory : the theory's central claim is that individuals (like the spheres Jean and Luc, Cyrano, and myself) are modally extended and thus the account of what the having of modal properties amounts to is, so to say, already built in the definition of the notion of a particular individual. So, de re modality does not require any further explanation or piece of theory, it is already given in the explanation of what an individual is. Once this explanation of what it is to be a particular individual is given, we do not need to appeal to any other individuals to analyze modal properties and so, even if the objector insists on saying that modal properties turn out also here to be extrinsic, there is no reason to think that this yields any difficulties here. Once we have said what an individual such as Jean is, we do not need to appeal to any other individual to account for the modal properties of, for instance, its actual modal part – this is simply already included in the account of Jean's nature, since it is a modal perdurant.

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§11. This quite naturally leads to a third line of response for the bundlebundle-bundle theorist : that the objection from Identity of Indiscernibles simply does not arise against his view. The objection arises against the original bundle theory because of easily imaginable cases of two objects that are exactly alike in all of their properties, and perhaps even because of some actual cases (think of, for instance, two electrons). The objection also arises against the bundle-bundle theory (the bundle theory fortified with four-dimensionalism) because, again, it is easy to imagine a case of two objects that are exactly alike in all of their properties during all the time they exist (perhaps, there also are such actual cases, as before). But the objection simply does not even arise in the case of bundle-bundle-bundle theory because, as noted before, it does not seem easy to find plausible counter-examples here. Two spheres or two electrons that are actually exactly alike, certainly could differ in some way. The objector would have to find a case of two objects that are necessarily exactly alike, and it seems plausible that such cases simply don't exist – at least the charge against the bundle theory is here much weaker than before 56. If this is true, then it seems that the bundle-bundle-bundle theorist does not even have to answer the objection.

The objection does not even arise

§12. But this reply, and more generally the whole bundle-bundle-bundle theory strategy, comes at a price : for one has to say not only that there are 'five-dimensional' individuals, but one has to make the stronger claim that all individuals are 'always' five-dimensional, and further, that they are maximally five-dimensional. The need for this stronger claim is easily seen : take two distinct modal perdurants (call them "Jean" and "Luc") that share a part in one world, for instance their actual part (call it "Jean@" or "Luc@"). What about the individual that is this part_? Is it one or is it two ? Is there one thing that is Jean@, as I just said, or are there two indiscernible but distinct things

Costs and problems

56

Still, the unsatisfied objector could claim that bundle-bundle-bundle theory simply 'postpones' the problem, and makes it perhaps less 'acute', while not really solving it since it seems to be at least logically possible for there to be two individuals that share all of their properties necessarily, even if actual or even fictional cases may be hard to imagine.

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Jean@ and Luc@ ? How are we to tell the difference ? Well, if we want to have at hand the bundle-bundle-bundle theory's reply here, what we need is to claim that Jean@ and Luc@ are not 'complete enough' to be individuals, we need them to be parts of 'modally bigger' modal perdurants, in order for them to be distinguished (or not distinguished, in the case where there is only one individual) by their modal properties. What this shows is that Jean@ alone is not allowed by bundle-bundle-bundle theory to be an individual. All individuals have to be five-dimensional, and 'only' fourdimensional world-bound parts of them are not to be accepted as individuals. To be an individual, the bundle-bundle-bundle theory has to claim, is to be five-dimensional. The following two cases illustrate this strategy (the capital letters stand, as usual, for properties) :

Fig. 42

LMN

RST

LMN

RST

IJK

OPQ

IJK

OPQ

FGH

FGH

FGH

On this very simplified figure, we have two distinct cases, that have to be accounted for as distinct by the bundle-bundle-bundle theory if it is to succeed in its task. The first case is the one where the two modal perdurants share an actual (four-dimensional) part; while the second case is the case where the two modal perdurants have both a part in the actual world, but those two parts are numerically distinct while being indiscernible with respect to their actual and intrinsic properties (say, two indiscernible spheres, or perhaps two electrons). Both cases are, of course, possible under the bundle-bundle-bundle theory. And how does it distinguish between the two possibilities ? That is, how can we distinguish between the two cases without begging the question by saying that in the first case there is one individual in the actual world, while in the second case there are two ? This can precisely be done only if the actual things are

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not said to be individuals, and if only the five-dimensional modal perdurants 'count' as individuals – the two modal perdurants will then be distinguished simply because they are discernible as wholes, and the actual things will thus be distinguished by their distinct modal properties : for instance the bundle-thing "FGH" in the first case has the modal property of being possibly L, and it also has the modal property of being possibly R; while, for instance, the first of the two "FGH"-bundles in the second case has the modal property of being possibly L, but does not have the modal property of being possibly R, and this is how it will be distinguished from the second thing (that is possibly R but that is not possibly L). But in addition to the claim that all individuals have to be fivedimensional, the bundle-bundle-bundle theorist has to make the further claim that all individuals are maximally five-dimensional : our example can be easily adapted to show the need for this. Take the two modal perdurants Jean and Luc and imagine that not only they share a four-dimensional part that exists in the actual world, but say that they share a 'five-dimensional sub-segment' – that is, they share a part that is a modal perdurant that stretches across, say, thirty-six possible words. And again, as before, unless we deny to this modally extended part shared by Jean and Luc to be an individual, the same problem will arise, because we will not be able to distinguish between the case where this part is only one, or where these are two indiscernible parts. And again, to be able to use the bundle-bundlebundle theorist's strategy to solve this puzzle case, we'll have to claim that this shared modally extended part is not an individual because to be an individual is to be maximally modally extended. So we have seen, I believe, that the bundle-bundle-bundle theory's strategy works – but only at the price that the thing that is my sandglass and that is on my desk now is not a regular individual, because it is modally too small – what is an individual is only a modal perdurant, maximally stretched across possible worlds, that includes the thing that is on my desk now as a part. (Perhaps, this is not as bad as it may seem to be : what it simply means is that to have a 'complete' individual one has to consider it as having all of its intrinsic, actual and modal properties. It's just part of the nature of my sandglass that it is a contingent thing, that has a lot of modal properties.)

260

Further, this strategy also faces the same worry we had with modal counterpart theory in §8 above : how is it possible to say that the two things in the second case above (even if we grant from the beginning that they are two) that are indiscernible with respect to their actual intrinsic properties have nevertheless distinct modal properties ? The friends of the claim that modal properties supervene on actual ones, would certainly feel very uneasy here. This question yields the problem of how the different parts of a modal perdurant are 'glued together' – the question of the nature of the bundling relation. So, let us examine this question now. The glue problem

§13. The glue problem is a hard one for the bundle-bundle-bundle theorist. And this is no big surprise since the glue problem is also a tricky one for the four-dimensionalist and the friend of modal perdurants, as we have seen in II.6.§11-13 and I.8.§7. Exactly as we had the problem to say how the different temporal and modal parts are unified (glued together) to make up a single temporal or modal perdurant, we now face the question to know what unifies such and such properties into a single bundle (or bundle of bundle of bundles). Bertrand Russell, who was a bundle theorist but not a bundle-bundlebundle theorist, tried to unify the different properties that make up a single bundle by a symmetrical and non-transitive relation called "compresence". This relation was taken as a primitive relation that ties together the different properties, where "compresence" means roughly "simultaneous presence" (see Russell (1948, p. 54-55)) – which, unfortunately, does not explain much, taking the bundling relation as being primitive and underexplained. Another possible approach that takes the bundling relation as being primitive was taken recently by Paul (2002 and 2004) – she claims that the properties making up a single bundle are parts of the bundle and takes the bundling relation to be a primitive mereological relation of fusion. Here again, the bundling relation is not given an analysis but perhaps taking it as a primitive is really the best theoretical option the bundle-bundle-bundle theorist can take, since, as we have seen, using something like the counterpart relation as the glue would not be a good option here because of the difficulties with counterpart theory we have seen above. A primitive relation certainly does not explain much, but allows for individuating particulars without yielding any troubles, and can

261

defend itself by arguing that alternative theories of particulars also have weighty primitives : primitive substrata, primitive substances, or primitively individuated tropes. But let us at least try now to look at an alternative that the bundle-bundlebundle theorist could perhaps propose if he doesn't want to accept a primitive bundling relation : perhaps he could follow the fivedimensionalist strategy we have seen in II.6.§13. The central claim was here that the primitive bundling 'glue' relation is a relation that is an entirely unrestricted and unqualified one, and that does not have any ontological force – it is, loosely speaking, a relation which is like a container without any content. But we can fill it with whatever restrictive conditions we want. Thus, while basically, on this view, any property can be 'glued' with any other to make up a bundle (which must then be recognized as a regular and real individual (as long as it is maximally modally extended, as we have seen above)), any preferred restrictions can be added to it to make the bundle more interesting – that is, to get the individuals that interest us. For instance, if you are interested in providing an ontology of ordinary material particulars, like soccer balls or human beings, which seem to us to stand out from their environment more than other particulars (like, for instance, the particular 'Bernard' who is a spacetime worm made up of a half of a soccer ball today, Cyrano's nose the 9th of February 2003, and all of the tropical fish of the 19th century), you may want to specify a list of restrictive criteria on the bundling relation that would include logical compatibility, similarity, spatio-temporal contiguity, causal connectedness, and so on. But this does not make the entire actual soccer ball or my actual neighbour Cyrano any more or less real than Bernard. Applied to the case of modal properties, this proposal simply means that the soccer ball has certain modal properties when considered as a tool for a game, and other different modal properties when considered as a pillow on the beach. Modal counterpart theory can, of course, also secure this result by using different criteria of similarity to determine the ball's counterparts, but it makes these modal properties to be unpalatably extrinsic; while bundle-bundle-bundle theory uses the same strategy to account for a 'glue' that is internal to the bundle (of bundles of bundles).

262

But it seems that here we have two reasons to restrict composition that we did not have in the case of modal perdurants under modal realism. Firstly, as we have already seen, one has to restrict composition after all because only maximally modally extended individuals are to 'count' as regular individuals, and secondly, there is a further need to restrict composition if one wants to distinguish between possible and impossible individuals, for an entirely unrestricted glue relation would make a single bundle out of the property of being wholly red and the property of being wholly green, which are incompatible – an individual that is both wholly red and wholly green is an impossible individual. It is worth noting that we did not have this problem in the case of temporal and modal perdurants under temporal and modal realism à la Lewis – because the realm of the possible and the actual (the different possible worlds) was given a primitive glue that provided us with clear borders in terms of spatio-temporal interconnectedness : possible worlds were said to be "unified […] by the spatio-temporal interrelation of its parts" (Lewis (1986a, p. 71)). Any object that has any spatio-temporal relation to any other object is a part of the same possible world. And this provides the great advantage of analysing what possible worlds are in a non-circular way (that is, without using any modal notions). (The disadvantage is that it cannot account for the possibility of there being a single universe that contains two or more spatio-temporally interconnected 'island universes' that are not spatio-temporally connected to each other – a possibility that was argued to be a plausible one by Bricker (2001).) Under bundle-bundle-bundle theory, it seems that unless we want impossibilia and impossible worlds to be ontologically on a par with the realm of the possible, we have to impose a restriction on the glue relation after all – and the weakest possible restriction would be the best, that is : logical possibility. In short, the bundles (and the bundles of bundles of bundles) must be made up of logically compatible properties. The drawback here is, of course, that if we provide possible worlds with such individuation conditions, they are then given an analysis in terms of logical possibility (and also, presumably, of maximality) which will make the analysis of modal notions circular – exactly as in the case of twocategory abstractionist theories.

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What all these difficulties show, I think, is that the 'unrestricted glue' strategy is of good use for the theorist of modal perdurants who works under modal realism, but does not work so well for the bundle-bundlebundle theorist. So it seems that perhaps the best theoretical option here is to take the bundling relation as primitive. (After all, it could be argued, having such a primitive is perhaps better than having the Lewisian modal realist's 'spatio-temporal interconnectedness' criterion, since this 'glue' perhaps misses some genuine metaphysical possibilities. Besides, note that the bundle-bundle-bundle theory's ambitions are larger than the modal realist's – for it is not only a theory of modality but also a theory about the nature of individuals. If a theory of the same ambitions were wanted, the modal realist's view would have to be combined with some theory about the nature of individuals (trope bundle theory, the substance-attribute view,…) which is very likely to contain some primitive individuating device as well.) §14. I hope I have shown in this chapter that the theory of modal perdurants can be accommodated with one-category abstractionism to yield a general metaphysical picture of what material objects are, and how they persist through time and possible worlds, and that the view has genuine theoretical advantages over modal counterpart theory (exactly as in the case of the theory of modal perdurants under modal realism) – if one is ready to pay the price : a primitive bundling relation and the claim that to be an individual is to be maximally modally extended57. So it seems that under any one-category ontology of our world and of possible worlds, the modal perdurants view seems to outrun its competitors. (Also, it seems to be an additional discovery that modal perdurants seem to work well only under a one-category ontology.) What of the competing theories of persistence across possible worlds that work under an abstractionist two-category ontology ? Here, I believe that the best account of persistence is the trans-world identity view (II.9) – but only because its competitors, namely, counterpart theory and modal perdurants, are very unpalatable under this two-category ontology. 57

Which seems also to include the cost of primitive modality, since the notion of maximality is likely to be a modal one.

Concluding remarks

264

Compared to the two views with modal perdurants under a one-category ontology, this trans-world identity view has many drawbacks (and some of them, come, precisely, from the two-categorical feature of the ontology of possible worlds) (see the quick summary in II.9.§10 and elsewhere). So, since I believe that both of the views that involve modal perdurants are superior to any of the views that work under two-category abstractionism or under fictionalism, I now would like to face the question : which one of these two accounts is to be preferred ? To simplify things, I will use here the label "concretist theory" to speak about David Lewis' modal realism fortified with the theory of modal perdurants, and "abstractionist theory" to speak about bundle-bundle-bundle theory. First, let us see in what important respects both the concretist and the abstractionist theories are similar. (a)

(b) (c)

Both claim that ordinary individuals like sandglasses have spatial, temporal and modal parts (and that this is how they manage to have temporary and accidental contingent properties). Their persistence conditions are then clearly given by their nature – in fact, once the 'five-dimensional' nature of them is given, no additional piece of theory is needed to account for their persistence through time and possible worlds. Both claim that possible worlds are of the same kind our world is (they are "like me and my surroundings", as Lewis puts it). Both take it that "actual" is an indexical term. (This was not explicitly argued for in the case of the abstractionist theory, but it is a consequence of (b) if one does not want to worry about his or her own actuality.)

What those similarities show is that the two views are structurally similar in some important respects. But they are different metaphysically because they disagree, in short, on to what kind of 'stuff' this structure applies. The concretist theory takes it that reality is ultimately constituted by concrete entities that are particulars, while the abstractionist theory claims that the fundamental constituents of reality are abstract entities that are universals.

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Together with (b) above, this yields an incredulous stare for each theory to face. The concretist theory was often given the well-known incredulous stare because it claims that there is a plurality (perhaps, an infinity) of concrete possible worlds, just like the actual world is. Further, it claims that ordinary individuals are things that are extended across possible worlds – that is, they are aggregates not only of actual entities but also of possible ones. The incredulous stare, here, is mainly aimed at the account of the nature of the possible. Now, the abstractionist theory has to face a similar incredulous stare : it also claims that there is a plurality of worlds of the same kind our actual world is, but since all of those worlds are abstract, I think the incredulous stare would more likely be aimed at the account of the nature of the actual world : it sounds simply extremely bizarre to claim that Cyrano, Jean-Luc, my sandglass, or myself are abstract individuals. But in the end, I think that both incredulous stares come in the first place from (b) – and the particular accounts (concretist or abstractionist) of the ultimate nature of reality just make it be expressed in different ways. What is being stared at in the concretist's case, I think, is that if I go around with a theory that makes me call me and my surroundings concrete, I then claim that possible pink dragons are also concrete. And what is being stared at in the abstractionist's case is that if I go around with a theory that makes me call me and my surroundings abstract, I then claim that possible pink dragons are also abstract. (It is not the bundle theory that is being stared at, but (b).) (Granted, the abstractionist's claim that I am an abstract individual sounds crazy, and could be given an additional incredulous stare on its own, but this is only due, I think, to the fact that we are used to talk about abstract entities under a two-category ontology view of the world. But once one takes this away and one starts to think of abstract 'stuff' as the only 'stuff' there is, one starts to realize, I believe, that such a picture of the world is no more or less crazy than the concretist's. It took me some time to convince myself of this, but I now think it's true. The only difference that really matters here, is, to my mind, the fact that the concretist's ontology is an ontology of particulars and the abstractionist's is one of universals.)

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§15. The best we can do when doing metaphysics is, I think, to build theories that describe at best the phenomena we encounter or that we appeal to in thought experiments. I think that both the concretist and the abstractionist versions of the theory of temporal and modal perdurants do this very well in the case of persistence through time and possible worlds. Which one of those two views is true, or which one of those two views has a better cost-benefit ratio, I do not know. But ultimately, I think, the world, and all worlds, are best accounted for as worlds of perdurants.

269

List of figures :

Number

Section(s)

Label

1

I.1.§4 I.8.§1 I.1.§4 I.1.§5 I.4.§16 I.1.§6 I.1.§7 I.2.§4 I.4.§1 I.4.§19 I.6.§5 I.8.§3 I.6.§8 I.6.§8 I.6.§9

Four-dimensionalism

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

I.8.§1 I.8.§3 I.10.§1 II.6.§3 II.3.§1 II.9.§2 II.3.§2 II.9.§3 II.4.§1 II.5.§3 II.5.§4 II.5.§7 II.5.§8 II.5.§11

The worm view Genuine endurantism Presentism Presentist perdurantism A Platonist strategy for the presentist The problem of change SOFism The fission case Undetached spatial parts, before t Undetached spatial parts, after t Undetached spatial parts, four-dimensionalism The stage view Map of France The modal objection Straightforward trans-world identity Trans-world identity with overlap Modal counterpart theory A branching structure of possible worlds Direct and indirect generation B-counterpart theory B-counterparts and identity A pseudo-case of trans-world identity

270

24 25 26 27

28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

II.6.§1 II.7.§8 II.6.§4 II.7.§8 II.8.§2 II.9.§1 II.12.§1 II.9.§3 II.9.§5 II.10.§2 II.10.§3 II.10.§4 II.10.§5 II.10.§5 II.10.§5 II.11.§2 II.11.§3 II.11.§4 II.12.§3 II.12.§4 II.12.§9 II.12.§12

Modal perdurants Five-dimensionalism Fictionalist modal perdurants Abstractionism

World-stories with overlap Trans-world identity under abstractionism Counterpart theory under abstractionism 1 Counterpart theory under abstractionism 2 Counterpart theory under abstractionism 3 S-counterpart theory World-dependent identity 1 World-dependent identity 2 Modal perdurants under abstractionism 1 Modal perdurants under abstractionism 2 Modal perdurants under abstractionism 3 Bundle-bundle theory Bundle-bundle-bundle theory Solution to the objection from Id.Ind. Two distinct cases of modal perdurants

271

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