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«Once Upon a Spacetime by Bradford Skow A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy ...»

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Different versions of supersubstantivalism give different accounts of what fundamental properties and relations points and regions of spacetime instantiate. At one extreme lies the view that the only fundamental properties and relations spacetime instantiates are geometrical ones. Hard-headed scientifically-minded philosophers are likely to respect this version most, because it is linked to a scientific research program in a way that the others are not. (Sklar considers this version a worthy topic of discussion, while dismissing a more modest version as a ‘linguistic trick’ (1974, pages 166, 233).) Inspired in part by the general theory of relativity, John Wheeler advocated this variety of supersubstantivalism. In general relativity Einstein eliminated the gravitational force: the motions that this force explained are in Einstein’s theory explained instead by the curvature of spacetime. Wheeler hoped that all forces could be eliminated, and all motion explained by the curvature of spacetime. (It’s this hope that he expresses in the quotation that heads this paper.) Of course, the sense in which such a theory ‘explains motion’ is now a little funny: if we’re supersubstantivalists, we don’t think there are particles distinct from spacetime, particles that move by being located in different places at different times, whose motions we can attempt to explain. When an extreme supersubstantivalist claims to explain the motion of bodies he means something like this: the whole story of the history of the universe is contained in the geometrical structure of spacetime; there are laws governing that structure which allow us to explain why a given instantaneous space has the geometry it does by citing the geometry of earlier instantaneous spaces together with the laws; and ordinary talk of the motion of bodies is in some sense talk of the curvature of spacetime.4 The Grand Unified Theory that Einstein sought was to be a theory that provided explanations like this: the theory would not postulate (dualistically-conceived) particles, but certain regions of spacetime in possible worlds permitted by the theory would look ‘particle-like’ (see (Earman 1995, page 16)). Producing such explanations is a real challenge, one Not all spacetimes permitted by general relativity are well-behaved; some cannot be divided up into a series of instantaneous spaces ordered in time. In such spacetimes we may not be able to explain why a given spacelike region of spacetime has the structure it does by appealing to the structure of some earlier spacelike region and the laws.

that has not yet been met: while Einstein showed how to ‘reduce’ gravity to curvature, no one has succeeded in reducing electromagnetism, or the other forces, to curvature in a plausible way.

Although the success of general relativity helped motivate this research program, its roots go back farther. Back in 1870 W. K. Clifford, inspired by Riemann’s theory of curved surfaces, hypothesized that what we ordinarily call the motion of matter is nothing but ‘variation of the curvature of space,’ and that ‘in the physical world nothing else takes place but this variation.’ Like Wheeler, Clifford hoped to produce scientific explanations of phenomena that appeal only to the geometry of space: he hints that ‘I am endeavoring in a general way to explain the laws of double refraction on this hypothesis’ (1882, page 22). Even earlier Newton secretly toyed with a version of supersubstantivalism according to which the only fundamental properties space instantiates are geometrical, though he makes no attempt to use the curvature of space to explain motion. (Newton thought space was flat, and in his time the geometry needed for dealing with surfaces with variable curvature— Riemannian geometry—had not been invented. I’ll look at Newton’s theory below.) I’ve been discussing extreme versions of supersubstantivalism. Other versions are more modest. More modest versions are more liberal about what fundamental properties they allow spacetime to instantiate. One modest version accepts as fundamental the (non-geometrical) fundamental properties we ordinarily think that fundamental particles instantiate—properties like mass and charge—and allows spacetime to instantiate them.

This more modest version does not face the daunting challenge that the extreme version does: that of rewriting the laws of electromagnetism and the other forces as laws governing the curvature of spacetime. In fact, existing spacetime theories (like Newtonian gravitational theory and electromagnetism) can easily be reinterpreted to make them compatible with the more modest form of supersubstantivalism.

3 Is Dualism the Default View?

Strictly speaking, dualism and supersubstantivalism are not incompatible. Both are true in a world with spacetime but no material objects. But our world is not one of these worlds, so we must choose.

Dualism seems to most substantivalists like the default position. They want powerful arguments showing that dualism is incoherent, or that it conflicts with some other strongly held beliefs, before they take supersubstantivalism seriously.

I don’t know of any arguments like that; so if that is what is required, supersubstantivalism is in bad shape.

How does dualism get this default position? Not because we can just see that material objects aren’t regions of spacetime. Maybe substantivalists give dualism default status because it is entrenched: maybe substantivalists have believed it for a long time, are used to picturing the world in its terms, and have never really considered the alternative. But psychological entrenchment does not justify giving dualism default status.5 If preferring supersubstantivalism requires strong arguments against dualism, that must be because there are good reasons in favor of dualism in the first place. But what are these reasons?

I can think of two reasons we give dualism default status, and substantivalists should not think either are any good.

First, we might oppose supersubstantivalism because we feel some motivation for relationalism. I’m sitting in my chair and my bamboo plant is across the room, and (it seems) there is absolutely nothing between us. But if supersubstantivalism is correct then we are both swimming in a sea of regions of spacetime, our borders contiguous with other things made of the same stuff that we are. So supersubstantivalism conflicts with the way things ordinarily seem.

Even if this is a correct account of the way things ordinarily seem—and surely sometimes it is—substantivalism already conflicts with it. And I do not see that dualism comes closer to matching the ordinary appearances than supersubstantivalism.

Second, we might oppose supersubstantivalism because it sounds odd to say that I bought my coffee from a region of spacetime. But, in general, the demise of ordinary language philosophy has taught us to be suspicious of arguments that start with ‘it would sound odd to say....’ And in particular, history should make us Maybe those who accept ‘conservative’ accounts of belief revision (like Harman (1986)) will disagree.

suspicious: there was a time when it sounded odd to say that I bought my coffee from a swarm of elementary particles.6 There are, in addition, more sophisticated philosophical reasons substantivalists might oppose supersubstantivalism. Maybe supersubstantivalism is false because material objects move but regions of spacetime do not; maybe it is false because material objects lack but regions of spacetime have temporal parts; maybe it is false because my bamboo plant could have been located elsewhere, but no region of spacetime could have been located elsewhere. These are important objections, and I address them below. But I don’t think they capture the reasons why we initially recoil from supersubstantivalism and give dualism default status.

I conclude that substantivalists should not give dualism default status. We should consider dualism and supersubstantivalism as competitors on an equal footing, and see where argument leads.

So what reasons are there to be supersubstantivalists? In sections 4 through 7 I discuss instances of two strategies for defending supersubstantivalism, one due to Descartes, and the other due to Newton.

4 Cartesian Supersubstantivalism

Descartes is typically classified as a relationalist. But while Descartes was certainly a relationalist about motion, it is less clear that he was a relationalist about ontology, rather than a supersubstantivalist. (I argued in previous chapters that relationalism about motion is not only consistent with substantivalism, it requires it.) In the Principles of Philosophy Descartes writes, ‘in reality the extension in length, breadth and depth which constitutes a space is exactly the same as that which constitutes a body’ (2:10).7 That sounds like a strong (and not particularly plausible) version of supersubstantivalism: not only is every material object (or ‘body’) identical with some region of space, but every region of space is a material object.

(Since Descartes lived in a pre-relativistic age, this version of supersubstantivalism identifies material objects with regions of space, not with regions of spacetime.) (Sider 2001, sect. 4.8).

Unless otherwise noted, all citations of Descartes are to the Principles (part:section).

Is Descartes really a supersubstantivalist? Field (1989) claims that supersubstantivalists can be distinguished from relationalists by asking the following question: is it possible that there be empty regions of spacetime? Only supersubstantivalists will answer ‘yes.’ Descartes says ‘no,’ and so counts as a relationalist by this criterion. But I’m not sure this criterion is a good one. A dualist might think that it is necessary that every region of spacetime is occupied by a material object. Surely a supersubstantivalist can accept the analogous claim, that it is necessary that every region of spacetime is a material object. Still, it may be that there is a merely semantic difference between some relationalists and supersubstantivalists—they just differ over how they are willing to use the words ‘region of space(time).’ I will set this issue aside and speak as if Descartes is properly classified as a supersubstantivalist.

Descartes’s argument for Cartesian supersubstantivalism rests on the claim that ‘the nature of body consists in...its being something which is extended in length, breadth and depth’ (2:4). If we say that talk of something’s nature is talk of the conjunction of all of its essential properties (and this does seem to be what Descartes

has in mind in 2:11), then Descartes’s claim amounts to this:

(1) Being spatially extended is the only essential property of material objects.

Descartes also accepts a partial converse of (1), namely (2) Necessarily, every extended thing is a material body.

But the arguments he gives in 2:4 and 2:11 (which I examine below) are clearly arguments for (1), and without extra premises (1) does not entail (2). Nor is (2) sufficient to establish supersubstantivalism: it entails that every region of space is a material body, but not that every material body is a region of space.

In 2:11 Descartes says ‘Yet this [namely, the idea of something that is extended in length, breadth, and depth] is just what is comprised in the idea of space.’ I take this to mean (3) Being spatially extended is the only essential property of regions of space.

This looks plausible. And we can get from (1) and (3) to Cartesian supersubstantivalism

if we add another premise:

(4) Distinct kinds of things cannot share all of their essential properties.

So there is only one kind of thing that has spatial extension as its only essential

property; and we have two names that apply to (all and only) things of this kind:

‘region of space’ and ‘material object.’8 This argument aims to establish a particular version of supersubstantivalism.

So we can evaluate it from two points of view. First, does it give us reason to accept supersubstantivalism in the first place? Second, if we are already supersubstantivalists, does it give us reason to accept Cartesian supersubstantivalism instead of some other version? I will take these questions in reverse order.

Cartesian supersubstantivalism is hardly the most plausible version of supersubstantivalism. Supersubstantivalists should allow for the possibility of regions of space that are not also material objects. So which premises do they reject? Not the premises about essential properties: presumably supersubstantivalists agree that it is essential to regions of space (and so to material objects) that they be spatially extended. They should deny the (suppressed) premise that material objects are a ‘kind of thing,’ things that can be characterized in terms of their essential properties. Instead, say that material objects differ from other regions of spacetime in their accidental properties—like, for example, mass and charge.

Of course this reply is not open to dualists; dualists do not think material objects differ from regions of space only accidentally. So (turning now to my first question), how do dualists resist this argument?

Dualists should reject (1). Descartes’s argument for (1), as it occurs in his discussion of the stone in Principles 2:11, is to cast about for a counterexample and fail to find one.9 He thinks that for any other property some material object has, One quick objection to this argument is to say that material objects can be pointsized, and so have no spatial extent at all. But in that case the same is presumably true of regions of space—if there can be pointsized material objects there can be pointsized regions—and the argument could be modified to take this into account. Descartes would not accept this new argument, though, since he thought it impossible for a material object to lack all spatial extent. And this plays a crucial role in his argument against atoms in 2:20.

In 2:4 Descartes argues that no perceptible properties, like hardness and color, are essential to material objects. Something similar goes on in Descartes’s discusthere can be a material object that lacks it; and so no other property can be essential to material objects.10 A dualist might say that mass is an essential property of material objects.

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