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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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(Descartes, of course, lived before any such property was recognized.) But this can’t be right, because there are massless particles. Bennett (2001, pp.30-32), following Locke and others, objects that Descartes fails to rule out solidity, or impenetrability, as an essential property of bodies. But I’m not sure that impenetrability is essential to material objects. Neutrinos may have some power to exclude other particles from occupying just the region they do, but it is very weak (that is why they are so hard to detect); do we really think it is impossible for there to be a kind of particle that is completely uncoupled from other kinds, and does not interact with them at all? In any case, dualists have a better reason to reject (1). They should say that it is essential to material objects that they occupy regions of space.11 But it is not essential to regions of space that they occupy regions of space. So these two kinds of spatially extended thing do not share all their essential properties.

Descartes’s argument for supersubstantivalism is not very good, but I think there is a better argument for supersubstantivalism that is Cartesian in spirit.

5 Spatiotemporality

Descartes thought there couldn’t be two kinds of spatial thing. I think that reflection on what it is to be a spatial (or, better, spatiotemporal) thing can still give us some reason to be supersubstantivalists, even if not the reason Descartes thought.

A virtue of supersubstantivalism, to the eyes of a metaphysician, is that it provides the materials for a better account of spatiotemporality than does dualism.

This gives us some reason to be supersubstantivalists.

sion of the wax in the second meditation; but there his primary aim is to argue that the nature of the wax ‘is in no way revealed by my imagination, but is perceived by the mind alone’ (page 85).

For most of the passage he argues that for any property a stone has, that very stone could lack it. But when he argues that heaviness is not essential to the stone, he cites the fact that fire (which he regards as a material body) is not heavy.

Markosian (2000) defends something like this view.

What is it to be a spatiotemporal thing? What is it to be extended in space and time? Supersubstantivalists have a simple answer: to be spatiotemporal is to be a region of spacetime, to be part of spacetime.

What do dualists say? They will say that to be spatiotemporal is either to be a region of spacetime, or to bear the occupation relation to some region of spacetime.

But this view has several disadvantages.

First, there is a problem about essences. It is essential to material objects that they be spatiotemporal. For dualists this means: for anything at all, if it occupies some region of spacetime, then it is necessary that it occupies some region of spacetime. But this is to accept a necessary connection between distinct existences.

Supersubstantivalists do not need to accept this necessary connection.

Second, there is a problem of inclusion. Which things are spatiotemporal?

Material objects certainly are. But some material objects are parts of other material objects; and composite material objects are located where their parts are. That is, it is necessary that if x is part of y and x occupies region L then y also occupies L.12 Why is this necessary? Dualists can give no answer. They cannot explain the necessary connection between parthood and occupation. Supersubstantivalists do not believe in an occupation relation, and so have no necessary connection to explain. (Or, better, supersubstantivalists do believe in an occupation relation, but

they deny that it is a fundamental relation, and instead analyze it in terms parthood:

a region of spacetime occupies just those regions that are parts of it. On this account, there is no mystery in the necessity that material objects occupy those regions that their parts occupy.13 ) L need not be the largest region y occupies. Some might accept a weaker condition than the one in the text. They might say that it is necessarily only that if x is part of y and x occupies L then y occupies a region that contains L. The difference between these two does not affect my argument.

I’m oversimplifying the way we use ‘occupies’ and our talk of locations and places generally. Supersubstantivalists will say that sometimes we use ‘occupies’ to express the converse of the parthood relation; sometimes we use it the way relationalists think we always use it: to express some complicated relation to other material objects, as when I stand on the subway platform and say, ‘every morning I stand in the same place and wait for the train’ to mean something like ‘every morning I stand next to this wall and wait for the train.’ This will come up again below.

Third, there is a problem of exclusion. Some philosophers want to expand the realm of the spatiotemporal. Penelope Maddy, for example, claims that sets are spatiotemporal. She uses this claim to defend the existence of sets by arguing that we can see sets, and so that we have empirical evidence for their existence.14 It is easy for supersubstantivalists to reject Maddy’s claim. They say that only regions of spacetime are spatiotemporal, and no set is a region of spacetime. It is not so easy for dualists. They must argue that sets cannot bear the occupation





relation to regions of spacetime. But it is open to someone like Maddy to say:

dualists admit a necessary connection between occupation and parthood. I admit an additional necessary connection between occupation and membership: sets occupy just those regions their members occupy. I cannot explain why there should be this connection; but neither can dualists explain why there should be a connection between occupation and parthood.

6 Newtonian Supersubstantivalism

Descartes hoped to derive supersubstantivalism from premises we should all accept. That’s an ambitious project. There is a less ambitious way to argue for supersubstantivalism. Instead of arguing that material objects must be regions of spacetime, we argue that they can be. Regions of spacetime can do all the work we need material objects to do. For the sake of simplicity, then, we should identify material objects with regions of spacetime.15 Newton took this approach. His manuscript ‘De Gravitatione’ contains an attempt to describe the nature of material objects.16 He ends up describing a possible world in which, he claims, it would be appropriate to say that certain regions of space are (also) material objects. Newton proceeds in stages.

First he asks us to imagine the following scenario. Suppose the dualism is true, that material objects really are distinct from spacetime. God chooses some region of empty space—call it ‘Joe.’ Whenever a material object is about to occupy (Maddy 1990), chapter 2, especially pp.58-59.

(Sider 2001) and (Bennett 1984) also give this motivation for supersubstantivalism.

(Newton 1962). Howard Stein discusses this manuscript in his (1970).

Joe, God exerts a force on that object in the direction away from Joe sufficient to prevent it from occupying Joe. So when they get close enough to Joe, superballs bounce right back; photons are reflected; and beer bottles shatter. Over time God may change which region he watches over in this way; we may assume that he changes it continuously and that all the regions have the same shape. (We may be tempted to say, as God varies which region of space enjoys his favor, that Joe is moving. But this is just a misleading appearance; Joe is a region of space, and Newton denies that regions of space can move.) Of course even in Newton’s physics material objects act on each other in ways other than by contact; but we can easily imagine God also causing each material object to be accelerated towards Joe, that acceleration being indirectly proportional to the square of the distance between that object and Joe (or the distance between that object’s center of mass and some point that falls inside Joe). Material objects in this world would move, then, just as if there were some material object occupying Joe and attracting them gravitationally.

Of this scenario Newton asserts, ‘it seems impossible that we should not consider this space [that is, Joe] to be truly body from the evidence of our senses....for it will be tangible on account of its impenetrability, and visible, opaque and colored on account of the reflection of light, and it will resonate when struck because the adjacent air will be moved by the blow’ (139).

Now it is doubtless true that were we in such a world, confined to exploring it with our senses, we would conclude that Joe is ‘truly body’; but since we are not so confined, but know more directly the metaphysical truth of the situation, it is clear that Joe is no material object. A world in which God behaves in the way described is a world in which God deceives some of his creatures. (Descartes would be appalled.) The problem is that while some regions of space—Joe, in particular—are masquerading as material objects, there are also, in the world, real material objects— that is, material-objects-according-to-dualists. Our use of ‘material object’ is not so permissive that it could apply to both regions of space and things distinct from regions of space in the same world (considered as actual). There’s an obvious way to avoid this problem: Newton next asks us to imagine a world that contains none of what dualists call ‘material objects,’ but instead contains only space, certain regions of which God has chosen to watch over as he watched over Joe in the previous scenario. (Of course, now watching over a given region involves ensuring that no other chosen region overlaps it, rather than ensuring that no dualist material object occupies it.) In such a world, Newton (perhaps) asserts—he declines to wholeheartedly endorse the thesis—supersubstantivalism is true.17 Newton’s assertion is implausible, even to someone sympathetic to supersubstantivalism. In the first scenario, the one in which there were also dualist material objects, there was something there for God to repel away from his chosen empty region of space. Without those things, though, in what way do the chosen regions of space differ from the unchosen regions? They do not differ in their intrinsic properties, since it is no part of God’s activity (as Newton has described it) to endow the chosen regions with special intrinsic properties. Nor does God endow these regions of space with the disposition to repel each other. For I take it that two things that differ in their dispositional properties must also differ intrinsically.

Intuitively, a bar of lead does not become as fragile as glass just because a magician resolves to cast a spell causing it to shatter whenever anyone strikes it with a light blow; God, though more powerful, no more alters the dispositions of the regions of space than the magician alters the dispositions of the bar.

So the special regions differ from the ordinary ones only in their relational properties: some regions have, and others lack, the property of being chosen. Surely there must be more of a difference than this between regions which are also material objects and regions which are not. It can seem that all we have here is a world containing no material objects, only empty space, in which God has chosen to play a game with himself whereby he ‘outlines’ certain regions of space and changes which regions are outlined according to certain definite rules.18 I am not sure why Newton wanted God to do so little for the regions of space he has chosen to be material objects. Why have God merely watch over them, when God could give them the power to watch over themselves, by endowing them with certain intrinsic properties? Perhaps the following idea motivated Newton: all that That is, supersubstantivalism is true and there are material objects.

(Bennett 1984) makes a similar complaint.

really matters, when we describe a supersubstantivalist world, is how the regions interact with other things; as long as they interact in the right sort of way, it doesn’t matter what they are like ‘in themselves.’19 7 Moderate Supersubstantivalism Newton’s strategy, again, is to argue that regions of space can do all the work we need material objects to do. I object to the way he implemented this strategy: material objects do more than just prevent other material objects from occupying the regions they occupy. Let’s keep the strategy and change the implementation.

The physical theories that have been considered fundamental since Newton postulate two kinds of material objects: particles and fields. What work do particles and fields do in these theories? I will start with the particles. Particles are the primary bearers of intrinsic properties like mass and charge; and they move around.

A moderate version of supersubstantivalism can allow regions of spacetime to instantiate mass and charge. So that bit of work can be done by regions of spacetime as easily as by material objects. But what about motion? Can a region of spacetime move?

Versions of supersubstantivalism that treat space and time as separate things— like Newton’s—have trouble here. According to these versions, material particles are regions of space. Normally substantivalists say that a particle moves if it occupies different regions of space at different times. But this won’t work if particles just are regions of space; whatever sense we give ‘occupies’ in this context, a region of space cannot occupy different regions of space at different times.

This kind of supersubstantivalist might do better by adopting a relationalist account of motion: a region moves just in case its distance from some other region changes in time. But it seems impossible for regions of space to move in this sense, either: it seems necessary that the distance between any two points of space be the same at all times. There is some conceptual room to maneuver around this Something like this line of thought occurs on page 140. Others have shared Newton’s motivating idea that dispositions don’t require categorical bases— Faraday (1965) inclined toward supersubstantivalism for similar reasons, and Blackburn (1993) gives the idea a more general defense.

impossibility, but the moves aren’t attractive. I’ll mention them, just to set them aside.



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