Objects and Persistence
Physics & Metaphysics Handout 7
H.S. Hestevold Spring 2014
ON THE ROAD TO NOWHERE: A DEFENSE OF SPACELESSNESS
Abstract:This is a draft of a defense of a Leibnizian relationalist theory of space. By embracing absolute directional relations, one can both reduce talk about spatial locations to talk about relations, and one can also offer plausible objections to the standard arguments for absolute space, preserving commonsense intuitions about movement and spatial orientation.
I.Introduction
In a rich exchange of letters, Samuel Clark defended Newton's theory of absolute space against Leibniz's relational theory of space.[1]Clark argued that space is among the things that exist and that every particular physical object occupies a particular place a particular region of space. To say of an object that it moves is to say of the object that it occupies different places at different times. Leibniz objected, charging that, strictly, there is no such entity as space. Instead, talk about an object's spatial location can be reduced to talk about the spatial relations that the object bears to other objects.After all, notes Leibniz, one can reduce talk about the place a certain person occupies in a genealogical line to talk about family relations: to say that there is a family line in which Elsie holds the place of both mother and daughter is to say that there are at least two people such that Elsie is the daughter of one and the mother of the other.[2] Similarly, then, to say that an object moves from one place to another is to say nothing more than that the distance relations that an object bears to other objects at one time are not the same distance relations that the objects to those objects at a later time.
Clarke raises several plausible objections to the relational theory, arguing that Leibniz's view fails to preserve certain deep-seated intuitions about motion and spatial orientation. Leibniz defends his relational view by, in short, rejecting the intuitions. In this paper, I sketch a modified relational theory of space and argue that, unlike Leibniz's view, it can preserve Clarke's intuitions about space.
II.Absolute directional relations.
For the sake of explicating the concept of an absolute directional relation and developing the relational theory of space, assume that protons, cells, rocks, tables, planets, and other such three-dimensionally extended objects are wholes constituted by simples physical particulars that lack proper parts.[3]
I assume that there are infinitely many (absolute) directional relations such that, for any two simples, there exists a unique directional relation call it “is to d19 of” such that one simple bears the relationis to d19 ofto the other simple.
Consider a thought experiment intended to clarify the commitment to infinitely many absolute directional relations. Suppose that there is a materially dense basketballlike sphere that is composed of indefinitely many material simples arranged onesimple thick.Inside the otherwise hollow sphere is a single simple C in the center of the sphere. For any simple S’ that is part of the sphere’s surface, there is some directional relation dN and some third simple S’’ such that S isdN to C and C is dN to S’’. If there is any rotation or lateral movement of the sphere, then S would no longer bearis dN to to C and C would no longer bear is dN to to S’’. If one rotates the sphere exactly 180° around an axis, then S'' would bearis dN to to C and C would bear is dN to to S’.
The following axioms may serve to characterize absolute directional relations:
ST1 For any simplesx and y and directional relation is dN to, if x is dN to y or y is dN to x, thenx ‡ y.
ST2 For any simplesx and y and directional relation is dN to, if x is dN to y, then y is not dN to x.
ST3 For any three simplesx, y and z and for any directional relation is dN to, if x is dN to y and ify is dN to z, then x is dN to z.
ST4 For any two simplesx and y, and for any directional relation is dN to, if x is dN to yat time t1, then it is possible thaty is dN to x at time other than t1.
III.Spacelessness
My hope is that embracing absolute directional relations allows one a defense of spacelessness the rejection of Newton's absolute space:
SP It is false that there exist spatial locations; and all talk of space and spatial locations can be reduced to talk about spatial directional relations.
Consider now how fundamental intuitions about spatial locations can be preserved in terms of absolute directional relations.
IV.Spatial location
Without absolute space, then spatially locating a three-dimensional entity will involve specifying a special set of directional relations that the object's simple parts involve:
D1 The directional relation is dN to is exhibited by material objectx =Df Either (i) there exist a y and z such that y and z are simple parts of x, and yis dN toz or zis dN to y, or (ii) there exist simples y and z such that y but not z is a part of x, and yis dN to z or zis dN toy.
D2 N is the spatial location of material entity x at time t =Df N is the set of all and only those directional relations exhibited by x at t.
V.Reducing place-talk to talk of directional relations.
Talk of places and empty space can likewise be reduced to talk about directional relations:
1. The place occupied earlier by Rowan’s car is the place now occupied by Blair’s car.
Reduction: The spatial location of Rowan’s car at an earlier time is identical with the spatial location of Blair’s car at the present time.
2. There is today a region of empty space as big as the Moon.
Reduction: There is a set E of directional relations such that (i) it is possible that E is the spatial location of a Moonsized object and (ii) for any three directional relations that are members of E, it is today false than any entity bears those relations simultaneously to other entities.
VI.The suppose-everything-moves defense of absolute space
The suppose-everything-moves defense of absolute space is this: “It is at least possible that every existing object moves at the same velocity in the same direction. For example, if there exists nothing more than a formation of four blocks, it is possible that the blocks all move in the same direction at a uniform velocity retaining their formation. If there is no absolute space, however, there is no difference between the formation at rest and the formation in motion: the spatial relations among the blocks don’t change as they move through space.”
Directional relations provide an objection to this defense of absolute space. When the formation of blocks is at rest, there is a simple part of one block that bears a certain absolute direction relation is dN to to a simple part of another block. As the entire formation of blocks moves at all, the former simple part ceases to bear is dN to to latter simple part.Thus, the directional relations that a formation of blocks exhibits do change as the formation moves uniformly, and this preserves the Newtonian intuition that there is a real difference between a formation of blocks at rest and the formation of blocks in motion.
VII.The suppose-everything-doubles defense of absolute space
The suppose-everything-moves defense of absolute space is this: “It is at least possible that every existing object doubles in size regardless of whether one could ever verify this. (After all, if everything doubles, then yardsticks and tape measures would double as well.) Such doubling is possible, however, only if absolute space exists: without absolute space, there would be no benchmark of any type relative to which all entities would have doubled; one could not insist that the objects occupy twice as much space after doubling! The Leibnizian cannot preserve the possibility that all objects double: there would be no relational differencebetween the objects before the doubling and the objects after the doubling."
In terms of absolute directional relations, there would be relational differences between the actual universe and the doubled-in-size universe. Imagine an actual cube. There exists a certain directional relation is dN*to that thesimple part C1 at the upperleft corner bears to simple part C2 at the lower-left corner. If the cube doubles in size in all directions, then, as the cube expands to the left and right and up and down, C1 and C2 will move to the left and thereby immediately cease to bear the directional relation is dN*to to one another. Of course, there may be other “inner” simple parts of the cube that come to bear that relation to one another as those parts move to the left with the cube's expansion.
VIII.The mirrorimage defense of absolute space
The mirror-image defense of absolute space is this: “It is at least possible that the material world had existed instead as a mirror image of itself that the spatial ordering of existing material entities had simply been reversed. This, however, is a possible state of affairs only if absolute space exists. Therelational spatial array of the material objects in the two possible worlds is identical; so, unless absolute space exists relative to which one can say that the location of the Space Needle and Empire State Building differ in the two worlds, there could not possibly be any difference between the two worlds, and the mirrorimage world would not be a possibility after all.”
The concept of a spatial location cast in terms of absolute directional relations allows an objection to the mirror-image defense of absolute space: the Space Needle’s spatial location in the actual world is other than its spatial location in the mirror-image world. With respect to the current Needle, there is a directional relation that a simple spirepart S and simple basepart B now bear to one another. If, however, the Space Needle’s orientation were flipped in the mirror-image universe, then S and B would not now bear that directional relation to one another. (Of course, there could be simple parts of the Empire State building that would bear that directional relation to one another.)
IX.Summary
Ontological simplicity is a mark in favor of absolute spatial relations: by admitting that the relations that exist include absolute directional relations, one can reduce claims that apparently imply the existence of spatial locations to claims that clearly do not imply the existence of spatial locations. Second, postulating absolute spatial relations allows one to block the standard arguments for the existence of absolute space.These points suggest that one who embraces absolute spatial relations is well down the road to nowhere.
X.Appendix: for further thought
A.Study Question. I am unhappy that I have relied on simples to explicate the concept of an absolute spatial relation. (And I would not be much happier if instead I had relied on Brentanoesque zero-dimensional constituents of materially dense three-dimensional wholes.)If I can reformulate the view without reference to nonthreedimensional entities, this would be yet a further mark in favor of spacelessness.
B.Study Question. Exactly, to what view am I committed regarding chirality? Am I an internalist or externalist? van Cleve argues that the logical possibility of four-dimensional space would pose a problem for internalists. If I am some type of internalist, does my view force me to take a stand with respect to the logical possibility of four-dimensional space or can I sidestep that issue? If I am committed to externalism, is my view subject to van Cleve's "fall-of-parity" objection? Does my view allow me to agree with Kant that it is logically possible that there exists nothing but a left hand?
H. Scott Hestevold
Department of Philosophy
The University of Alabama
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[1]The Leibniz-Clarke Correspondence ed. by H.G. Alexander (Manchester and New York: Manchester University Press, 1956).
[2] Fifth Paper, The Leibniz-Clarke Correspondence.
[3] See Peter van Inwagen, Material Beings (Ithaca: Cornell University Press, 1990) and Trenton Merricks, Objects and Persons (Oxford University Press, 2003). No stand is taken here on whether such wholes must be "clouds" composed of a finite number of simples or whether they could be materially dense three-dimensional objects composed of indefinitely many simples. Instead of casting this view in terms of simples, it could be cast in terms of zero-dimensional constituents -- "point boundaries" of three-dimensional wholes; for a defense of this Brentano-esque view, see [deleted for blind review].