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8 Modern Space as Relative Locke and Leibniz Our Idea of Place is nothing else, but such a relative Position of any thing. -John Locke, An Essay Concerning Human Understanding Men fancy places, traces, and spaces, though these things consist only in the truth of relations and not at all in any absolute reality. -Gottfried Wilhelm Leibniz, Fifth Paper in Reply to Clarke All our knowledge, both of time and place, is essentially relative. -James Clerk Maxwell, Matter and Motion We have just witnessed a revealing vacillation-by no means the first we have encountered-between an absolutist and a relativist conception of space: between the view that space is one vast (and usually empty) arena and the alternative view that it consists entirely in relations between things. Descartes, in attempting to do justice to both conceptions by his distinction between internal and external place, ends by doing justice to neither. His compromise is as unsatisfying as were earlier middle-ground solutions to the problem of the void (e.g., the idea of the world as a finite plenary presence surrounded by an infinite vacuum). All such compromises, after all, only hold together provisionally what is already available as a definite choice. Where Gassendi and Newton made outright decisions to regard space (and, a fortiori, place) as 162 Modern Space as Relative 163 absolute, Descartes clings both to absolutism in his notion of space as internal place and to relativism in his description of external place. Only with regard to the void is he unhesitatingly decisive, vehemently rejecting voidness in favor of an infinitely divisible and nonlacunary material plenum. In this regard he is to be joined by Gottfried Wilhelm Leibniz, who also argues for a comparably dense plenum, albeit on very different grounds. But it will take the single-mindedness of Leibniz to espouse, in a wholly uncompromising way, the idea that space and place alike are altogether relative in their constitution. Leibniz is anticipated in this last respect by John Locke, whose Essay Concerning Human Understanding appeared in 1690, almost half a century after the publication of Descartes's Principles ofPhilosophy and twenty-five years before the Leibniz-Clarke correspondence took place. Locke's treatment of place and space begins with a concerted critique of Descartes, especially the latter's effort to make corporeality and spatiality strictly equivalent. "Space is not body," underlines Locke in the Essay, "because it includes not the Idea of Solidity in it." 1 Solidity-the resistance or impenetrability of a physical body-cannot be reduced to Extension, which "includes no Solidity, nor resistance to the Motion of Body."2 Space is as distinct from Solidity as Thought from Extension. Hoisting Descartes on the petard of his own criterion of conceivability , Locke declares that "there is no necessary connexion between Space and Solidity, since we can conceive one without the other.,,3 And if solidity-that is, the primary predicate of "matter"-has no conceptual or intrinsic tie to space, space itself is free to be the occasion of occupation by virtually anything, including nothing. We arrive thus at what Locke likes to call "pure Space," that is, space that has no preordained constituency.4 On the Lockean account, the simple idea of such empty, open space has three modifications, three "simple modes": "capacity" or sheer volume; "figure ," or the relation between the extremities of a body; and "distance," which is the space between two or more bodies.5 Distance is the crucial dimension so far as place is concerned. It is said to be "Space considered barely in length between any two Beings, without considering any thing else between them." 6 Descartes's emphasis on the volumetric-an emphasis that enabled him to assimilate space to matter, both possessing a common tridimensional axiality-gives way in Locke to a stress on the unidimensional factor of distance or length. For he holds this factor to be determinative of place (as also of time).7 As distance is a modification of space, place is in turn a modification of distance. It is indeed a very particular modification, leading Locke to formulate one of the most structurally specific theories of place we have yet encountered. As in simple Space, we consider the relation of Distance between any two Bodies , or Points; so in our Idea of Place, we consider the relation of Distance betwixt any thing, and any two or more Points, which are considered, as keeping 164 The Supremacy of Space the same distance one...

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