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  • Leibniz's Metaphysics of Time and Space
  • Emily Grosholz
Michael Futch . Leibniz's Metaphysics of Time and Space. Boston Studies in the Philosophy of Science, 258. Dordrecht-Boston: Springer, 2008. Pp. x + 205. Cloth, $219.00.

Most discussions of Leibniz's metaphysics of time and space begin and end with the correspondence between Leibniz and Samuel Clarke, Newton's friend and defender. But Leibniz's ideas about time and space are far richer than this exchange suggests, and Michael Futch shows that the study of those investigations will enhance current discussion among philosophers and cosmologists. Futch's scholarly attention to a wide range of texts (many only edited in the last two decades) is matched by his philosophical acuity. His detailed expositions of texts are not tedious or pedantic because he never fails to bring out their philosophical interest and pertinence. So, too, the book's bibliography is especially valuable.

The book opens with a discussion of Newton's substantivalism, which treats time and space as substance-like structures that exist independent of the objects located in them, versus Leibniz's reductionism, which holds time and space to be merely relations, ontologically dependent on the things that exist: space is the order of coexistences, time the order of successions. Futch gives useful historical background that explains why the debate takes the form that it does (it is as much about God as it is about space and time) and what makes it "modern" (it marks the emergence for the first time in Western metaphysics of a sub-stantivalist account of time as well as space; for Gassendi, Barrow, and Newton all denied Aristotle's influential principle that time is ontologically dependent on change). Futch also gives a comprehensive review of the many different argumentative strategies that Leibniz uses to defend his reductionism. Some depend on the principles of sufficient reason or the identity of indiscernibles; others on his conviction that ultimate reality is composed of substances and their attributes, on Aristotle's principle redux, and on the claim that time and space are continua and therefore indeterminate entia rationis lacking the determinacy of real things.

Chapter 2 introduces a series of richly informed discussions of related issues. In chapter 3, Futch raises the (essentially modern) question of whether space and time are one, that is, whether multiple universes exist. He traces Leibniz's arguments against branching time and multiple time streams, and the possibility of disunified space, based on the vision of [End Page 246] space and time as relations among thoroughly connected compossibles. In chapter 4, he examines Leibniz's reasons for holding that space and future time are unbounded (arguments mostly stemming from the principle of perfection or the principle of plenitude), and notes that Newton's substantivalism also championed the infinity of space, but regarded the material world as finite. Leibniz debates at length, however, about whether the past is limitless. Late medieval proofs of the impossibility of infinite past time seem unconvincing to him, and ultimately, he argues that belief in a moment of genesis must rest on a demonstration that the world increases in perfection at a uniform rate. It is an idea that certainly accords with Leibniz's temperamental optimism, but the important point is that Leibniz so willingly speculates that time is infinite in both directions.

Chapter 5 presents Leibniz's view of the anisotropy of time as based on the asymmetry of causation. Temporal relations of priority are based on a logical order of priority: a concept's requisites, conditions of its possibility, are logically prior to it; the requisites of real things include their causes, and that logical priority is expressed as temporal succession. Thus, for Leibniz, a monad's location in time is determined by the relations of its organic body to other organic bodies, relations that are in turn referred to causal relations. This means that, for Leibniz, time is strictly linear, and the alleged metaphysical possibility of circular time is rejected.

In the last chapters of the book, Futch argues that Leibniz's conception of monads is essentially atemporal and that his God is radically transcendent. Futch writes, in §7.3.2, that "the temporal ordering...

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