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Substance and Individuation in Leibniz.

J. A. Cover and John O'Leary-Hawthorne, Substance and Individuation in Leibniz. Cambridge: Cambridge University Press, 1999. Pp. x, 307.

Everyone interested in Leibniz ought to read this fine, stimulating book. It is admirably written in the tradition exemplified by the references below and will especially appeal to those familiar with the analytical exposition in those works.

The first chapter effectively frames the book's canvas by outlining the young Leibniz's engagement with Scholastic controversies over individuation. The Cartesian dualism of thinking and extended substances does not have the resources to confront, the subtle issues involved. Taking thought and extension as essential has the merit of banishing forms from scientific explanations, but the mature Leibniz forcefully argued that the Cartesian essences are too abstract to yield individual substances. As usual with Leibniz, one of the interpretative difficulties is determining the degree to which he remained committed to his earliest philosophical thoughts later in his career. Must the mature Leibniz be read as vindicating a Scholastic approach to various theses, or is he instead extending and making more sophisticated a broadly Cartesian theory to the point that it can deal with important problems studied by the Scholastics, but often ignored by the Cartesians?

The second chapter is about relations. On the face of it, Leibniz clearly holds the metaphysical thesis that relations have no extra-mental reality. There is, however, a persistent strain of interpretation according to which a Leibnizian reduction of relational predicates to nonrelational ones is beset with logical difficulties. Mates argued, in effect, that these apparent difficulties arise from not carefully distinguishing predicates from properties, or as Cover and O'Leary-Hawthorne put it, one must distinguish the formal and material senses of 'predicate'. Cover and O'Leary-Hawthorne bolster Mates's account by (among other things) stressing that monads "contain" features of other monads only objectively or representationally, and not formally. Representation is a feature of perceptions that arises not from causal influx, but from pre-established harmony. It is, therefore, intrinsic in a strong sense. This means that it constitutes an appropriate basks for supervenient relational properties.

The next chapter defends a distinctive interpretation of Leibniz on modality and essence. Leibniz is often read as being a superessentialist holding that every feature of a monad is included in its complete concept and is therefore necessary to it in every philosophically interesting sense of the term 'necessary' but one. The exception is an absolute necessity whose opposite involves a contradiction. A different reading has been proposed by Sleigh (1990, chap. 4), in which Leibniz accepts superintrinsicalism while denying the stronger superessentialism. Let us gloss superintrinsicalism (alas, rather roughly) as the doctrine that if a monad--has some particular feature f, then there is no possible world in which to exists without f. Sleigh then works to characterize essential features of individual substances as those contained in a concept "leaner" than the complete concept, the concept of what is natural to the individual substance.

Cover and O'Leary-Hawthorne call Sleigh's interpretation moderate essentialism/sin and style their own strong essentialism as fining philosophical space between moderate essentialism and superessentialism. Their interpretation of Leibniz's essentialism is stronger than moderate because they both accept superintrinsicalism and agree with the superessentialist that the complete concept is strictly complete. The main problem for a superessentialist is to decouple the doctrine from a necessity incompatible with freedom. Sleigh's interpretation does this by cutting down on what is essential. Cover and O'Leary-Hawthorne rely instead on the possible world apparatus to block fatal necessity. This obliges them to attribute to Leibniz trans-world identification of monads. Most interpreters reject trans-world identity because (in effect) superintrinsicality together with a strict reading of pre-established harmony excludes it. Cover and O'Leary-Hawthorne accordingly slacken pre-established harmony. The actual world harmonizes very nicely, but other unharmonious worlds contain individuals from the actual world with their complete concepts intact.

The fourth and fifth chapters contain rich discussions of haecceitism and of Leibniz's principles of sufficient reason and of the identity of indiscernibles. The sixth chapter is an important discussion of what Leibniz meant by the "law-of-the-series" (as the authors write it) for a particular substance. Leibniz clearly meant that the law-of-the-series determines how a substance is unfolded into temporal states. But what is the ontological status of the law-of-the-series itself? The usual interpretations blandly assert that substances "have" laws or that laws are "in" substances, perhaps as dispositions (see, for example, Adams, 314-16). Cover and O'Leary-Hawthorne instead take Leibniz to be strictly identifying the law-of-the-series and the substance, and they work to elucidate that strong interpretation. Their principal suggestion is that the law-of-the-series be understood as a function--in other words, a substance is a function. The function takes total, temporary states as both arguments and values, and every state is both an argument and a value of the function. Cover and O'Leary-Hawthorne see this as setting three kinds of puzzles: about the initial state, about miracles, and about the sense in which every state contains past and future states.

The authors note various difficulties facing this interpretation and bring some ingenuity to bear in attempting to solve them. The difficulties themselves depend on a crucial assumption that is not discussed, namely that the "total temporary state" of a substance is well defined. The totality of total temporary states is no more problematic than the totality of the complete concept of a substance. But can their temporality be made precise enough to accommodate the formal structure of a function? Leibniz would not regard a state as real if its duration were merely a point in a temporal continuum, nor would he accept temporal atoms. A temporal state, therefore, must involve a temporal interval, but how long an interval? Not even God could have a sufficient reason for choosing an interval of any particular length, so something has gone wrong.

A different way to develop the identity of law-of-the-series and substance begins with the thesis that the interval of a substance's duration is continuous, and not composed of states at temporal atoms. It is a Leibnizian thesis that in a continuum, the whole is prior to the parts. This is another way of saying that a continuum is not constructed from points; on the contrary the concept of a point in a continuum or of a part of a continuum is posterior to the concept of the whole continuum, in a temporal continuum, therefore, if we attempt to identify, a particular state, this can be done only by specifying the boundaries of its temporal interval. And the boundaries will be the limits of the preceding and succeeding states of the very same whole. But those states can be specified only by specifying their other boundaries and so on. No state can be fully determinate unless the prior whole is determinate. This strategy parallels Spinoza's account (at proposition 28 of part 1 of the Ethic) of file determination of finite "things"--a full determination would require a regress ending only in infinite substance. One might object to the reading I am suggesting by noting that the temporal states of a monad are temporary perceptual states and that these are actual rather than possible. But the doctrine that in a continuum the whole is prior to the parts was understood by Leibniz to apply to what is ideal and possible, not to what is actual. The objection falls because it is the time measuring the states that is continuous. The states themselves do not resolve into other monads as intersubjective spatial phenomena do; instead the process of boundary determination resolves them into the one monad of which they are states. To summarize, any state of a monad follows from the law-of-the-series insofar as a specification of any state resolves into the whole series or the monad itself. This alternative reading is immune to problems about the first state (that is, initial condition) or asymmetry between marls and traces, etc.

The book's final chapter considers how Leibniz's system is threatened by a collapse into a single created substance. It takes some space to state the problem properly, but a simplified form of it is raised by the consideration that harmony guarantees that all the properties of all the substances in the universe are compatible. Why then shouldn't all these properties belong to a single created substance, why not a comprehensive, single law-of-the-series? The one substance threat is easily met on the whole-entity conception of substance that makes the whole prior to its states or properties. If the entire law-of-the-series is ontologically prior to its properties, then we need not worry about whether the properties aggregate into distinct, individual substances.


Adams, R. 1994. Leibniz. New York: Oxford University Press.

Mates, B. 1985. The Philosophy of Leibniz. New York: Oxford University Press.

Russell, B. 1900. A Critical Exposition of the Philosophy of Leibniz. London: Allen and Unwin.

Sleigh, R. 1990. Leibniz and Arnauld. New Haven: Yale University Press.


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Author:Nelson, Alan C.
Publication:The Philosophical Review
Article Type:Book Review
Date:Jan 1, 2004
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