Version: v1, Published online: 1998
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4. Metaphysics: substance, monad and the problem of the continuum
Leibniz is famous for his claim that he solved the problem of the composition of the continuum. In so far as the continuum (length, area, volume) is divisible, it would seem to be made up out of parts. But what parts could make it up? If the parts are extended (like atoms), then they too are divisible, and we require an account of their composition as well. On the other hand, if the parts are non-extended (like points), then it is difficult to see how they could make up an extended magnitude. Leibniz’s solution was this: the mathematical continuum should not be thought of as being composed of parts at all; while it has parts, those parts are the result of the division of the whole, and thus are posterior to it. On the other hand, Leibniz claimed, while real physical extensions have parts, there are no physical continua. Physical extended things are at root discrete multitudes whose constituents are substances (‘Remarques sur les Objections de M. Foucher’ (Remarks on the objections of M. Foucher) (1696); (Leibniz to de Volder, 19 January 1706). This raises one of the central problems for Leibniz’s philosophy: what are these substances that constitute the metaphysically ultimate constituents of the world?
While there are many paths into his views on substance, Leibniz’s critique of Descartes’ notion of corporeal substance is a convenient starting place. Descartes held that the essence of body is extension. What this meant is that bodies are geometrical objects made concrete, entities that have no properties that are not grounded in extension. Colour, taste, sound and so on are not themselves in bodies, but are only sensations in minds caused by our interaction with extended substances. While Leibniz as a mechanist agreed with this last claim, he rejected the Cartesian conception of body on which it is based (see Descartes, R. §§8, 11).
Leibniz offered a number of arguments against the Cartesian conception of bodily substance: (1) The notion of extension presupposes some quality that is extended, like whiteness in milk or resistance to new motion in every body, and so is not the kind of thing that by itself could constitute the essence of anything (Leibniz to de Volder, 30 June 1704; ‘Note on Cartesian natural philosophy’, 1702). (2) In so far as extended things are divisible, they are aggregates made up out of parts. But the reality of the aggregate presupposes some genuine individuals of which the aggregate is composed; no such individuals can be found in Cartesian bodies (Leibniz to Arnauld, 30 April 1687; Monadology §§1–3). (3) If the world is full and there are no vacua, and if the world is filled with Cartesian extended substance, then there can be no change in the world. For any supposed change would consist in one portion of body replacing another, identical in every way (‘On nature itself’). (4) If body were just extension, then it would be perfectly inert, and would have to be moved by God. If so, then God’s creation would be imperfect for lacking creatures which cannot themselves carry out any of God’s commands. Indeed, such a world would reduce to Spinoza’s world in which finite things are just modes of God (‘On nature itself’). Because of arguments like these, Leibniz wanted to take the Cartesian mechanist analysis of body back one step further, and resolve even extension into something more basic still, a world of substances that are genuinely individual, genuinely active, and which contain properties that distinguish individual substances from one another.
While there are a number of important discussions of the nature of substance in Leibniz’s writings, two are especially noteworthy: the one he gave in the Discourse on Metaphysics at the start of his mature period, and the one he gave at the very end of his life in the Monadology. (There is a third important conception of substance that arises in the dynamical writings, discussed below in connection with his physics.)
Leibniz begins Section 8 of the Discourse on Metaphysics by noting that ‘it is evident that all true predication has some basis in the nature of things, and that, when a proposition is not an identity, that is, when the predicate is not explicitly contained in the subject, it must be contained in it virtually’. (This principle, which probably derived from Leibniz’s logical studies a few years earlier, was closely connected with the Principle of Sufficient Reason in Leibniz’s mind; the containment of the concept of the predicate in the concept of the subject constitutes the ‘sufficient reason’ for the truth of a proposition. This connection with his logic has caused some commentators to see Leibniz’s metaphysics as fundamentally logical in its inspiration.) And so, Leibniz claims, ‘the subject term must always contain the predicate term, so that one who understands perfectly the notion of the subject would also know that the predicate belongs to it’. He concludes that ‘the nature of an individual substance or of a complete being is to have a notion so complete that it is sufficient to contain and to allow us to deduce from it all the predicates of the subject to which this notion is to be attributed’. Since he held that there must be something in the substance itself in virtue of which this complete notion holds of it, he also concludes that at any given time, a substance must contain marks and traces of everything that is true of it, past, present and future – though only God could see them all. (It is not clear whether this committed Leibniz to holding that all properties of a given individual are essential to that individual, making him a kind of ‘superessentialist’, or whether he takes the weaker position that they are merely internal to the individual, making him a ‘superintrinsicalist’. Opinions differ among the commentators.)
In the Monadology Leibniz offers a somewhat different characterization of substance. Using the term ‘monad’ that he adopted to express the notion of an individual substance in the late 1690s, he expounds: ‘The monad…is nothing but a simple substance that enters into composites – simple, that is, without parts. And there must be simple substances, since there are composites; for the composite is nothing more than a collection, or aggregate, of simples. But where there are no parts, neither extension, nor shape, nor divisibility is possible. These monads are the true atoms of nature and, in brief, the elements of things’ (Monadology §§1–3). So understood, the Leibnizian world is grounded in non-extended simple substances, whose principal property is non-divisibility and thus, Leibniz inferred, non-extension.
From these basic characterizations of the individual or simple substance (what Leibniz called a ‘monad’ after the mid-1690s), he inferred a number of important properties. The individual substance or monad is a genuine unity that cannot be split, something explicit in the Monadology account, less so on the earlier account in the Discourse. Consequently, it can begin only by divine creation, and can end only with divine annihilation; it is naturally ungenerable and incorruptible. On both accounts, individual substances or monads are the sources of all their activity, and cannot be altered or changed by the direct action of others; it is in this sense that Leibniz said that ‘monads have no windows through which something can enter or leave’ (Monadology §7). In the Discourse he derives this from the fact that a substance contains within itself all of the grounds of all its properties; there is no need – and no room – for any external causality. In the Monadology it is derived directly from the fact that monads are non-extended. The apparent action of one substance on another must be analysed in terms of the relations between the internal states of the one and the internal states of the other (as discussed below). Finally, because of the relations that hold between one substance and another, Leibniz argued that each individual substance or monad reflects the entire world of which it is a part, a thesis closely connected with the hypothesis of pre-established harmony (also discussed below). Though all the individual substances reflect the same one world, they each reflect it from a different point of view, adding the perfection of variety to God’s creation (Discourse §§9, 15; Monadology §§4–7). This conception of harmony can be traced back to the Paris period and, perhaps, to Leibniz’s earliest writings on physics.
On Leibniz’s view, substances are distinguished from one another by their momentary perceptions, and by the appetitions, the internal source of a substance’s activity that lead from one perceptual state to another. In so far as a substance has such appetitions, ‘the present is pregnant with the future’ (Monadology §22). Since there can be no external influences, each monad is created by God with a kind of internal programme, as it were, which determines all of the states that it will take and the order in which it will take them. Although the Cartesian soul is an important model for the individual substance (Leibniz to de Volder, c.1699), there are significant differences. While the momentary states are called perceptions, not all such perceptions are conscious. (Conscious perceptions are said to be ‘apperceptions’ in Leibniz’s terminology, though because nature makes no leaps in this best of all possible worlds, there must be a continuous gradation between the unconscious and the conscious.) In scholastic thought, appetition is the general faculty that leads to change in a substance, of which will (or rational appetite) is a special case in rational souls. For Leibniz, too, not all appetition is rational. For these reasons, he distinguished carefully between rational souls, like ours, and monads with lesser degrees of consciousness and rationality – what he sometimes calls ‘bare monads’ (Monadology §§8–24).
Garber, Daniel. Metaphysics: substance, monad and the problem of the continuum. Leibniz, Gottfried Wilhelm (1646–1716), 1998, doi:10.4324/9780415249126-DA052-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/biographical/leibniz-gottfried-wilhelm-1646-1716/v-1/sections/metaphysics-substance-monad-and-the-problem-of-the-continuum.
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