Four Themes in Leibniz’s Disputatio Metaphysica de Principio Individui (1663): Cover and O’Leary-Hawthorne’s Substance and Individuation in Leibniz, Chapter 1 §3.1


In §3 of Chapter 1 of their Substance and Individuation in Leibniz, Cover and O’Leary-Hawthorne provide us with a brief overview of the early Leibniz of the Metaphysical Disputations of the Principle of Individuation (1663).[1]  The authors’ presentation is quite technical and assumes a lot of prior knowledge of scholastic issues about this topic.  Nevertheless, the detail is crucial for having an accurate understanding of Leibniz’s early work and so here, I will begin trying to work through the difficulty it presents for those readers who are perhaps not as lettered in these topics as the authors expect.  I will here concentrate upon §3.1, perhaps addressing the latter sections of this paragraph in subsequent posts.

In §3.1, the authors present four themes from Leibniz’s early work.  But before they present these four themes, they provide us with the delimitation of Leibniz’s problematic in the Disputatio in terms of four issues (26-28).  First, they indicate that unlike other approaches to the topic, Leibniz is mostly concerned with providing an account of the indivisibility or (incommunicability) and numerical difference of individuals.  He leaves out of consideration a reflection upon traditional Aristotelian topics associated with this theme, like identity through change or impredicability.  Second, Leibniz is mostly concerned with individual substance itself, leaving to the side a consideration of accidents.  Also, he takes the path of Scotus, unlike that of Thomas, in abstracting away from differences of individuation for created material and immaterial beings.  He concentrates upon what is the same in all processes of individuation.  Third, Leibniz is offering a metaphysical account, not a epistemological or linguistic account.  The fourth delimitation is the same as the first general theme that the authors present.

First Theme: Internal Individuation

The first theme is that for Leibniz the principle of individuation is internal to the individual, not external.  The authors write, “It is absolutely fundamental to Leibniz’s thinking on individuation that whatever individuates a substance must be something wholly internal to that substance itself” (28).  Leibniz is seeking an internal principle of individuation.  The authors point to the intuitive basis of this reasoning:

Consider some bona fide existing individual substance.  That substance would it seems be the very individual it is even were it alone in the world.  Take that idea seriously and it immediately becomes impermissible to bring in individuators of a substance that involve relation, or that make reference to other substances—indeed, even a relation of numerical difference to other things (29).

So, because we can imagine a certain individual existing all by itself in another universe, this suggests that what individuates a thing is internal to it and not based upon its relations with other things.

This raises a question for me that has to do with an issue that the authors themselves raise, which they address in fn. 24, but in such a short manner, that I’m not sure I understand their defence of Leibniz’s position.  Before they defend Leibniz they point out that within the context of contemporary metaphysics, this intuitive argument may not be embraced.  They point to Kripke’s idea that an origin story is necessary for corporeal substance (e.g., sperm and egg for a living mammal; hunks of matter for material artifacts, etc.).  I imagine this Kripkean viewpoint would be in sync with relationalist viewpoints on individuality (Whitehead, Simondon, Latour, Ingold, and any other material ontologist that takes causal relations to be necessary for individuation).  On this view, I think such people might object to this imaginative presentation of the lone-existing thing.   After all, is not the thing we take to be a thing itself only the result (even if a non-reducible, emergent result) of its relations with others?  In other words, if we take away these relations that have constituted the thing as it is, then are we not left without a thing that we can then imaginatively transport into another universe, where it itself exists alone?  For instance, if we took away the constitutive relations that have generated a brick (the brickmaker, the materials which he used to make the brick, not to mention the purpose it serves or the meaning it has in a human context), then are we not left with nothing, since the brick is itself existentially or ontologically constituted by these relations?

Yet, although this line of reasoning does seems fair to me, I also wonder if the original lone object universe nevertheless remains a sound form of argumentation.  There seems to be nothing essentially contradictory or implausible about a lone existing brick universe—where there is only one brick that is the universe itself.  Why is this universe less plausible than the existence of our universe?  I imagine it is only because we assume the relations that constitute the brick in our universe (the brickmaker and his materials, etc.) and so use them as rules to be imposed upon another universe.  However, in another universe, a brick may be the kind of thing that spontaneously emerges.  This would be equivalent to the spontaneous and non-explicable emergence of energy and matter in our own universe (e.g., the big bang).  There is much need here for further research, including (most importantly) the logic and rules of possible worlds argumentation, research that I intend to continue into the future.

Second Theme: Numerical Unity

The second theme that the authors identify in the early Leibniz is that “metaphysical unity must be explained in terms of numerical unity” (29).    Leibniz’s main concern is to reject the idea that numerical unity is just a species of a more fundamental genus of unity.  The authors write, “his point is to reject pictures according to which some common entity, having less than numerical unity, combines with an individuator or contracting difference to yield a singular individual enjoying numerical unity” (30).  It seems that Scotistic common nature and haecceity are the main targets here.  The authors here present a brief description of Leibniz’s views on specific unity, arguing that his is a “qualified Saurezian nominalism” (31).  In short, the universal or common is merely an abstraction in the intellect from individual, singular substances in the order of the real.  Here the authors quote Leibniz, framing this quote as a fundamental rejection of the Scotist position: “since ‘there are no universals before the operation of the mind, there is no composition from the universal and the individuating principle…There is no real composition, not all of whose members are real'” (31).  In other words, the common nature is not one real thing that enters into combination with another real thing (an individuating principle), resulting in a real individual.

Third Theme: Nominalism

The third theme the authors identify is Leibniz’s nominalist view on universals.  For Leibniz, universals are not something real in things, existing independently of the intellect.  This view comes out most forcefully in his critique of Scotus’ approach.  Scotus understood a thing’s common nature as a real entity, one that was indifferent to its instantiation in this or that particular.  Thus, it could not serve as the principle of individuation.  Scotus therefore needed some other entity to provide this individuating difference; namely, his haecceity.  Leibniz rejects this view on the basis of the principle of separability, in which “whatever things differ before the operation of the mind are separable…” (32/§23).  To be honest, I haven’t quite figured out this argument and so I won’t elaborate upon it at this point.  What is more interesting to me is the flip side of this thesis: that just because Leibniz rejects the real nature of essences (as things separable from individuals), he does not reject “recognizing in individuals real natures” (33).  The authors write, “for Leibniz, as for Saurez, the nature in Socrates is individual to Socrates himself…a nature that, Leibniz goes on to say, is not ‘indifferent’ [cf. Scotus] to being determined as a nature of Socrates or of Plato or of someone else, indeed a ‘nature of Socrates [which] individuates itself” (ibid.).  It is here that the authors identify the core thesis of Leibniz’s Disupatio:

And for Leibniz that claim of self-individuation is in fact the core thesis of the Disputatio itself: ‘every individual is individuated by its whole entity’ (§4).  Since ‘one adds nothing to being,’ that by means of which a thing is one in number is that by means of which it is (§5)—that is, self individuated natures are individuated singlular substances” (33).

The authors hold that it is in this sense that one should understand Leibniz’s refusal to distinguish between essence and existence as separate aspects of a substance later in the Disputatio.

Fourth Theme: Rejection of Formal Distinctions

The fourth theme that the authors identify is Leibniz’s rejection of the idea of formal distinctions.  In the scholastic period, some held that there was an intermediate distinction between a real distinction (one actually occurring in the world) and a purely conceptual distinction (one not reflected in the world, but the result of an operation of the mind).  This intermediate distinction was called a formal distinction.  For example, the authors point to the tendency to think of God as a simple (non-composite) substance, but nevertheless the desire to make distinctions within his otherwise simple nature (such as between his justice and his mercy).  This is not a real distinction, since otherwise God would be a composite substance, nor is it a purely mental distinction, since God’s justice and mercy are in fact (so they would think) ‘real’ aspects of God.

In contrast to this position, Leibniz wanted only to retain real distinctions and mental distinctions.  On the one hand, the real distinction is that which holds between a real separability between thing and thing.  They quote Leibniz: “everything that before the operation of the mind really differs from another, such that neither is part of the other either wholly or partly, can be separated from the other” (36/§23).  On the other hand, the mental or rational distinction is made by the mind but does not map onto any really seperated things.  However, the authors point out that this does not mean that for Leibniz these rational distinctions are pure fictions.  Rather, Leibniz is “allowing that certain distinctions not mapping onto real distinctions in the world are nevertheless proper for the intellect to make” (36).  The authors say that Leibniz follows Saurez on this point, who marked out the distinction between the “purely fictional” and the “proper” with his distinction between the ‘reasoning reason’ and the ‘reasoned reason.’  The former refers to a distinction produced (in the generative sense) by the mind, while the latter refers to a “pre-existing reality, before the discriminating operation of the intellect, and only requires the intellect to recognize it, but not to constitute it [in the generative sense]…[I]t does not arise entirely from the mere operation of the intellect, but rather from the occasion offered by the thing itself, on which the mind is reflecting” (37).   Nevertheless, although Leibniz allows this, the only distinction he allows in terms of the world itself is the real distinction.  One of his motivations for holding this is so that he can argue that nothing constituted in relation to the intellect can itself be a principle of individuation; instead, the principle of individuation must arise from really distinct things themselves.

[1] Cover, J.A.; John O’Leary-Hawthorne, Substance and Individuation in Leibniz, (New York: Cambridge University Press, 1999).

PicCred: Becky Comber


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