Leibniz's Criticisms of Matter

Matter & Mechanism

The view of the material world for which Descartes and Locke both argue was incredibly influential, both for the growth of natural science, and for the conception of the human being as a member of the natural world. G.W.F. Leibniz, while sympathetic to aspects of the mechanical system, particularly its attempt to offer explanations in natural philosophy based on a small set of resources (the features of material body) and appeal to a limited set of laws (the laws of motion), nevertheless was extremely critical of both materialism and those aspects of mechanistic explanation realiant upon it. Here we’ll look at the central features of the theory of matter which Leibniz criticizes, as well as basic elements of his positive theory.

Mechanism is the explanatory thesis that the natural world in all its diversity can be explained solely by a small set of features of bodies (size, shape, motion, and solidity) plus laws of nature governing their interaction. This explanatory claim often went along with another claim concerning the nature of body—viz., that body should be understood as a substance existing independently of mind, and either understood as the substantial minds (if one were inclined to Materialism), or as a kind of substance distinct from and intelligible independently of mind or mental substance (as a Cartesian dualist would claim).

A question that immediately arises concerning material substance, understood as essentially extended in space, is whether it is infinitely divisible or only divisible to some finite degree or level. The notion of ‘divisible’ that is relevant here is not one concerned with divisibility in practice – i.e. whether someone could actually infinitely divide a chunk of matter, but rather divisibility in principle – i.e. whether the nature of matter itself admits of infinite or only finite divisibility. We’ll see that Leibniz denies that either a finitist or an infinitist answer is metaphysically satisfactory, and uses this as a motivation for constructing his idealist metaphysics.

Leibniz Against Matter

Leibniz articulated a variety of criticisms concerning the prevailing notion of matter amongst the scientifically minded intelligentsia of the seventeenth century. We’ll look at two criticisms—first, his criticism of Descartes’s claim that material bodies are independent substances, and second his criticism of the ultimate reality of matter.

Matter is not a Substance

Recall that in Descartes’s metaphysical system, the world consisted of two kinds of thing, material substance and mental substance. As substances, material bodies and minds are supposed to be individual subsistant things that depend on nothing else for their existence (nothing, except God, at any rate).

By substance we can understand nothing other than a thing which exists in such a way as to depend on no other thing for its existence. And there is only one substance which can be understood to depend on no other thing whatsoever, namely God. (Principles 1.51)

Thus, for Descartes a material substance and a mind are both individual and independent kinds of thing.

Leibniz insists not only on the independence requirement that Descartes articulates, but also that there must be unity to an individual substance such that there is some account of its status as one (as opposed to many) thing. Leibniz emphasizes this point clearly in the New System:

after much reflection, I perceived that it is impossible to find the principles of a true unity in matter alone, or in what is only passive, since everything in it is only a collection or aggregation of parts to infinity. Now, a multitude can derive its reality only from true unities, which have some other origin and are considerably different from mathematical points which are only the extremities and modifications of extension, which all agree cannot make up the continuum. Therefore, in order to find these real entities I was forced to have recourse to a formal atom, since a material thing cannot be both material and, at the same time, perfectly indivisible, that is, endowed with a true unity. (p. 139)

Leibniz argues here that the ‘true unity’ required to attribute to matter the status of substance (as thus as recognizing individual material bodies as substances) cannot be found in matter itself. Essential to Leibniz’s argument here is his distinction between a mere collection or aggregate and a genuine unity. Later in the New System Leibniz claims that a mere collection or aggregate could never be a unity.

Such a unity could not occur in the machines made by a craftsman or in a simple mass of matter, however organized it may be; such a mass can only be considered as an army or a herd, or a pond full of fish, or like a watch composed of springs and wheels. Yet if there were no true substantial unities, there would be nothing substantial or real in the collection (142)

Leibniz’s point is that however organized an army or flock of birds may be, neither the army nor the flock is anything above and beyond its parts—it is merely an aggregate. Since there is nothing to an aggregate individual beyond its parts—in Leibniz’s terms, there is no principle of unity for the aggregate (though perhaps Leibniz would change his mind if he knew about the murmurations of starlings)—i.e. there is no sense in which the whole aggregate is independent in the way required for it to be a substance.

The obvious move here is to say that some material bodies are indivisible unities—viz., atoms. Leibniz anticipates this with his claim that “what is material can’t at the same time be perfectly indivisible.” But this isn’t, of itself, a convincing argument that Leibniz offers since it is simply the denial of the atomist’s thesis that some material bodies are indivisible. The atomist claims that there is a kind of “ground floor” of materiality, where there are material bodies—atoms—without any parts. Leibniz, however, does provide something in the way of an argument against this.

if there were no true substantial unities, there would be nothing substantial or real in the collection. That was what forced Cordemoy to abandon Descartes and to embrace the Democritean doctrine of atoms in order to find a true unity. But atoms of matter are contrary to reason. Furthermore, they are still composed of parts, since the invincible attachment of one part to another (if we can reasonably conceive or assume this) would not eliminate diversity of those parts. There are only atoms of substance, that is, real unities absolutely destitute of parts, which are the source of actions, the first absolute principles of the composition of things, and, as it were, the final elements in the analysis of substantial things. We could call them metaphysical points: they have something vital, a kind of perception, and mathematical points are the points of view from which they express the universe. But when corporeal substances are contracted, all their organs together constitute only a physical point relative to us. Thus physical points are indivisible only in appearance; mathematical points are exact, but they are merely modalities. Only metaphysical points or points of substance (constituted by forms or souls) are exact and real, and without them there would be nothing real, since without true unities there would be no multitude. (142)

Leibniz claims several things here. First, he argues that the notion of a material atom is “contrary to reason.” Why would that be? One of Leibniz’s fundamental intellectual commitments is to what he calls the “Principle of Sufficient Reason” (PSR). The PSR states that everything that exists must have an intelligible ground for its existence. Put another way, every fact or entity must have an explanation.

Leibniz’s claim that atoms of matter are contrary to reason, then, is equivalent to the claim that their existence would violate the PSR. Leibniz’s idea here is that the existence of an material atom would mean the existence of an extended being that was not divisible. But Leibniz thinks that it is either arbitrary or it is simply a contradiction to claim that an extended being is not divisible. This is because extended beings are extended in space, and just as it is always mathematically possible to divide the space that an object occupies into further spaces, so too should it be possible to divide the object itself into further parts, each of which is an occupant of this space. This was particularly true of those, like Descartes, who thought of material extension as identical with spatial extension (i.e. that there was no distinction between matter and the space that it occupies). To argue, as the atomist does, that some material bodies are indivisible, is to assert that there is an arbitrary stopping point in the cycle of division, an arbitrariness that goes against the PSR.

Leibniz also provides a second argument against the idea that atoms are genuine unities.

[atoms] are still composed of parts, since the invincible attachment of one part to another (if we can reasonably conceive or assume this) would not eliminate diversity of those parts. (142)

Here his argument again appeals to the claim that things extended in space are going to have parts, presumably corresponding to the different parts of space that they occupy. Leibniz argues that the indivisibility of an atom (assuming, for the sake of argument, that it is indivisible) is not enough to show that it lacks parts. The idea here seems to be that even if the attachment of one part to another were “invincible”, stil, by virtue of the fact that the being occupies space, and thus has different regions in each part of space, it is thereby composed of a plurality of parts. If the atomist then admits the existence of such parts then Leibniz can appeal to his first argument as given above. Things with parts are dependent on their parts and thus are not independent in the way required of substantial unities. They are, in Leibniz’s terms, ‘accidental’ rather than ‘real’ unities.

Matter is not Ultimately Real

If Leibniz’s arguments against the substantial status of matter are successful then they show that matter is not to be understood as an ultimate, and independent, entity. But Leibniz does not stop with this point. He further argues that the very reality of matter should be called into question.

Let’s look again at the aggregate passage:

Such a unity could not occur in the machines made by a craftsman or in a simple mass of matter, however organized it may be; such a mass can only be considered as an army or a herd, or a pond full of fish, or like a watch composed of springs and wheels. Yet if there were no true substantial unities, there would be nothing substantial or real in the collection (142)

So matter, even understood as an aggregate, would not even be real if there were not substantial unities which grounded it. Leibniz thinks that this substantial entity must be a non-material entity—a “metaphysical point”, or what he would later call a ‘monad”. Leibniz argues that the reality of matter requires the existence of “true unities’, but matter is not the kind of thing that could itself be a ‘true unity’ so there must be something else—a “real and living point”—whose existence grounds and explains the existence of matter. How does Leibniz’s argument work? Here is one way of fleshing it out:

  1. Matter (material body) is nothing but a collection or aggregate of parts
  2. Any real aggregate must ultimately be composed of parts which are not themselves aggregates—viz., “true unities”
  3. True unities cannot be material (b/c they must be indivisible) or mathematical (b/c mathematical points are not real)
  4. ∴ Matter depends on a non-material true unity

Would the atomist or ‘corpuscularian’ agree with this argument? Both would agree with the first premise, that material bodies are collections of parts. But why should they endorse premises (2) and (3)? Leibniz does nothing to motivate these premises beyond the kind of analogical arguments surrounding the unreality of aggregates like flocks of birds or piles of stones—aggregates are nothing more than the sum of their parts.

In the background of Leibniz’s argument is something we might call the ‘Principle of Borrowed Reality’ (PBR). Leibniz makes this point quite clearly in a letter to the Jesuit priest and philosopher Antoine Arnauld:

I believe that where there are only beings by aggregation, there aren’t any real beings. For every being by aggregation presupposes beings endowed with real unity, because every being derives its reality only from the reality of those beings of which it is composed, so that it will not have any reality at all if each being of which it is composed is itself a being by aggregation, a being for which we must still seek further grounds for its reality, grounds which can never be found in this way, if we must always continue to seek for them. (To Arnauld (April 30, 1687), p. 85)

Is the PBR plausible? There is certainly something intuitive about it. A building is only as real as the materials that constitute it. A painting is only as real as the flecks of paint that make it up. What’s more, it seems that the corpuscularian is at a disadvantage here because they too would seem to want to endorse the principle, as it is part of the explanatory power of corpuscularianism (or any hierarchical metaphysical theory) that the macroscopic world is built out of, and ultimately depends upon, the features of the microscopic world and interactions between such microscopic entities.

So, just as the finitist or atomist response to the issue of division is unsatisfactory because of its arbitraryness (and thus its violation of the PSR), the infinitist answer to the issue of division violates the PBR. Thus, according to Leibniz, given matter’s composite nature we cannot countenance matter as substantial or real. Leibniz’s positive views on the status of matter seem to change over the course of his life. At the point of writing the New System (1695) Leibniz considered matter to be real but not ultimately so, its existence and unity being dependent on the existence of substantial forms or souls.

Only metaphysical points or points of substance (constituted by forms or souls) are exact and real, and without them there would be nothing real, since without true unities there would be no multitude. (142)

By the time he writes the Monadology (1714) Leibniz has given up on the reality of matter altogether, arguing that it is only a perception existing in the mind of the perceiver. He states this clearly in a 1712 letter to Bartholomew des Bosses, Jesuit teacher of theology and a professor of mathematics at Cologne.

I consider the explanation of all phenomena solely through the perceptions of monads functioning in harmony with each other, with corporeal substances rejected, to be useful for a fundamental investigation of things…It is true that things which happen in the soul must agree with those which happen outside of it. But for this it is enough for the things taking place in one soul to correspond with each other as well as with those happening in any other soul, and it is not necessary to assume anything outside of all souls or monads. According to this hypothesis, we mean nothing else when we say that Socrates is sitting down than that what we understand by ‘Socrates’ and by ‘sitting down’ is appearing to us and to others who are concerned. (Letter to des Bosses, 16 June, 1712)

This position, subsequently called “phenomenalism”, construes the material world as nothing more than the orderly perceptual appearances of an underlying non-material order of mind-like substances or “monads”.


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