SORITES, ISSN 1135-1349

Issue #04. February 1996. Pp. 10-20.

«One for Leibniz»

Copyright (C) by SORITES and Vernon Pratt

One for Leibniz

Vernon Pratt

By the end of the 17th Century it was very generally agreed that the universe was entirely made up of small solid corpuscles which moved and changed direction as they bumped and were bumped. There was, in other words, a consensus in favour atomism, as a version of the mechanical philosophy,<1>Foot note 1_1 with material atoms thought of as «extended, continuous, homogeneous little lumps, which are intrinsically indivisible».<2>Foot note 1_2 This consensus however was not quite unanimity. Leibniz' voice in particular was a counterpoint to the consensual plainsong. He rejected the billiard-ball as an appropriate model for what there basically was, and he turned to animals for a better understanding of the basic structure of the universe.

What I want to do is to attempt a unified account<3>Foot note 1_3 of the requirement he put upon what it was to be fundamentally real. This will lead me to challenge the influential thesis that Leibniz is to be understood as attempting to reassert the basic conceptions of Scholasticism -- right up until the point of his final idealistic thoughts, coming upon him with the turn of the century and issuing in The Monadology.

The sense of `fundamentally real' should become (somewhat) clarified in the discussion, but I should say at this stage that I mean it to have the sense in which Leibniz came to deny that atoms were `fundamentally real', the sense in which he denied that atoms could be self-subsistent substances. It was the task of physics he thought, to articulate the laws governing the movements of its self-subsistent substances, its fundamenta, and these laws were thought of by Leibniz as providing the basis for explaining all phenomena. But what features was physics to assume in its fundamenta? It was the task of metaphysics to supply this answer, to characterise correctly the fundamenta which a correct physics should have as its subject matter. Physics, he explains, concerns itself, with «the laws of nature which we learn from experience»; metaphysics is «to account for» those laws.<4>Foot note 1_4

Leibniz' difficulty with the billiard-ball atom, when advanced as the fundamental building block of the universe, and thus as a self-subsistent substance, can be put by saying that it lacked a `principle of unity'. In a way he could be said to have adhered to this view from the moment it led him to reject the mechanical philosophy in that form to the late statement of his metaphysics in The Monadology. The problem in understanding Leibniz completely is largely that this summary formulation is by no means unambiguous. It can be taken to express a number of different possible points, and they do not all strike Leibniz as central at all stages of his philosophical development.

Mechanical cohesion

Leibniz came to be dissatisfied with the material atom only after a thorough induction into the mechanical philosophy.<5>Foot note 1_5 Before his change of view, in his work towards the projected Demonstrationes Catholicae in 1669, he was already identifying a weakness of atomism which could be construed as a problem of `unification'. His thesis here is that `body is not self-sufficient and cannot subsist without an incorporeal principle', and he attempts to prove it in part by arguing that if they did not, there could be no complete explanation of why a body had the shape and magnitude it does.<6>Foot note 1_6

This is one expression of Leibniz' well-known dissatisfaction with the Cartesian thesis that what is fundamentally real as far as the physical universe is concerned -- the stuff out of which everything in the universe (with the exception of minds) is made -- can be identified with extension. Leibniz is arguing that it cannot be so identified: there has to be more to what is fundamentally real than that. As he puts it later:

If a body is a substance [i.e. in this context something existing in its own right] it cannot consist in being extended ....<7>Foot note 1_7

This is the overall thrust of Leibniz' argument of 1669, and has often been explored. But, from the point of view of arriving at an understanding of `unity', there is detail in this particular argument that still requires clarification, in particular the reference to cohesion. Leibniz asks how the cohesion of bodies is to be explained -- the fact that `bodies or their parts cohere with each other'? Corpuscularians, he says, have maintained that the cause of such cohesion is that the parts of bodies physically interlock with each other -- `through the interweaving of certain shapes such as hooks, crooks, rings, projections'. But, he argues, there is obviously a regress here: for if the cohesion of bodies is to be explained in terms of their parts hooking into each other, what is to explain the cohesion of the hooks that this explanation of cohesion invokes? `Must we assume hooks on hooks to infinity?'<8>Foot note 1_8

In 1669, Leibniz does not see this as a reductio ad absurdum. His conclusion is rather that the regress must be halted somehow, and that in order to do so there must be posited, as the ultimate building block of bodies, a something that is indivisible. These indivisible somethings are, he says, the atoms of the Corpuscularians, `which, by their varied shapes, variously combined, bring about the various qualities of sensible bodies.' Because they are `indivisible', the cohesion of the atom itself is not to be accounted for in terms of corporeal parts: it can only be done by invoking something that is not corporeal: which is what he set out to prove. (In fact he thinks of this as a new proof of God. )<9>Foot note 1_9

One thought therefore is that the problem of unity is one that appeared from the perspective of corpuscularianism. If it is correct to explain the cohesion of bodies made up of particles in terms of the shape and size of those particles, as Leibniz the corpuscularian believed, then a particle cannot itself be only a body: or else there would be an infinite regress. The problem of unity construed in this way is the problem of explaining how the coherence of a body can be achieved non-corporeally.<10>Foot note 1_10

Leibniz in 1669 offers little in the way of a solution, except to say that `in explaining the atoms, we may therefore rightly resort to God, who endows with firmness these ultimate elements of things.'<11>Foot note 1_11

Even if this is indeed a correct identification of one thought that Leibniz means to convey by insisting on the requirement of `unity' in anything that is to be accounted fundamentally real, there are certainly two others, others which become articulated as Leibniz makes the transition from the mechanical philosophy first to the `philosophy of the metaphysical point'<12>Foot note 1_12 of his middle period to the idealist metaphysics he espoused in the Monadology.

Indivisibility is one of these. In speaking of the unity requirement in what is fundamentally real, Leibniz is in places at any rate meaning to insist that what is fundamentally real cannot be, in a sense that needs clarification, `divisible'.


Leibniz' thesis here could be interpreted along either of two lines. A first thought might be that what Leibniz is attempting to bring out in this way is the contradiction there appears to be between extension on the one hand and indivisibility on the other. Nothing can be both extended and indivisible.

In his early thought of course -- as a subscriber to the mechanical philosophy -- Leibniz attached no validity to this objection to atomism. As is clear from the passage already cited, he accepted the possibility of a materially extended but indivisible thing, objecting, as I have explained, only that the cohesion of the materially extended atom presented a problem. In this sense, to be divisible is to be such as might be, in principle, cut into two bits.

Later, it may be that Leibniz came to see the absence of `divisibility' in this sense as a requirement of any fundamentum -- which is to say that maybe he came to think of it as an objection to a materially extended fundamentum that no materially extended thing could in principle resist dissection.


But a second line of thought -- presented under the same `indivisibility' banner -- certainly becomes (in Leibniz' developing thought) much more significant. There is a distinction, according to this second argument, between on the one hand things which can be divided while remaining things of the same sort, and on the other things which suffer division only at the expense of annihilation. Two halves of a horse are not horses, but two pools can easily be made by dividing a single pool. If the term substance is invoked to cover things of the first kind, this is the point, fundamental for Leibniz, that there is a distinction between substances and aggregates. A substance, he says, `cannot be divided in two, or one substance made out of two.'<13>Foot note 1_13

Aggregates are `substantial entities put together by nature or human artifice'. They are to be contrasted with things possessing `true unity'. `Perfect unity should be reserved for animate bodies, or bodies endowed with primary entelechies; for such entelechies ... are ... indivisible and imperishable as souls are.'<14>Foot note 1_14

Leibniz maintains, from his middle period on at any rate, that what is fundamentally real has to be indivisible in the sense in play here. This is a sense of `indivisible' which is quite the reverse of being resistant to the knife. Dissection destroys what is fundamentally real. The fundamentally real is for that reason `indivisible'.

What is unsatisfactory about the material atom, interpreting Leibniz in that way, is that there are no conceptual resources in its definition to allow us to think of it as a thing in its own right as opposed to a simple collection or shred. He would then be arguing that the material atom has to be conceived of as possessing some feature in addition to those hitherto acknowledged by the mechanical philosophy, a feature that makes the difference between collection or shred and the «truly single being» which the fundamentum must in Leibniz' view be.

Leibniz' insistence on a substance having a `principle of unity' then certainly refers to the requirement that to be a thing existing in its own right a thing must be `indivisible', most significantly in the sense that it must be a thing which is not an aggregate: even if it is made of parts, those parts must posses collectively an `integrity' which makes them more than an aggregate. Horses are like this, but piles of stone are not. Human beings are, but human arms are not.

So we reach the position that for Leibniz self-subsistent things must have integrity, be `indivisible' in that sense, and the question arising out of that: Why should Leibniz maintain that? What is the connection between being a self-subsistent thing and being in this sense `indivisible'?

For a proper answer we must now attempt to do some justice to a sustained theme we encounter in his arguments about what is real: the importance for what is real of having a `principle of activity'.

A Principle of Activity

The great source of Leibniz' pre-occupation with action in the context of his thinking about substance was Scholastic. There, in the writings of one its most sophisticated representatives, and one Leibniz clearly respected, was to be found the doctrine of the suppositum, with its thesis that actiones sunt suppositorum -- an action is necessarily attributed to a suppositum, understood as an self-subsistent substance.<15>Foot note 1_15 That is to say, in the case of an action there must be some answer to the question Who or what did it? and the Who or What must be a self-subsistent substance. It is the doctrine that only self-subsistent substances can have actions ascribed to them.

Leibniz reveals his reliance on this doctrine in a paper of 1668, which discusses transubstantiation.

The defence he gives of this doctrine is brief:

Taken as an individual being which subsists in itself, or substance (either one), is a suppositum. In fact, the Scholastics customarily define a suppositum as a substantial individual. Now actions pertain to supposita. Thus a suppositum has within itself a principle of action, or it acts. Therefore a being which subsists in itself has a principle of action, or it acts. Therefore a being which subsists in itself has a principle of action within it. Q.E.D.<16>Foot note 1_16

He starts here by pointing out that what the Scholastics<17>Foot note 1_17 meant by suppositum was a self-subsistent substance (i.e., a real thing existing in its own right); and then reminds us of their thesis -- which he appears to have simply adopted -- that `actions pertain to supposita'. This entails, he says, that a suppositum must have within it a principle of action: which is to say, since a self-subsistent substance is what a suppositum is, that a self-subsistent substance has within it a principle of action. So a summary would be:

1. to be a self-subsistent substance a thing must be a suppositum

2. to be a suppositum a thing must be capable of action


3. to be a self-subsistent substance a thing must be capable of action.

And since

4. to be capable of action is to possess a principle of action

we can conclude:

5. to be a self-subsistent substance a thing must possess a principle of action.

The interesting feature of this argument is proposition (4): the movement that appears to take place between a point in logic and a point about the capacity to generate spontaneous change. The Scholastic doctrine that an action is to be ascribed to a suppositum is most easily construed as a doctrine about logical categories. On this basis, it is taken to say that the category of action is such that it only makes sense to speak of an action having been performed if there is an answer to the question What self-subsistent substance (possibly Who) performed it? If there is an event which for some reason we cannot ascribe to a self-subsistent substantial Who or What, we cannot speak of it as an action.

It might be said in the philosophical context of today that if this is the doctrine of suppositum it says nothing about how the change that we are describing as an action was produced. Yet for Leibniz, it is a statement about the origin of change. He presents it as the key premise in authorising the conclusion that a self-subsistent substance must have within it a principle of change, and he apparently means by this that a s substance must be capable of initiating change (generating change on its own). This is why he looks to animals for his account of what a substance is: for the characteristic of animals is that they are capable of spontaneity, of initiating action. <18>Foot note 1_18

In making use of the medieval doctrine of suppositum Leibniz is in effect articulating a theory of action. The first part of this theory -- the suppositum part -- is that only self-subsistent substances can act. It rules out ascribing actions to parts of substances such as an arm of a human being or a sail of a windmill, and it rules out too the possibility of aggregates performing acts. It rules out my arm knocking a vase off a shelf, and it rules out a pile of stones killing someone. It insists that only self-subsistent substances can be the authors of actions.

The second part insists that an action is an origination of change.<19>Foot note 1_19 If a happening is at the head of a causal chain that runs back to the Creation it cannot be the action of any substance but the Creator. An action starts a causal chain. In a truly mechanical universe there would be no actions, save the Creator's.<20>Foot note 1_20

Before bringing in his view of activity and its importance, I said that Leibniz maintained that to be fundamentally real a thing must be `indivisible' in the sense of not being an aggregate, of being instead an entity possessed of `integrity'. I said that his view of action would throw light on why he needed to maintain this. The link between what is fundamentally real and `integrity' is now clear: he thought that only integrated entities could be agents or actors. Only non-aggregates, in his terminology, could have actions attributed to them. So a necessary condition of being fundamentally real was to be a `unified' entity, an entity having integration.

Some more flesh is put upon these bones when we consider the way in which Leibniz proposed to take account of these points. If the atom lacked the required `integration' (it was just a bit of stuff) what did Leibniz suggest we put in its place?

What he represented himself as doing was turning back to the Scholastics. We needed something to bring integration to bits of matter, and for him at any rate, with his Scholastic university education, the Scholastic form was at hand. Here is his own account of his intellectual journey:

At first, after freeing myself from bondage to Aristotle, I accepted the void and the atoms, for it is these that best satisfy the imagination. But in turning back to them after much thought, I perceived that it is impossible to find the principles of a true unity in matter alone ... therefore I was forced to have recourse to a formal atom, since a material being cannot be at the same time material and perfectly indivisible, or endowed with true unity. It was thus necessary to restore and as it were, to rehabilitate the substantial forms which are in such disrepute today ....<21>Foot note 1_21

The Scholastic apparatus was that there was stuff and there were forms. Substances, «single beings», occurred when a parcel of stuff was associated with a form. The form made a parcel of stuff into a thing (and one of a particular kind). So much of course was the Aristotelian legacy, and it certainly allows a sense in which the Scholastics could be said to have thought that their form conferred «unity».

During one period of his thought therefore, Leibniz represented himself as maintaining that a fundamentally real thing was a parcel of matter made into a unified thing in virtue of its possessing a form.

This sounds thoroughly Aristotelian, thoroughly Scholastic, and it has lead to the view that during this period, dubbed by Garber Leibniz' Middle Period, the essence of Leibniz' position was Scholastic, and that his contribution to the debate about what was truly real was to reassert Scholasticism.<22>Foot note 1_22

A proper understanding of Leibniz' concern with unity, I want now to suggest, prompts us to enter a caveat, I think quite a large caveat, to this thesis. My point is that some of his representations to the contrary, the `form' that Leibniz puts to work in his Middle Period metaphysics is really importantly different from the form of the Scholastics.

The Leibnizian `form'

First, the observation already made, that Leibniz' concept of what is truly real is not the same as the Scholastic concept of substance. The Scholastic category of substance includes houses and clocks. These things are made the sort of thing that they are in virtue of their possessing the relevant form. But houses and clocks are for Leibniz mere aggregates. They are not fundamentally real (though made of things that are, of course). Leibniz' fundamenta are a subset of Scholastic substances, just the ones that are `animated'.<23>Foot note 1_23

This is one difference.

A second is this. What drives Leibniz to reject the atom is that it lacks a principle of action. But as a matter of fact, as Leibniz fully realised, the Scholastic form was deficient in precisely this crucial way. The Scholastic form too lacked a principle of action.

«Active force», Leibniz says, «differs from the mere power familiar in the Schools, for the active power or faculty of the Scholastics is nothing but a close possibility of acting, which needs an external excitation or a stimulus, as it were, to be transferred into action. Active force, in contrast, contains a certain act or entelechy and is thus midway between the faculty of acting and the act itself....»<24>Foot note 1_24

What the Scholastic form lacks, Leibniz is recognising, is its own capacity to initiate. But it is precisely this capacity which he is insisting a truly fundamental thing must possess.

So that is the second divergence. When he invokes the notion of form, not only is it a form that animates some things and not others, but it has a principle of action lacking in its Scholastic forerunner.

There is a third point. Though I have said that Leibniz in his Middle Period represents himself as positing, as the fundamental building block, a scrap of matter `unified' by a form -- a Leibnizian form, as I would insist -- he is also defending in that same Middle Period the thesis that matter cannot be `unified' at all. That is to say, he reached the view that nothing you can do to matter will make it into a thing capable of initiating action.

Previously, as I have explained, in his mechanical phase, he tried the view that adding a soul to the matter of the Cordemoy atom would solve the problem of cohesion. So at that stage it might be argued that Leibniz was essentially persisting with Scholastic ideas. But a subsequent step, a step that takes place within the `middle period', is to reject the idea of matter altogether.

What Leibniz posits instead of the `unification' of matter by form is that the basis for a self-subsistent substance must be, not something extended, but a point, something he refers to also as an atom of substance:

... material atoms are contrary to reason. It is only atoms of substance, that is to say, real unities that are absolutely destitute of parts, which are pued... the absolute first principles out of which things are compounded...<25>Foot note 1_25

Though these atoms of substance are spoken of by Leibniz as `points', he makes it clear that they are not mathematical points (that on its own would eliminate matter more directly than Leibniz in his Middle Period would wish). Nor, emphatically, are they very small but materially extended corpuscles -- for that would be leave them as material and the problem of `unification' unsolved. They are, Leibniz says, metaphysical points.

It is only metaphysical points, or points of substance, which are exact and real, and without them there would be nothing real....<26>Foot note 1_26

It is perfectly true that Leibniz retains in this context of the end of the material a role for what he is still prepared to call a `form': a self-subsistent substance is, he explains, one of these metaphysical points animated by a `form'. My point is that with Leibniz's substitution for matter of the metaphysical point he has left the Scholastic conception of substances consisting of matter animated by form decisively behind.

In fact what Leibniz attempted to retrieve from the Scholastics was not their forms but their doctrine that actiones sunt suppositorum. Once this principle were granted, you had to supplement the conception the mechanical philosophy had of the atom. And for this purpose Leibniz had to propose not the reintroduction of the Scholastic form, but the introduction of a new device which simply drew inspiration from the latter. (It drew equal inspiration of course from the mechanical philosophy itself. For we have to ask: Why did the lack of a principle of activity, in the sense identified by Leibniz as essential to an self-subsistent substance, not concern the Scholastics?)

Jupiter and beyond

If that is what his idea of a substance has become, immediately it confronts a major difficulty: How could Leibniz conceive of a point, something in principle lacking in extension, as a building block for the whole universe, as the fundamentum by reference to which the laws of physics could explain all? How can something lacking extension be the building block for a spatial universe? For his solution Leibniz turned not to the Scholastic inheritance, which (admittedly) he rather passes himself off as doing, but, again, to a conception which was radically new. The Leibnizian substance as it takes final definition is a metaphysical point serving as the locus for a Cartesian mind.

But that begins something else, Leibniz' final phase, the first years of the new century, of which The Monadology was the fruit.


What I have tried to do here is to explain how Leibniz' variously expressed difficulties with what could be truly real fall into place once his concern with the origination of change is seen as fundamental. The truly real cannot be an aggregate because an aggregate cannot originate change. That is the sense in which the truly real must be `unified' or `indivisible'. But if this is so, there is something importantly missing from an account of Leibniz thought in the `middle period' (when he was thinking through the notion of the fundamentally real with Arnauld) which speaks of him as championing the Scholastic conception of substance as matter with form. The Scholastic form precisely lacked the `principle of activity' which for Leibniz was the crux of the substance question. And moreover, though he still talks of the key significance of the `form', the conception of self-subsistent substance he actually articulates during this period substitutes for Scholastic matter the metaphysical point, so that the break with Scholasticism, letter and spirit, is surely hard to deny.

Vernon Pratt

Lancaster University

E-Mail: V.Pratt@lancaster.ac.uk