Leibniz and Substance
Woolhouse (Roger)
Source: Woolhouse - Descartes, Spinoza, Leibniz - The Concept of Substance in Seventeenth Century Metaphysics
Paper - Abstract

Paper StatisticsBooks / Papers Citing this PaperNotes Citing this PaperLink to Latest Write-Up Note


Write-up2 (as at 27/06/2020 17:15:22): Woolhouse - Leibniz and Substance

  • This note provides my analysis of "Woolhouse (Roger) - Leibniz and Substance". I must have written it as an undergraduate at Birkbeck, probably around 2002.
  • It starts off with the text I originally wrote – which is a very detailed analysis. I wrote these analyses in that way to force myself to focus on the detail of the argument. Sometimes they are longer than the original paper. I doubt they are of any value to anyone other than me, but may provide a different “take” on the paper or chapter under review and may help someone to understand what’s going on.
  • I’ve left this text substantially as it was, but have (started to) add further notes below to discuss some of the issues raised insofar as they impact on my research into Personal Identity.

Detailed Analysis
  • Leibniz remarked towards the end of his life that considerations of the concept of substance are of the greatest importance and fruitfulness for philosophy. He thought these fruits included truths, hitherto only partly known and barely demonstrated, about God, minds, and the nature of bodies which are of the greatest use for the future of other sciences. An exposition of his ideas is difficult, because
    1. he left no master-work and
    2. his ideas changed considerably over time.
  • Woolhouse focuses on Leibniz’s ‘middle’ period between 1680 and 1700, to which belongs the Discourse on Metaphysics and the Correspondence with Arnauld. During this period, Leibniz’s ideas came to some kind of resolution and their first public expression in the controversial New System of the Nature of Substances (1695). By the end of his life, Leibniz’s account of substance, as given in the Monadology (1714), had undergone some radical changes from that explained to Arnauld. However, Woolhouse thinks that, as far as Leibniz’s agreements and disagreements with Descartes are concerned, Leibniz’s later thought presents no really new considerations.
  • Central to Leibniz’s account is the concept of an individual created substance. Aristotle had distinguished between second and first substances, ie. between kinds and the individuals that belong to them3. Aristotle is thinking of individual things when he says that a substance has properties and is not itself the property of anything else. This is Leibniz’s starting point in the Discourse.
  • For Descartes, God created two kinds of substance – corporeal and incorporeal, but there are individual created substances only of the incorporeal kind. There are individual substantial minds but not bodies, which are just pieces of created extended substance, not individual substances themselves.
  • Leibniz is dissatisfied with this aspect of Descartes’ metaphysics and thinks that Descartes’ extended substance is not part of substantial reality. Leibniz does believe in individual corporeal substances, but thinks that their substantiality and individuality do not derive from their being corporeal or extended, but from their union with something like an individual substantial mind. Individual mental substances are paradigmatic for Leibniz, because reflection enables us to find the idea of substance within ourselves, since we are substances. Minds make corporeal substances possible because the substance of body is union with a sustaining mind. However, in the Monadology, matter is merely “well-founded phenomenon” and mind-like monads are the only reality of any kind.
  • Spinoza allows substantial reality of (at least) two kinds, but not individual substances of either kind, agreeing with Descartes that material bodies are not substances (they are finite modes) but going beyond Descartes in thinking something similar of minds. Leibniz thinks this is a step in entirely the wrong direction. When annotating the Ethics he remarked on P14 (“no substance but God”) that, while he, himself, was unsure whether bodies are substances, he was sure that minds were. In a passage similar to Descartes’s Principles 1.16, Leibniz claims that experience shows us that we are particular thinking things, distinct from others of the same kind; otherwise we would fall into Spinozism, that there is only one substance, namely God.
  • One question that concerned Leibniz was the co-operation of God with created things; so, in Discourse §8, he attempts to distinguish the actions of God from those of creatures. To do this, and understand the nature of created things, we need to explain what an individual substance is.
  • He begins by saying that it is true that if a number of predicates are attributed to a subject, but that subject is not attributed to anything else, then it is a substance. However, this is only a nominal and superficial explanation of substance and doesn’t tell us what it is for a substance to have an attribute.
  • Leibniz’s suggestion for what it is to be truly attributed to a subject is as follows:
    1. Every true predicate has some basis in the nature of things.
    2. There are identities, in which the predicate is expressly contained in the subject.
    3. Otherwise, the predicate must be included in the subject virtually, what the philosophers call in-esse, saying that the predicate is in the subject.
    4. Either way, the subject term must include the predicate in such a way that anyone perfectly understanding the concept of the subject will also know that the predicate pertains to it.
    5. Given this, we define an individual substance or complete being as having a concept so complete as to be sufficient to make us understand and deduce from it all the predicates of the subject to which the concept is attributed.
  • Leibniz set off from the traditional Aristotelian definition of substance, but his deeper explanation is non-traditional, though he implies that it is. Woolhouse thinks it’s unclear what Leibniz’s explanation amounts to, what it’s meant to explain and what Leibniz intends by his question about true attribution.
  • Reconstructing the question from the answer, and also taking into account Leibniz’s interest in the relative activity of created substances and God, Woolhouse thinks that Leibniz wanted to explain why created substances have the properties they do – whether through God’s or their own activity. Leibniz eventually concludes it’s through their own activity, though it’s not immediately obvious that this is the direction in which he’s heading, so Woolhouse follows him step by step.
  • For Leibniz, a substance is not simply the possessor of properties or predicates, but the possessor of a concept so complete as to allow these to be deduced from it. He continues to say that a consequence is that a body’s entire nature cannot just be extension (size, shape, motion) but must include something soul-like, a substantial form.
  • Woolhouse points out that some predicates of an individual substance, say a person, are permanent but others transient or intermittent – blue eyes as against a temporary limp or occasionally sitting down. So, what sort of complete concept or nature contains all these, why can’t the nature of body consist solely in extension and what is the relation between a complete concept and a substantial form?
  • Substantial forms belong to the Aristotelian metaphysics of substance which Huygens considered part of the irrelevant paraphernalia that Descartes swept away. The development of the mechanical philosophy in which Descartes, Spinoza and Leibniz were involved rejected any ideas of hylomorphism in physical explanation in favour of the corpuscularian theory. Why, therefore, Leibniz’s appeal to substantial forms?
  • Leibniz denies that he’s reintroducing substantial forms into natural philosophy, where he is as corpuscularian as one can be, insisting that one must explain nature along mathematical and mechanical lines; substantial forms serve no purpose in the details of physics and should not be used to explain particular phenomena.
  • Substantial forms are, Leibniz thinks, required for any metaphysical account of the world. Without an adequate metaphysics, physics is unsatisfactory because without foundations. The metaphysical principles of detailed physical enquiries require substantial forms. Leibniz thinks that in the final analysis of the principles of physics and mechanics, the mechanical principles are not explicable purely by the modifications of extension, and the nature of force requires something else.
  • Woolhouse leaves Leibniz’s account of the use of substantial forms in the metaphysical foundations of physics until the next couple of chapters, here concentrating on their place in the account of substance. There are two aspects of substantial forms
    1. their traditional function as the organising active natures of substances as they develop and change and
    2. they produce the unity and individuality of individual corporeal substances, making them entia per se.
  • Leibniz’s worry about Cartesian extension is that, on its own, it can’t provide for individual extended substances because extended substances, and therefore extended things qua extended, are essentially composite and divisible. Arnauld noted that it is the infinite divisibility of extension that makes it difficult to conceive of its unity and that this was the reason Leibniz had for reinstating substantial forms. However, Arnauld did not share Leibniz’s concerns for, like Descartes, he considers the parts of a marble block to be substantial, even though not individual substances, because they are not modes or states of some other substance. Arnauld accuses Leibniz of setting up a special definition of substance as that which has a true unity, to which Leibniz correctly responds that the Scholastics saw things this way too.
  • Arnauld and Leibniz debate the ability of substantial forms to produce unified material substances or entia per se. Leibniz admits the inadequacy of some of his answers, but says that there is a genuine problem that extension hasn’t solved.
  • Arnauld asks what happens to a tile’s substantial form if it is broken in two, to which Leibniz’s response is that a tile doesn’t have the kind of unity to which a substantial form applies. It is like a heap of stones, with an accidental unity, united by accident or aggregation and not united per se or in itself. Clearly, the tile has more cohesion than the heap of stones, but mere physical connection, no matter how close or tight, cannot produce more than accidental unity. Leibniz’s examples of such aggregates include diamonds in a ring, fish in a frozen pond, a flock of bound sheep and a chain of links. Even ordered societies and machines with parts connected in other than straightforward physical ways and conspiring to the same end are not substantial unities because their unity is fabricated in our minds and exists by convention. A more than mechanical unity is required for the attribution of substantial form.
  • Entia per se are animate machines whose soul or substantial form creates substantial unity independent of the external union of contiguity. Leibniz is sure that human beings are genuine substantial unities, but not so sure about other promising cases such as animals or trees.
  • Leibniz takes up the hylomorphic analysis of individual substances into matter and form, according to which a living person is a composite of substantial form (the rational soul) and the bodily material of flesh and blood. The human body is a body because its material is ensouled or animated, organised by an entelechy or form. On death, the body ceases, strictly speaking, to be a body at all and is just a mass of material; death happens to the composite human being as a whole as a disorganisation of the previously organised whole. Descartes understands a living human being quite differently as the union of two substances, mind and body, rather than as one substantial composite of form and matter; a dead body, like a broken clock, is as much a body as a living one and death happens to the body, not to the mind-body unity; the mind leaves the body because the body is broken or run down rather than the body dying because the mind ceases its union with it.
  • So, Leibniz revives the pre-Cartesian perspective in which the living human being is a composite of a soul, or substantial form, animating and organising an amount of material. While the human body is an extended material substance, it does not derive its substantiality from its being material and extended but from the form that organises it; absent the soul, the corpse cannot correctly be called a substance.
  • Leibniz tends to think that other animals are also individual substances, having souls but lacking consciousness, the alternative being to treat animals as did Descartes as inanimate mechanisms.
  • Leibniz, while denying substantiality to the body without the soul, does allow that the disembodied soul is a substance. This is a departure from an awkwardness (for Aquinas) in traditional hylomorphism in which only the composite of matter and form is a substance, though immortality demanded that the specifically rational part of the human soul could exist apart from matter. However, while allowing the theoretical possibility of disembodied forms, he denies that this is ever the case in practise.
  • For Leibniz, substances are indivisible, since it was the divisibility of extension that made it unsuitable as a substantial attribute and led him to reintroduce substantial forms. As applied to immaterial substances, Leibniz shares this view with Descartes. Leibniz also thinks substances immortal and indestructible, and, though Arnauld shares this view with respect to human souls, he’s less happy about applying the same principle to animals (almost on the grounds of overcrowding, given his example of 100,000 silkworms perishing in a fire yet their souls being supposed to continue in existence).
  • Arnauld accepts indivisibility on the part of man – since one cannot conceive of half a man – but is troubled by worms where we end up with two for one. Leibniz’s response is that, though both halves of the worm continue to move, only one is really ensouled, the other being simply matter, a bit like an amputated limb (though Leibniz doesn’t put the point like this).
  • While Arnauld accepts the one case of indivisibility – man – he won’t accept any cases of indestructibility, saying that the corporeal whole human being does perish when the soul is separated from the body, after which the human body is no longer indivisible. Leibniz, however, doesn’t consider that souls become detached from bodies at death, but considers the death of an animated corporeal substance to be but a transformation of the corporeal substance, and not a separation between soul and body at all. When a living insect is torn up and destroyed, its souls remains in a certain part that is both alive and sufficiently small to avoid further attack. Even burning, though it reduces the body in size, doesn’t separate soul from body, leaving something animate even in ashes. Animal death is a transformation into organic little bodies which have contracted from a larger body that has undergone corruption.
  • Leibniz takes the orthodox Thomist view that a dead human body isn’t a substance when considered in abstraction from a substantial form as a purely material thing. But given that it’s not a material substance, nor, as for Descartes an arrangement of material substance, what is it? It’s an aggregate, an ens per accidens, but what is it an aggregate of? Leibniz stated to Arnauld that it was an aggregate of substances, but what substances, since they cannot either be the corporeal substances of which human bodies were elements or the immaterial substances which formed the other element of corporeal bodies?
  • The natural presumption would be that the parts of an extended body (whether human, animal, watch or tile) to which they aggregate are themselves portions of extended body, and hence aggregates themselves. Leibniz thinks that aggregates have only so much reality as exists in their constituent parts and, consequently, that extended body considered apart from any form will not even be a real entity. Aggregated extended matter, such as soulless corpses and marble tiles, has no independent reality as substance in its own right; so, unless there are material substances for it to be aggregated from, it will have no reality at all, but just be like the rainbow – a true phenomenon. Since matter can be infinitely divided, we will never get to something on which we can say that it is really an entity.
  • Arnauld suggests, as some Cartesians such as Gerauld de Cordemoy have held, that the division, instead of continuing for ever, terminates in perfectly hard and indivisible, if minutely extended, atoms, whose indivisibility would give them a substantial unity and reality on which the larger aggregated bodies would depend for their own reality. Leibniz, however, while applauding the recognition that unity is an important feature of substances, doesn’t share this view.
  • Leibniz’s solution for the substantial unities out of which marble tiles can be aggregated is a combination of Cordemoy’s purely material atoms and his own hylomorphic account of living corporeal substances. Matter is divided into unitary but not ultimate parts, but these parts are substantial, being small, animated living material substances. The body of any living being can be further divided into more substances. The substantial forms of these parts of bodily aggregate are not minds in the human sense, but only analogous to minds. Even their matter would be mere phenomenon were it not an aggregate of further individual material substances – it is a matter for empirical investigation just where a chunk of non-substantial matter needs further subdivision to reveal the smaller corporeal substances of which it is aggregated, and not something Leibniz’s theory need decide. He doesn’t know how far we need divide a piece of flint in order to arrive at organic bodies, but doesn’t take this ignorance as prejudicial to his theory.
  • In later years, Leibniz believed that there are no corporeal substances, and that since a bodily mass has no substantial parts from which it can derive its reality, it is, like the rainbow, no more than true phenomena. His view then was that the whole of substantial reality consists of mind, but in the period under consideration here, his view is that just as a living human being is a composite of form and matter, so its matter – the body taken by itself – is an aggregate of parts which are themselves substantial composites of form and matter. The body, apart from the soul, has only the unity of aggregation, but retains reality because its constituent parts have substantial unity because of the numberless living bodies that are included in them4. Every part of non-substantial extended matter is divided into corporeal substances, so that there is an almost infinite number of little animals in a drop of water.
  • Woolhouse recaps: for Leibniz, individual substances have complete concepts, consequently, the body cannot consist merely in extension and substantial forms must be reintroduced to provide for true unities or entia per se. However, we have yet to see the connection between complete concepts and substantial forms.
  • This doctrine that an individual substance is something with a complete concept from which all its predicates can be deduced echoes Leibniz’s theory of truth. For Leibniz, in any true proposition the concept of the predicate is somehow involved in the concept of the subject. Woolhouse doesn’t discuss here how these metaphysical and logical doctrines of Leibniz relate, either philosophically or temporally; however, he notes that some people have seen the connection and consequently interpreted Leibniz’s metaphysical view in a quasi-logical, atemporal way. Russell’s view was that Leibniz’s doctrine that all the states of a substance are contained in its notion as amounting to no more than the “obvious fact” that every proposition about the future is already determined as either true or false, even though we may be unable to decide which.
  • Russell’s “obvious fact” is the idea that truth is timeless, so that if something is true at a certain time, then not only will it always be true thereafter that it was true at that time, but it was always true beforehand that it would be true at that time. It is not that the later truth depends on the earlier obvious fact that it would be true, but the reverse, that the fact that something will be true in the future is dependent on the relevant fact being true at that time in the future when it happens.
  • Not everyone finds it as obvious as Russell that there are determinate truths about the future and that truth is timeless in this way, but did Leibniz and does it explain about substances having complete concepts? It does in one respect, for Leibniz supports his claim that the concept of a substance involves all its predicates, past, present and future by saying that it is already true now that a future predicate will be a predicate in the future, and so is contained in the concept.
  • However, this quasi-logical, atemporal account doesn’t connect Leibniz’s complete concepts of substances with the metaphysical idea of substantial forms. We must recognise that
    1. individual substances, unlike atemporal geometrical figures about which there really are unchanging truths, exist in time and change their properties through it and
    2. substantial forms are active, organising natures of substances as they develop and change through time.
    Leibniz means by the complete concept that the predicates that become true of a substance do so by virtue of its substantial form. Its future is written into it just as the future of the oak is in the acorn – there are at all times in the soul of Alexander traces of all that has, and marks of all that will, happen to him. All that happens to a substance comes from its own depths, so the present is big with the future.
  • This further explains why Leibniz rejects as substances Descartes’ extension and even Cordemoy’s atoms – they can have nothing to do with the temporal development and change typical of an individual substance. Extension expresses only the present state, and no action or change can be deduced from it and a man consisting only of atoms cannot contain within him all past and future states.
  • The reason Leibniz had to give an account of individual substances in the Discourse was because of his aim to distinguish the actions of God from those of creatures. We can now understand his rejection of the idea that God does everything, for individual substances have a self-sufficiency that makes them the source of their actions, so that all that happens or will happen to a substance comes from its own depths (though God is still involved as it is dependent on God). This independence is partly a matter of initial creation, though Leibniz thinks that God preserves created substances and even produces them continually by a kind of emanation.
  • While the changes that happen to created substances and the predicates that become true of them are the development of their own natures, God is still responsible for creating and sustaining them with those natures. Leibniz thinks that God’s ordinary concourse is preservative – maintaining each substance on course and subject to the laws established for it – and thinks that those who believe God does everything have lost the distinction between this and God’s extraordinary concourse, which would apply to everything.
  • Leibniz has a detailed answer to why God created substances with the particular natures they have, rather than others. This world is one of an infinite number of possible worlds that might have been created, but the only one that can, in fact, exist – because it is the best of these possible worlds and consequently God’s wisdom causes him to know it, his goodness causes him to choose it and his power causes him to create it5.
  • What it means, according to Leibniz, for God to choose to create a particular world can be filled out by the following example. Imagine, for the sake of argument, that Adam (in our world) sinned on the 10th day. What was it about the world on the 8th day that made it such a world for Adam to sin on the 10th day rather than one in which he never sinned? An answer would be to say that from the start God’s intention had been, by extraordinary concourse, to bring it about that Adam sinned on the 10th day.
  • This “God does everything” view is that of Malebranche and other contemporaries of Leibniz who adopted occasionalism. Malebranche distinguishes between two forms of causation:
    1. real, active or primary and
    2. occasional or secondary.
    God is the only type (1) cause and in the created world there are only type (2) causes, all change coming about from God’s direct activity.
  • This occasionalist account is not Leibniz’s, because it conflicts with his view that individual created substances are themselves active as governed by their own natures. What explains Adam’s sin was that he embodied a form whose development over time would bring it about. Apart from God’s sustaining them in their courses, individual created substances are themselves responsible for the predicates that become true of them. The occasionalists effectively deny them substantiality by denying them activity and leaving it to God to do everything – which is more or less Spinoza’s position, which Leibniz recognised as being due to pushing too far the denial of force and action to creatures and making them mere modifications of the one divine substance.
  • Leibniz adds to the original doctrine of hylomorphism in two ways. While traditional hylomorphism allowed that many of the features of an individual substance relate to the form it embodies, it didn’t think all of them did. An oak’s vegetative soul wasn’t supposed to guide the whole of it’s destiny, for many things, such as the exact number of acorns it produced, were deemed accidental, and it was also supposed that things on occasion came to be true of it as a passive recipient of an outside cause, for instance the number of leaves lost in a storm. While its form governed the utilisation of water and other nutrients, these still needed to be supplied from outside.
  • In Leibniz’s view, God left nothing to chance in choosing what substances were best to create but has examined every aspect of the world in every manner. Everything is numbered, even the hairs of our head. A substance’s concept is so complete that we can deduce from it all its predicates. However, might not something become true of a substance as the result of another substance’s activities, rather than its own?
  • Leibniz rejects inter-substantial causation, because all the actions and passions of a substance come from its own depths. Changes to substances come from an internal principle and an external cause cannot influence their interior.
  • This view has been recently challenged, says Woolhouse. It has been argued that, though nothing that becomes true of a Leibnizian substance does so because of God’s extraordinary concourse, it doesn’t all become true solely on account of its own activity and nature but because of interaction between itself and other substances.
  • To clarify matters, we need to impose a distinction on Leibniz’s terminology. Leibniz speaks indifferently of concept on the one hand and form, nature or soul on the other. We can think of the concepts of individual substances as the detailed ideas God had in mind of possible substances prior to creation, but their natures or souls as the embodiments of those concepts as actually created.
  • The traditional view has it that there is a complete overlap between a substance’s concept and nature, with the latter being the embodiment of the whole of the former. Recent interpretation suggests this overlap is only partial; while all that what God wants to come true actually does, only part comes true because of that substance’s nature corresponding to its concept, the rest coming true because of mutual interaction between substances whose natures relate to only part of their concepts.
  • Woolhouse points out6 how the centrality of activity in Leibniz’s concept of substance can hardly be over-stressed, quoting from passages from his earliest to latest years:-
    1. Being which subsists in itself is that which has a principle of action within itself.
    2. The essence of substance consists in the primitive force of action.
    3. Actions belong to substances; everything that acts is an individual substance and every individual substance acts continually.
  • During the period Woolhouse is considering, Leibniz increasingly came to think of the active principle in substances – their form or soul – as a primitive, active force or power. Active force is so basic, that rather than Leibniz seeing it as a feature of substantial form, he explains substantial form in terms of it. In all corporeal substance is an active, primitive force corresponding to the soul or substantial form; and so on.
  • This primitive active force within corporeal substances primarily relates to their form rather than matter of their bodies. They also possess a passive force which does relate to their matter, though things are not as simple as “active to passive as form to matter”. Leibniz distinguishes between primary and secondary matter. The matter constituting the bodies of animated corporeal substances or non-substantial marble tiles is secondary matter. Both primary and secondary matter have passive force, but secondary matter has active force derived from the primitive active force of the corporeal substances from which it is aggregated. Woolhouse expounds the meaning of all this in the next chapter.

Further Notes & Animadversions
  • I could have applied this Notes as Footnotes to the above text, but have decided to give myself more “room” to discuss the matters raised.

In-Page Footnotes

Footnote 2:
  • This is the write-up as it was when this Abstract was last output, with text as at the timestamp indicated (27/06/2020 17:15:22).
  • Link to Latest Write-Up Note.
Footnote 3:
  • This is the correct order – individuals are first substances, kinds are second substances.
Footnote 4:
  • This seems to be an accurate paraphrase of a comment made by Leibniz to Arnauld, but seems wrongly to grant substantial unity to aggregates (the constituent parts of the human body).
Footnote 5:
  • So, according to Leibniz, God is bound by his own nature to create the universe he did create.
Footnote 6:
  • Has Woolhouse cleared up the controversy or left it hanging?

Text Colour Conventions (see disclaimer)

  1. Blue: Text by me; © Theo Todman, 2020

© Theo Todman, June 2007 - July 2020. Please address any comments on this page to theo@theotodman.com. File output:
Website Maintenance Dashboard
Return to Top of this Page Return to Theo Todman's Philosophy Page Return to Theo Todman's Home Page