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The notion of a substance played a key role in the metaphysical thought of the Middle Ages. As we have seen, Aristotle conceived of a substance as an individual subject enduring through change, and having independent existence. In the thirteenth century, the celebrated philosopher and theologian St Thomas Aquinas, taking his cue from Aristotle, defined a substance as an ens per se existens – an ‘entity existing through itself’ (independently, or in its own right).¹ But if the idea of an independent being is construed in the strongest possible sense, as something whose existence is entirely self-sufficient, then one might conclude that the term ‘substance’ should strictly speaking be reserved for God alone (since, according to standard Christian doctrine, He alone is the eternal source of all being, and the existence of everything else is dependent on Him). And this is precisely the line taken several centuries later by René Descartes, at the start of the following extract from the Principles of Philosophy (Principia Philosophiae, published in Latin in 1644).

God, according to Descartes, is the sole substance in the strict sense; created things can count as substances only in a secondary sense. But in his account of created things, Descartes makes a striking departure from the framework for understanding reality which Aristotle had offered. The Cartesian² framework for explaining the physical world offers a radically new ‘ontology’ – a radically new conception of what there is. As we saw in the previous extract, Aristotle grouped individual substances together as belonging to natural kinds (species and genera); and among ‘scholastic’ medieval philosophers (those who followed a broadly Aristotelian approach), a great deal of energy was spent in classifying natural phenomena, and explaining the way things behaved in terms of the essential characteristics of the natural kind to which they were taken to belong. (The traditional classificatory scheme involved four principal elements, earth, water, air and fire, each made up of different combinations of the four qualities, Cold, Wet, Dry and Hot.) Ushering in the scientific revolution of the seventeenth century, Descartes argues that to understand natural phenomena we need instead to adopt a mathematical approach. What matters for explanation in physics are not differences in ‘kind’ but a quantitative analysis, expressible in terms of strict mathematical laws. Hence we find, in place of the traditional plurality of individual substances belonging to various natural kinds, just one essential kind of matter: the whole universe is composed of a single ‘extended stuff’, and all phenomena are to be explained quantitatively, in terms of the size, shape and motion of its particles.

Descartes’s account of the world thus conceives of matter as a single extended body, indefinitely modifiable as to its dimensions, and dependent only on the supreme substance, God, for its existence and the movement of its parts. Finally, to complete the picture, there are, in addition to the creator and the physical world, created minds or souls: individual centres of consciousness, whose existence, Descartes maintains, does not require anything material (for more on this notion of the immaterial mind, compare Part IV, extract 4, below). Descartes’s ontology thus gives us three categories of substance: first, substance in the strict sense – the independent, self-sufficient creator, God; second, extended substance, or matter; and third ‘thinking substance’ – the category to which created minds belong.

What is meant by ‘substance’ – a term which does not apply univocally to God and his creatures.

In the case of those items which we regard as things or modes of things, it is worthwhile examining each of them separately. 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. In the case of all other substances, we perceive that they can exist only with the help of God’s concurrence. Hence the term ‘substance’ does not apply univocally, as they say in the Schools, to God and to other things; that is, there is no distinctly intelligible meaning of the term which is common to God and his creatures. In the case of created things, some are of such a nature that they cannot exist without other things, while some need only the ordinary concurrence of God in order to exist.³ We make this distinction by calling the latter ‘substances’ and the former ‘qualities’ or ‘attributes’ of those substances.

The term ‘substance’ applies univocally to mind and to body. How a substance itself is known.

But as for corporeal substance and mind (or created thinking substance), these can be understood to fall under this common concept: things that need only the concurrence of God in order to exist. However, we cannot initially become aware of a substance merely through its being an existing thing, since this alone does not of itself have any effect on us. We can, however, easily come to know a substance by one of its attributes, in virtue of the common notion that nothingness possesses no attributes, that is to say, no properties or qualities. Thus, if we perceive the presence of some attribute, we can infer that there must also be present an existing thing or substance to which it may be attributed.

To each substance there belongs one principal attribute; in the case of mind, this is thought, and in the case of body it is extension.

A substance may indeed be known through any attribute at all; but each substance has one principal property which constitutes its nature and essence, and to which all its other properties are referred. Thus extension in length, breadth and depth constitutes the nature of corporeal substance; and thought constitutes the nature of thinking substance. Everything else which can be attributed to body presupposes extension, and is merely a mode of an extended thing; and similarly, whatever we find in the mind is simply one of the various modes of thinking. For example, shape is unintelligible except in an extended thing; and motion is unintelligible except as motion in an extended space; while imagination, sensation and will are intelligible only in a thinking thing. By contrast, it is possible to understand extension without shape or movement, and thought without imagination or sensation, and so on; and this is quite clear to anyone who gives the matter his attention.

How we can have clear and distinct notions of thinking substance and of corporeal substance, and also of God.

Thus we can easily have two clear and distinct notions or ideas, one of created thinking substance, and the other of corporeal substance, provided we are careful to distinguish all the attributes of thought from the attributes of extension. We can also have a clear and distinct idea of uncreated and independent thinking substance, that is of God. Here we must simply avoid supposing that the idea adequately represents everything which is to be found in God; and we must not invent any additional features, but concentrate only on what is really contained in the idea and on what we clearly perceive to belong to the nature of a supremely perfect being. And certainly no one can deny that we possess such an idea of God, unless he reckons that there is absolutely no knowledge of God to be found in the minds of men …

How thought and extension may be distinctly recognized as constituting the nature of mind and of body.

Thought and extension can be regarded as constituting the natures of intelligent substance and corporeal substance; they must then be considered as nothing else but thinking substance itself and extended substance itself – that is, as mind and body. In this way we will have a very clear and distinct understanding of them. Indeed, it is much easier for us to have an understanding of extended substance or thinking substance than it is for us to understand substance on its own, leaving out the fact that it thinks or is extended. For we have some difficulty in abstracting the notion of substance from the notions of thought and extension, since the distinction between these notions and the notion of substance itself is merely a conceptual distinction. A concept is not any more distinct because we include less in it; its distinctness simply depends on our carefully distinguishing what we do include in it from everything else …

The arguments that lead to the certain knowledge of the existence of material things.

Everyone is quite convinced of the existence of material things. But earlier on we cast doubt on this belief and counted it as one of the preconceived opinions of our childhood.⁴ So it is necessary for us to investigate next the arguments by which the existence of material things may be known with certainty. Now, all our sensations undoubtedly come to us from something that is distinct from our mind. For it is not in our power to make ourselves have one sensation rather than another; this is obviously dependent on the thing that is acting on our senses. Admittedly one can raise the question of whether this thing is God or something different from God. But we have sensory awareness of, or rather as a result of sensory stimulation we have a clear and distinct perception of, some kind of matter, which is extended in length, breadth and depth, and has various differently shaped and variously moving parts which give rise to our various sensations of colours, smells, pain and so on. And if God were himself immediately producing in our mind the idea of such extended matter, or even if he were causing the idea to be produced by something which lacked extension, shape and motion, there would be no way of avoiding the conclusion that he should be regarded as a deceiver. For we have a clear understanding of this matter as something that is quite different from God and from ourselves or our mind; and we appear to see clearly that the idea of it comes to us from things located outside ourselves which it wholly resembles. And we have already noted that it is quite inconsistent with the nature of God that he should be a deceiver. The unavoidable conclusion, then, is that there exists something extended in length, breadth and depth and possessing all the properties which we clearly perceive to belong to an extended thing. And it is this extended thing that we call ‘body’ or ‘matter’.

The basis for our knowledge that the human body is closely conjoined with the mind.

By the same token, the conclusion that there is a particular body that is more closely conjoined with our mind than any other body follows from our clear awareness that pain and other sensations come to us quite unexpectedly. The mind is aware that these sensations do not come from itself alone, and that they cannot belong to it simply in virtue of its being a thinking thing; instead, they can belong to it only in virtue of its being joined to something other than itself which is extended and movable, namely what we call the human body. But this is not the place for a detailed explanation of its nature.

Sensory perception does not show us what really exists in things, but merely shows us what is beneficial or harmful to man’s composite nature.

It will be enough, for the present, to note that sensory perceptions are related exclusively to this combination of the human body and mind.⁵ They normally tell us of the benefit or harm that external bodies may do to this combination, and do not, except occasionally and accidentally, show us what external bodies are like in themselves. If we bear this in mind we will easily lay aside the preconceived opinions acquired from the senses, and in this connection make use of the intellect alone, carefully attending to the ideas implanted in it by nature.

The nature of body consists not in weight, hardness, colour, or the like, but simply in extension.

If we do this, we shall perceive that the nature of matter, or body considered in general, consists not in its being something which is hard or heavy or coloured, or which affects the senses in any way, but simply in its being something which is extended in length, breadth and depth. For as regards hardness, our sensation tells us no more than that the parts of a hard body resist the motion of our hands when they come into contact with them. If, whenever our hands moved in a given direction, all the bodies in that area were to move away at the same speed as that of our approaching hands, we should never have any sensation of hardness. And since it is quite unintelligible to suppose that, if bodies did move away in this fashion, they would thereby lose their bodily nature, it follows that this nature cannot consist in hardness. By the same reasoning it can be shown that weight, colour, and all other such qualities that are perceived by the senses as being in corporeal matter, can be removed from it, while the matter itself remains intact; it thus follows that its nature does not depend on any of these qualities …

The extension of the world is indefinite.

What is more we recognize that this world, that is, the whole universe of corporeal substance, has no limits to its extension. For no matter where we imagine the boundaries to be, there are always some indefinitely extended spaces beyond them, which we not only imagine but also perceive to be imaginable in a true fashion, that is, real. And it follows that these spaces contain corporeal substance which is indefinitely extended. For, as has already been shown very fully, the idea of the extension which we conceive to be in a given space is exactly the same as the idea of corporeal substance.

Similarly, the earth and the heavens are composed of one and the same matter; and there cannot be a plurality of worlds.

It can also easily be gathered from this that celestial matter is no different from terrestrial matter.⁶ And even if there were an infinite number of worlds, the matter of which they were composed would have to be identical; hence, there cannot in fact be a plurality of worlds, but only one. For we very clearly understand that the matter whose nature consists simply in its being an extended substance already occupies absolutely all the imaginable space in which the alleged additional worlds would have to be located; and we cannot find within us an idea of any other sort of matter.

All the variety in matter, all the diversity of its forms, depends on motion.

The matter existing in the entire universe is thus one and the same, and it is always recognized as matter simply in virtue of its being extended. All the properties which we clearly perceive in it are reducible to its divisibility and consequent mobility in respect of its parts, and its resulting capacity to be affected in all the ways which we perceive as being derivable from the movement of the parts. If the division into parts occurs simply in our thought, there is no resulting change; any variation in matter or diversity in its many forms depends on motion. This seems to have been widely recognized by the philosophers, since they have stated that nature is the principle of motion and rest. And what they meant by ‘nature’ in this context is what causes all corporeal things to take on the characteristics of which we are aware in experience …

God is the primary cause of motion; and he always preserves the same quantity of motion in the universe.

After this consideration of the nature of motion, we must look at its cause. This is in fact twofold: first, there is the universal and primary cause – the general cause of all the motions in the world; and second there is the particular cause which produces in an individual piece of matter some motion which it previously lacked. Now as far as the general cause is concerned, it seems clear to me that this is no other than God himself. In the beginning in his omnipotence he created matter along with its motion and rest; and now, merely by his regular concurrence, he preserves the same amount of motion and rest in the material universe as he put there in the beginning. Admittedly motion is simply a mode of the matter which is moved. But nevertheless it has a certain determinate quantity; and this, we easily understand, may be constant in the universe as a whole while varying in any given part. Thus if one part of matter moves twice as fast as another which is twice as large, we must consider that there is the same quantity of motion in each part; and if one part slows down, we must suppose that some other part of equal size speeds up by the same amount. For we understand that God’s perfection involves not only his being immutable in himself, but also his operating in a manner that is always utterly constant and immutable. Now there are some changes whose occurrence is guaranteed either by our own plain experience or by divine revelation, and either our perception or our faith shows us that these take place without any change in the creator; but apart from these we should not suppose that any other changes occur in God’s works, in case this suggests some inconstancy in God. Thus, God imparted various motions to the parts of matter when he first created them, and he now preserves all this matter in the same way, and by the same process by which he originally created it; and it follows from what we have said that this fact alone makes it most reasonable to think that God likewise always preserves the same quantity of motion in matter …

The only principles which I accept, or require, in physics are those of geometry and pure mathematics; these principles explain all natural phenomena, and enable us to provide quite certain demonstrations regarding them.

I will not here add anything about shapes or about the countless different kinds of motions that can be derived from the infinite variety of different shapes. These matters will be quite clear in themselves when the time comes for me to deal with them. I am assuming that my readers know the basic elements of geometry already, or have sufficient mental aptitude to understand mathematical demonstrations. For I freely acknowledge that I recognize no matter in corporeal things apart from that which the geometers call quantity, and take as the object of their demonstrations, i.e. that to which every kind of division, shape and motion is applicable. Moreover, my consideration of such matter involves absolutely nothing apart from these divisions, shapes and motions; and even with regard to these, I will admit as true only what has been deduced from indubitable common notions so evidently that it is fit to be considered as a mathematical demonstration.