Meditation VI: The Conceivability and Divisibility Arguments

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Meditation VI: The Conceivability and Divisibility Arguments

The Argument Introduced
The Conceivability Argument occurs in Meditation VI. It is Descartes’ most celebrated argument. It was criticised in its day and has been ever since. The argument purports to establish that minds are non-physical substances and hence that a mind is not identical to any bit of the body, such as the brain. A person is a special unity of two substances: physical substance (the body) and mental substance (the mind). Only humans are such special unities. Animals have bodies but lack minds and angels have minds but lack bodies.
Here’s the passage:
First, I know that everything which I clearly and distinctly understand is capable of being created by God so as to correspond exactly with my understanding of it. Hence the fact that I can clearly and distinctly understand one thing apart from another is enough to make me certain that the two things are distinct, since they are capable of being separated, at least by God. The question of what kind of power is required to bring about such a separation does not affect the judgment that they are distinct. Thus, simply by knowing that I exist and seeing at the same time that absolutely nothing belongs to my nature or essence except that I am a thinking thing, I can infer correctly that my essence consists solely in the fact that I am a thinking thing. It is true that I may have (or, to anticipate, that I certainly have) a body that is very closely joined to me. But, nevertheless, on the one hand I have a clear and distinct idea of myself, in so far as I am simply a thinking, non-extended thing; and on the other hand I have a distinct idea of body, in so far as this is simply an extended, non-thinking thing. And accordingly, it is certain that I am really distinct from my body, and can exist without it.
The key lines are highlighted. Let’s now put together the argument:

  1. [T]he fact that I can clearly and distinctly understand one thing apart from another is enough to make me certain that the two things are distinct.

The Distinctness Criterion: if you can clearly and distinctly conceive of X apart from Y and Y apart from X, then X and Y are distinct.

  1. [B]y knowing that I exist and seeing at the same time that absolutely nothing belongs to my nature or essence except that I am a thinking thing, I can infer correctly that my essence consists solely in the fact that I am a thinking thing… I am simply a thinking, non-extended thing.

The Essence of Mind: I clearly and distinctly understand a mind to be a essentially a thinking, non-extended substance.

  1. I have a distinct idea of body, in so far as this is simply an extended, non-thinking thing.

The Essence of Body: I clearly and distinctly understand a body to be essentially a extended, non-thinking substance.

  1. It is certain that I am really distinct from my body, and can exist without it.

Conclusion: mind and body are distinct substances.

Preliminary Analysis
Descartes is claiming that he has two clear and distinct ideas about the essences of mind and body. These ideas represent them as having distinct essences. It is therefore possible to conceive of them as distinct. And so, by the Distinctness Criterion, they really are distinct.
There are a number of obvious things we should question:

  • Has Descartes grasped the essence of body correctly?

  • Has Descartes grasped the essence of mind correctly?

  • Should we accept the Distinctness Criterion?

Let’s begin with the latter.

The Distinctness Question :Conceivability, Possibility & Leibniz’s Law - I
Descartes claims that since minds and bodies have different properties, they are different substances. Now, this follows in Descartes’ system because substances are defined by a unique principal attribute: see Interlude: Substance and Attribute* above. But we needn’t tie it to Descartes’ particular system.
There’s a general principle at work here that is called Leibniz’s Law, after the philosopher Leibniz. We’ll explain why shortly. The principle concerns the concept of identity:
(LL) X and Y are identical substances ↔ X and Y share all their properties.
This should have some intuitive plausibility. Imagine you have two TV screens before you showing you objects X and Y. You investigate all the properties of X and Y and find they are the same. Surely you’d think that the two TV screens are showing you the same object – that X is Y. For if they were distinct, then there must be some property one has that the other lacks that makes them distinct. Even the most identical-looking of twins have some differences. They will perhaps have different numbers of hairs, different memories, different attitudes and, ultimately, they will differ in how the atoms in their body are arranged at any one time, for example.
(They will also be in different places at any one time but this is irrelevant for reasons we’ll come to. We’re excluding ‘relational’ properties of time and place – being in a certain place at a certain time – from the ones that matter. We’re interested in ‘intrinsic’ properties – those that specify ‘internal’ features of the things.)
Now, (LL*) follows from (LL):
(LL*) X and Y are distinct substances ↔ X and Y don’t share all their


So. To prove that X and Y are distinct substances, we need only show that they have different properties. This is just what Descartes is doing. He is arguing that since minds and bodies have distinct properties, they are distinct substances.
The Distinctness Question :Conceivability, Possibility & Leibniz’s Law - II
Whilst (LL) has some intuitive plausibility, it seems pretty easy to show that it’s false. Consider Clark Kent. Here’s a property he has. He is believed by Lois Lane to be a mild-mannered reporter. Now consider Superman. Superman does not have this property. Lois does not think Superman is a mild-mannered reporter but a cape-wearing superhero. So, by (LL*) – which follows from (LL), remember – Clark Kent and Superman are distinct things. But they are not. They are one and the same person!
What’s gone wrong? The problem is that (LL) and (LL*) are only valid for extensional properties not intensional properties. Explaining this will require a bit of a run-up.
Let us say that words – many of them, at least – refer to things. The name “Barack Obama”, for example, refers to a certain person. The noun “badger” refers to the property of being a badger. Along with what a word refers to, we can distinguish the way in which it refers to it. The expressions “Barack Obama” and “The President of the USA” both refer to the same thing but they refer to him in different ways. One picks him out in virtue of a label he was given at birth. The other picks him out via his possession of a certain property conferred on him through winning the Presidential elections in 2008. Let us equate these ‘ways’ with meanings. So, “Barack Obama” and “The President of the USA” have different meanings although they have the same reference.
An extensional context is one in which the truth of a sentence depends on the references of the expressions in it and not on their meanings. If I simply say:

  1. Barack Obama lives in Washington.

I say something that is true. It remains true if I swap “Barack Obama” for “The President of the USA”. It is irrelevant how I talk about Barack – what makes it true is that the physical thing, the person, inhabits a certain other physical thing, a city. Speaking thus, the context is extensional.

Now consider the following sentence.

  1. Bernard believes that Barack Obama lives in Washington.

We have sentence (1) embedded in (2). (2) is prefixed by the sentential operator “Bernard believes that…” This creates an intensional context. The truth of (2) depends not on the references but on the meanings. Here’s why. It is quite possible that Bernard thinks that George W. Bush is still president, that he lives in Texas and that Barack lives in Washington. So, (2) is true. But (3) isn’t:

  1. Bernard believes that the President of the USA lives in Washington.

So, despite the fact that “Barack Obama” and “The President of the USA” refer to the same thing, you can’t swap them. For what makes (2) true and (3) false is Bernard’s way of viewing the world, not how the world actually is. Although these terms co-refer, Bernard doesn’t realise they do.

In extensional contexts, you can substitute co-referring terms salva veritate – without changing whether they are true or false – whereas in intensional contexts, you cannot. Psychological verbs create intensional contexts. Bernard could hope to see Barack Obama in Washington but not the President of the USA, be afraid that Barack Obama is hiding in his garage but not be afraid that the President of the USA, and so on.
It is not only psychological verbs that create intensional contexts. Modal operators such as “it is necessarily true that” do too. “50” and “the number of US states” refer to the same thing, the number 50. But whereas (4) is true, (5) is false:

  1. It is necessarily true that 50 is less than 51.

  2. It is necessarily true the number of US states is less than 51.

For history could have been otherwise and there could have been a 51st state.

So why does this matter? Lois believes that Clark Kent has a certain property and believes that Superman does not have it. Descartes’ argument is that he conceives (has a clear and distinct idea) that mind has one essential property and conceives that body has another. The italicised verbs are psychological verbs. They create intensional contexts. The properties they assign are intensional properties. And Leibniz’s Law doesn’t work for intensional properties.
The reason is that identity is a feature of how things are, not how things are thought to be. The world is what it is it can be represented by minds in many different and incorrect ways.
The Distinctness Question :Conceivability, Possibility & Leibniz’s Law - III
Lois misrepresents the world as one in which Clark Kent and Superman are distinct. So what it is to say that Descartes’ ‘clear and distinct’ ideas of mind and body as distinct are not equally misleading and that there is just one substance with mental and physical properties after all?
Just so that we’re clear, what Descartes needs is the following argument:

  1. Mind has the essential property of thought

  2. Body has the essential property of extension.

  3. By LL*, different properties → different substances

  4. Therefore, minds and bodies (=physical bodies) are distinct.

But what Descartes has is:

  1. I conceive that mind has the essential property of thought.

  2. I conceive that body has the essential property of extension.

  3. If I can conceive of two things as distinct, they really are distinct.

  4. Therefore, mind and body are really distinct.

What Descartes needs to establish is that what seems clearly conceivable is real. Now, we have good examples of where conceivability doesn’t imply possibility.

  • Time travel. Seems conceivable but is arguably impossible – consider the Grandfather Paradox.

  • Non-Euclidean nature of space. Many people thought that this was the only conceivable geometry but it turns out it is one of infinitely many.

  • Goldbach Conjecture: Every positive integer ≥ 3 is the sum of two primes. Seems we can imagine in some sense it being true or false given that it is unproven.

So, does it work in Descartes’ case?

Antoine Arnauld argued in the Fourth Replies that it didn’t. He argued that someone could fail to grasp the Pythagorean property (PP) possessed by all right-angled triangles. So, someone could believe a triangle to lack a property it necessarily cannot – a property not even God could take away from it.

Descartes replied in two ways. First, he replied that you can’t really have the kind of ideas Arnauld supposes. He says that (i) whilst you can understand what a right-angled triangle is without grasping that it has the PP, you can’t grasp what the PP is without grasping that it holds of right-angled triangles. By contrast, you can grasp that the mind is distinct from body and body is from mind; (ii) even if you don’t grasp that the PP holds of right-angled triangles, you have to grasp that some relationship holds between the square on the hypotenuse and the squares on the other two sides. This is deeply suspect, to say the least.

Second, he replied that neither a triangle nor the PP are substances and hence not complete things. This requires us to talk more about substances and why Descartes is a substance dualist.
The second objection is one we’ll pursue in the extra material at the end. We’ll pick up here the former objection. Descartes is basically saying that he has got properly clear and distinct ideas of the essences of mind and body that therefore get reality right and so enable him to jump from his conception of X and Y as distinct to the reality of them being distinct. Does he?
The Distinctness Question: Clarity and Distinctness
Let’s recall the definitions of clarity and distinctness
I call a perception ‘clear’ when it is present and accessible to the attentive mind - just as we say that we see something clearly when it is present to the eye’s gaze and stimulates it with a sufficient degree of strength and accessibility. I call a perception ‘distinct’ if, as well as being clear, it is so sharply separated from all other perceptions that it contains within itself only what is clear. [...] For example, when someone feels an intense pain, the perception he has of it is indeed very clear, but is not always distinct. For people commonly confuse this perception with an obscure judgment they make concerning the nature of something which they think exists in the painful spot and which they suppose to resemble the sensation of pain; but in fact it is the sensation alone which they perceive clearly. Hence a perception can be clear without being distinct, but not distinct without being clear. (Principles 45-46: CSM I, 207-8: AT VIIIA 22)
On the one hand, one can say that any attempt to define a true thought in terms of its clarity is hopelessly subjective and vague: what seems true for you might not seem true to me. On the other hand, if we are to do any philosophy at all, we must allow for the possibility that we can grasp true thoughts and so we must have some story to tell. It may be true that a true thought is one that corresponds to reality but if we cannot tell when this occurs, we might as well give up. We might then suggest that Descartes should have appealed to something like objective proof: X is recognisably true if we can grasp the proof of X. But, apart from being something Descartes agreed with anyway – why else would he have written anything if didn‘t think it constituted an objective proof? – it merely pushes the problem one stage back. What is the sign of a correct grasp of the proof?
A proof is technically a collection of sentences (premises)  and a conclusion C. A valid proof is one where  entail C. A useful valid proof is one where (a) each proposition in  can be easily understood and (b) the logical jump from each stage in the proof to the final conclusion is as simple as possible. (Conceived of as a recipe for proving rather than the proof itself, we have in effect just defined an algorithm – if we add, that is, that the proof can be carried out in a finite number of steps.) You can’t try to say that the grasp of X as true consists in the correct grasp of a proof of X for fear of an infinite regress. Some propositions must be graspable as true directly.
Indeed, this is just what Descartes does with the cogito. He denies that the cogito is a syllogistic argument of the form: (I) I think; (II) All thinking things exist; (III) I exist. The connection between thinking and existing is something that one must grasp directly, by a flash of intuition. Something like this must happen with all basic thoughts. In pointing out that the basic thoughts are those where the subject matter is clearly understood (clear) and where we are excluding any implications of the thought (distinctness), Descartes is therefore giving good advice.
So, the question is whether the conceptions of mind and body are immediately graspable in this way or whether they are too complex.
The Body Question
Descartes establishes the essence of body as extension in Meditation V:
Quantity, for example, or ‘continuous’ quantity as the philosophers commonly call it, is something I distinctly imagine. That is, I distinctly imagine the extension of the quantity (or rather of the thing which is quantified) in length, breadth and depth. I also enumerate various parts of the thing, and to these parts I assign various sizes, shapes, position and local motions; and to the motions I assign various durations.
Descartes, you will recall, is a mechanist. The physical world is stuff in motion; the interactions are determined by the shapes and sizes of the bits of stuff. The universe is a plenum and matter is infinitely divisible.
Thomas Hobbes (1588-1679), said that mind just is matter. Mental activity is brain activity. He, like Descartes, was an early example of what we would now call a scientist but differed through being more Empiricist than Rationalist: for Hobbes, the truth is to be discovered by observation and experiment and not by pure reason.
Hobbes thought of matter as made up of atoms in empty space. The very fact that they could coherently disagree shows that Descartes was wrong to say he clearly understood the essence of matter. As you perhaps have realised, history favoured Hobbes. At the start of the 18th century, Newton won the argument that space must exist as a void against the relationist view of Leibniz. In the 19th century, atomism came of age. The English chemist John Dalton published his A New System of Chemical Philosophy in 1803 which put forward the theory that elements were composed of atoms which combine in chemical reactions to make compounds. Importantly, he provided the first table of atomic weights.
In the 20th century, our understanding of what matter is changed radically. In the early part, scientists realised that atoms weren’t literally atomic – indivisible – but contained parts: protons, neutrons and electrons. Other particles then started to be discovered and it is still unclear just what particles there are and how they function. One thing is clear: Descartes certainly didn’t have a clear and distinct understanding of what matter is.
The Mind Question
It is in Meditation II that Descartes says that a mind is a thinking thing, where “thinking” covers any mental activity that doesn’t imply the existence of a physical world. So, believing that there’s a badger before me is thinking. There may be no badgers but the concept exists and I can employ it in thought. Knowing that there’s a badger before me is not such a mental state as it implies that there is a badger before me (knowledge is factive, remember.)
Descartes brings together a diverse set of mental activities. What distinguishes them as mental? There are three possibilities.

  • Consciousness: awareness of thinking.

  • Intentionality: thoughts have a content.

What did Descartes have in mind? Descartes talks of our awareness of our thoughts and goes so far as to say to Gassendi in the fifth replies that we’re always thinking:

You say that you want to stop and ask whether I think the soul always thinks. But why should it not always think, since it is a thinking substance? It is no surprise that we do not remember the thoughts that the soul had when in the womb or in a deep sleep, since there are many other thoughts that we equally do not remember, although we know we had them when grown-up, healthy and wide-awake. (CSM I 246-7: AT VII 356-7)
This suggests consciousness. But now what do we mean by “consciousness”

  • Phenomenal consciousness: There is something it is like to be a believing / sensing / emoting thing.

  • Subjective consciousness: Subjective awareness = the awareness of the perspectival nature of thought; self-consciousness in of the thin self, of the “I”.

Descartes didn’t have the terminology to hand that we have. It is probably best to say that he didn’t distinguish the two. When we think, we are aware of there being a thought and sometimes this awareness takes the form of a sensation (e.g. when we are in pain / sensing something.) In Principles I:9, he writes:

By the term “thought”, I understand everything which we are of aware of as happening within us, in so far as we have awareness of it. (CSM 195: AT VIIIA 7)
Subjectivity and Divisibility
It is subjective awareness that seems to be at work in the Divisibility argument:

  1. A body is divisible.

  2. A mind is not.

  3. Mind ≠ body.

Descartes observes that we distinguish the will and the intellect but he points out that these are conceptual distinctions only, such as distinguishing the shape of a sphere from the sphere itself. They are features of a single mind. We know that we can affect the mind by affecting the body: by amputating limbs or excising cerebral tissue, we can limit the range of sensations and cognitive functions. We do not obviously remove the subjective viewpoint, however. It is hard to see how a mind could lose that.

Impossible or just hard? Can we imagine someone whose mind is fragmented so that their actions are not co-ordinated? The will acts independently of the intellect which doesn’t take notice of sensation? There are cases of cognitive malfunction, notably when the frontal lobes are damaged, where people cannot “get it together”. This might suggest a model of the mind where there are very many autonomous departments that normally are integrated into a single perspective. When they come apart, there is no single mind: there are various faculties acting (to some extent) autonomously. If the various faculties can be located in different bits of the brain – along with the “integrating faculty” – then this suggests that the mind is divisible after all.
In response, one might say that this challenges thick subjectivity: the complete, integrated perspective on the world we normally have. It doesn’t challenge thin subjectivity: that thoughts, when they occur, are perspectival. Someone who lacks thick subjectivity would be in effect a collection of mini-minds all doing their own thing. What you cannot take away is the subjectivity of thought to leave just the thought. So, even if a mind is divisible into many minds, you can’t reduce a thought beyond its being a subjective experience. Either there is a sensation or thought or there isn’t. There are no half-measures.
The Nature of Mind
Is Descartes right? Pierre Gassendi criticises Descartes for separating intellection and imagination on the basis of introspective differences. Might there be one faculty rather than two? Gassendi is much more of an empiricist than Descartes. His point is that science will have to establish the essence of mind, not philosophical reflection. Ultimately, he presses the same objection that Gassendi, Hobbes and others do: that even if we grant that mind appears different from body, it does not follow that mind is in fact separate from body as we could simply be ignorant of what mind and body really are. Indeed, Gassendi objected that Descartes’ defining himself as a mind – a as a thinking thing – was alright as far as it goes but it does not go very far. He compared Descartes to a blind man who defines the sun as a “heating thing”. The blind man has grasped a key property of the sun but not told us what sort of thing the sun is – what the substance of the sun is.
What’s at issue here is what we mean by “mind”. Descartes thinks that the mind must be a substance because thoughts are properties. Thoughts are had by something: the subject, the “I”. Now, Descartes notoriously moves from the thought that thoughts require a subject to the existence over time of a single subject. He assumes, that is, that if I have two thoughts at two different times, it is the same “I” that has those thoughts. Kant saw no easy passage from the former to the latter. Hume went one stage further and denied that he had any idea of the mind as a substance. He simply observed a sequence of subjective thoughts. But this is not an issue we need consider here.
What we must consider is whether the mind is a subject, albeit even for an instant. Here, Descartes seems on safer ground. There is a unity to experience that is analogous to the unity of a subject of predication. Just a cube can be blue and heavy and wooden, so too can I perceive that it is raining, feel an itch and wonder where my badger has gone. (And Kant agreed.)
Of course, we can say now that there is much more to the mind than Descartes believed. We talk of the unconscious, for example. But one might wonder whether there has been a shift in meaning from mind = that bearer of properties we can access by introspection to mind = that which explains behaviour. Descartes was happy to allow our behaviour could be determined by non-mental activities. Reflex reactions occur when the animal spirits move the body without getting the mind involved, for example. So, perhaps Descartes simply means the conscious mind by “mind”.
So Where Are We?
This depends on what we’re understanding ‘thought’ as:

  • If we take Descartes as focusing on the perspectival nature of self-conscious thought, then the challenge to Descartes is to think of how a material thing, necessarily made up of parts, could be in some sense identical with a self or “I” that necessarily lacks them.

  • If we take Descartes as focusing on the phenomenological aspect of experience, then the challenge is to explain how matter can give rise to feelings.

  • If we take Descartes as focusing on the intentionality of thought, then the challenge is to explain how states of matter can “be about” something.

The most progress has been made with the third challenge. We have computers – material things – which have internal states that have content. A state of a computer can represent what is on the screen, for example, or a list of programs currently active. Indeed, a database can represent people’s names, addresses, and so on.

The other two are more problematic. We do not have machines that feel or are self-aware. It is not easy to understand how such things are to be created.
Philosophers typically respond to Descartes by arguing that there’s just a failure of conceivability. We have plenty of cases where distinct concepts refer to the same property. Our concepts of water and H2O are different and yet they pick out the same thing. We cannot easily grasp how the familiar liquid is produced by the combination of two gases but we don’t disbelieve the science. On top of this, we have explained more and more of the world in physical terms. The evidence is, therefore, that the mind is simply a so-far unexplained bit of physical reality. You’ll pursue this when studying Dualism in the Philosophy of Mind course.

Extra: Substance, Attribute, Mode *
When thinking about the mind, Descartes first establishes that his existence is closely connected to thought. He then moves to think of himself as essentially a thinking thing and of various mental activities as types of thought. Similarly, when thinking about the mind, he picks out the properties of having length, breadth and depth and moves to talking of them as essential properties of physical things. We might ask how Descartes establishes that these properties define two kinds of substance.
You may also have noticed that Descartes talks initially of minds as essentially thinking and of bodies as essentially extended. Subsequently (in the Conceivability Argument), he talks of minds as essentially thinking and non-extended and bodies as essentially extended and non-thinking. The second question we might to ask is why there could not be a single substance that is essentially thinking and extended.
Here are the short answers to these questions. In Descartes’ metaphysics, substances are defined by principal attributes and all properties of a substance are modes (≈varieties, different ways) of that attribute. Extension is the principal attribute of substance because shapes are different ways of being extended. Thought is the principal attribute of mind because all mental activity is a variety of thought qua conscious and contentful thought. A substance can only have one principal attribute and so if the principal attributes of X and Y are not identical, X and Y are distinct substances – as the Conceivability argument needs. For more on this, see the sections that follow.
Note that if we forget all about (LL) and (LL*) are just keep within to Descartes’ metaphysics, we don’t avoid the conceivability problem: that Descartes may have an insufficiently developed conception of the principal attributes of mind and body to assert their distinctness.
Extra: The Distinctness Question :Conceivability, Possibility & Leibniz’s Law
The principle (LL) is in fact a combination of two principles with grand-sounding names of the Principle of Identity of Indiscernibles (PIdIn) and the Principle of the Indiscernibility of Identicals (PInId).
(PIdIn) If X and Y share all their properties, then X = Y.

(PInId) If X = Y, then X and Y share all their properties.

The former comes from Leibniz. Leibniz writes:
[It] is not true that two substances may be exactly alike and differ only numerically…[Discourse on Metaphysics, §9]
That is, no two distinct substances can be exactly alike in sharing all their properties. Not even God could create two things that are absolutely identical. Who would have thought otherwise? Well, Thomas Aquinas held that God created the angels to be exactly alike differing only ‘in number’.
The latter seems just an obvious feature of being a thing. If it were not true then we could have a single thing X/Y and yet it could have incompatible properties! It would be like something entirely blue and entirely green or spherical and cubic – impossible!
As it happens, both parts of Leibniz’s Law have been challenged.
Some philosophers have wondered if there is anything incoherent about a universe that contains just two gold spheres of identical size, shape and constitution. If that is coherent, we have two objects that are alike in every way and yet are distinct. So, (PIdIn) doesn’t hold.
As for (PInId), suppose you paint your door (d) red on Monday and blue on Tuesday. Then d is red on Monday and d is not red on Tuesday. So, since there is a difference of property, we cannot properly be speaking of the same door on two different days. Of course, we do speak thus. To deny this would be to assert that every change in property entails a change of thing. Put more bluntly, nothing could ever change: there is only creation and destruction. So, this raises the question of how we are to understand change. (Though some argue that the essentialism – the view that there can be no change – is in fact correct.)
Extra: Substance and Substance Dualism – I*
Gassendi objected that Descartes’ defining himself as a mind – a as a thinking thing – was alright as far as it goes but it does not go very far. He compared Descartes to a blind man who defines the sun as a “heating thing”. The blind man has grasped a key property of the sun but not told us what sort of thing the sun is – what the substance of the sun is.
Hobbes seemed to argue that Descartes must be a materialist too: all substance must be material:
It is quite certain that the knowledge of the proposition 'I exist' depends on the proposition 'I am thinking' as the author himself has explained to us. But how do we know the proposition 'I am thinking'? It can only be from our inability to conceive an act without its subject. We cannot conceive of jumping without a jumper, of knowing without a knower, or of thinking without a thinker. It seems to follow from this that a thinking thing is something corporeal. For it seems that the subject of any act can be understood only in terms of something corporeal or in terms of matter, as the author himself shows later on his example of the wax: the wax, despite the changes in its colour, hardness, shape and other acts, is still understood to be the same thing, that is, the same matter that is the subject of all these changes.
So what does Descartes think about substances? This is not an easy question to answer.
Gassendi’s claim is that knowing the properties of a thing doesn’t tell us enough about the underlying substance. Hobbes’ claim is that the only kind of underlying substance we can think of is material. Descartes said they were both wrong.i Contra Gassendi, we only know about substances through their properties and contra Hobbes, this does not mean that they must be material.
Here’s his reply to Hobbes:
He is quite right in saying that 'we cannot conceive of an act without its subject'. We cannot conceive of thought without a thinking thing, since that which thinks is not nothing. But he then goes on to say, quite without any reason, and in violation of all usage and all logic: 'It seems to follow from this that a thinking thing is something corporeal.' It may be that the subject of any act can be understood only in terms of a substance (or even, if he insists, in terms of 'matter', i.e. metaphysical matter); but it does not follow that it must be understood in terms of a body.
And here’s an important bit of the Principles where Descartes speaks about substances in the most detail:
52. That the term is applicable univocally to the mind and the body, and how substance itself is known. Created substances, however, whether corporeal or thinking, may be conceived under this common concept; for these are things which, in order to their existence, stand in need of nothing but the concourse of God. But yet substance cannot be first discovered merely from its being a thing which exists independently, for existence by itself is not observed by us. We easily, however, discover substance itself from any attribute of it, by this common notion, that of nothing there are no attributes, properties, or qualities: for, from perceiving that some attribute is present, we infer that some existing thing or substance to which it may be attributed is also of necessity present.
53. That of every substance there is one principal attribute, as thinking of the mind, extension of the body. But, although any attribute is sufficient to lead us to the knowledge of substance, there is, however, one principal property of every substance, which constitutes its nature or essence, and upon which all the others depend. Thus, extension in length, breadth, and depth, constitutes the nature of corporeal substance; and thought the nature of thinking substance. For every other thing that can be attributed to body, presupposes extension, and is only some mode of an extended thing; as all the properties we discover in the mind are only diverse modes of thinking. Thus, for example, we cannot conceive figure unless in something extended, nor motion unless in extended space, nor imagination, sensation, or will, unless in a thinking thing. But, on the other hand, we can conceive extension without figure or motion, and thought without imagination or sensation, and so of the others; as is clear to any one who attends to these matters.
So: every substance has a single defining principal attribute. It is that we only know substances through their properties: in particular, through their principal attributes. To talk of a substance is just to talk of a type of thing and the type is given by the principal attribute. For example, to go Aristotelian, a pen is something that writes. The function defines the thing. A mind is then a thing that thinks. The “thinks” is the important bit, not the “thing”.
What’s important here is that Descartes is telling us to keep our eye on the properties of things. This may seem odd. Don’t we explain the properties by explaining the substance? Gassendi’s objection is easier to understand if we think of substance in modern physical terms, as Gassendi was in effect wanting to do. If we think in this way, then we’re interested in the deeper physical nature of matter. When we talk about the sun, we want to know what it is made of in virtue of which it heats. We want to know about the fusion of atoms and the release of energy. Similarly, when we want to know how magnets attract, we want to know about the nature of the material that gives them this force. So, finally, when we talk about the mind, we want to know what it is made out of in virtue of which it has the properties it has.
But let’s now look at things in the other direction – a more metaphysical direction. Suppose you ask me what sort of thing the sun is. I tell you by telling you about its properties. For what else can I do? It is through heating and having a certain shape and location and doing such-and-such things that the sun is what it is. To talk of the sun as a substance is just to talk of it as a particular bundle of properties. The word “substance” is really doing no special work here. Just so long as we speak in the language of properties, we need to speak of properties as being the properties of something and we use the word “substance” to talk of a collection of instantiated properties. Put another way, there is no such thing as the underlying substance of a collection of properties.
Now let us try to combine the two ways of looking at things. We think of the sun as a bundle of properties. We ask whether we can reduce or explain these properties in terms of anything simpler. After all, to say that the sun is a heating and shiny and …thing risks committing the scholastic error of simply naming things we want to explain with longer words. True enough and of course Descartes would agree. He’s believes in a physical world of just one substance The essence of this stuff is extension: taking up room. Descartes wants to explain everything in terms of the size, shape and motion of physical stuff. Now, look at this again. To talk about extension is to talk of a property: we say something’s extension or the property it has of having such-and-such a shape. Likewise, so too is the motion and size of something a property. Once again, we find ourselves talking about things in terms of their features.
So, when it comes to explaining how the sun works, Descartes will want to offer a genuinely physical explanation (and he does try to) that appeals to the properties of physical stuff: matter. But in so doing, he is reducing talk of complex properties to talk of simpler properties.
Let us now turn to the mind. The principal attribute of mind is thought. So, to talk of the mind as a thinking thing is to identify a mind via subjective mental properties. Now, the temptation is to ask what the underlying substance must be. But perhaps this is begging the question against Descartes. It is unfair, in other words, to assume that mental properties must inhere in some underlying mental stuff with quasi-material properties. A mind is just to be identified as a something-with-these-mental properties.
We arrive, therefore, at the following idea. To speak of minds and bodies is necessary just because we have two distinct types of principal attribute: thought and extension. When we talk about size and shape and motion, we are talking of modifications or modes of extension. For example, the cubic shape of a cube is just a way of being extended and the spherical shape of a ball is just another way of being extended. When we talk about mental states, we are talking about modes of thinking. Fearing a badger is one way of thinking and hoping for coffee is another. Now, there’s no way that modes of extension can be identified with modes of thought. This is the crucial claim Descartes makes. We can now express this in a different way: there must be two types of substance.
The upshot of this is that it opens up a way for Descartes to be a dualist unencumbered by the charge of admitting some sort of ghostly ectoplasmic stuff for the mind to be. All Descartes would need to establish is that thinking cannot be identified with any sort of mechanical activity. Now, there are people who advance such a view today who would deny being substance dualists:

  • Functionalists. A functionalist argues that mental properties are not identical to physical properties but functional properties that may be realised by different physical systems.

  • Property Dualists. There is just one type of physical stuff but there are non-physical properties. These may be emergent or epiphenomenal properties.

  • Conceptual Dualists: There is just one type of physical stuff but there are different and incommensurable ways of looking at the physical world. Mental talk cannot be reduced to physical talk.

Extra: Substance and Substance Dualism – II*
There is another angle to the substance issue, however, that we must consider. Just before the two passages from the Principles above, Descartes writes:
51. What substance is, and that the term is not applicable to God and the creatures in the same sense. But with regard to what we consider as things or the modes of things, it is worth while to examine each of them by itself. By substance we can conceive nothing else than a thing which exists in such a way as to stand in need of nothing beyond itself in order to its existence. And, in truth, there can be conceived but one substance which is absolutely independent, and that is God. We perceive that all other things can exist only by help of the concourse of God. And, accordingly, the term substance does not apply to God and the creatures univocally, to adopt a term familiar in the schools; that is, no signification of this word can be distinctly understood which is common to God and them.
In this definition – and it is one that is doing the work in the Meditations – a substance is something that can exist by itself. (Note that Descartes says that, strictly speaking, nothing exists by itself except God.) Now this does present an obvious problem for the “non-standard” readings of Descartes. For example, a hammer is a functional thing but hammerness is not a property that can exist outside of a hammer. It is not, strictly speaking, separable. A ghostly hammer will still need ghostly stuff to be made out of.
Now, one way of reading these claims is the following:

  • To say X and Y are really distinct is to say that they are not just conceptually distinct in the way that the spherical shape and sphere are. It is to say that one is not reducible to the other.

We can think of the sphere and we can think of its shape. But the shape is not really separable from the sphere. The sphere and the shape are just modes of extension. By contrast, fearing a badger s not a mode of extension – it is something totally different. Consider Principles 60:

60….Strictly speaking, a real distinction exists only between two or more substances; and we can perceive that two substances are really distinct simply from the fact that we can clearly and distinctly understand one apart from the other…And even if we suppose that God has joined some corporeal substance so closely that they [mind and body] cannot be more closely conjoined, thus compounding them into a unity, they nonetheless remain really distinct. For no matter how closely God may have united them, the power which he previously had of separating them, or keeping one in being without the other, is something he could not lay aside; and things which God has the power to separate, or to keep in being separately, are really distinct.
The first part of this says seems to confirm the reading: distinctness is a matter of being able to understand one apart from the other because they have different natures: e.g. functional and physical. But the passage then offers something more traditional:

  • To say that X and Y are distinct is to say that God could create one without the other.

You can’t create hammerness without a hammer. Surely not even God could remove the matter from a hammer to leave the hammerness! So, if the mind can exist all by itself, then there must be some sort of “mental stuff” after all.

Extra: Substance and Substance Dualism – III*
Descartes denies that the mind has extension. This is the conclusion of his divisibility argument. Yet he is keen to emphasise that this does not mean that the mind is unrelated to the body. We are not in our bodies like pilots in a ship but in some way united with the whole of it, he tells us in Meditation VI. In a latter to Hyperaspistes (1641), Descartes writes:
If ‘corporeal’ is taken to mean anything which can in any way affect a body, then the mind too must be called corporeal in this sense; but if ‘corporeal’ is taken to mean whatever is made up of the substance called body, then the mind cannot be said to be corporeal…

The mind is co-extensive with an extended body even though it has no real extension in the sense of occupying a place and excluding other things from it. How this can be, I explained above by the illustration of heaviness conceived of as a real quality.

His illustration “above” was the following. The heaviness of gravity of a body is a feature of the whole of it but it can act in one place, such as when a weight pulls down a rope and “concentrates” the gravity in the point at which the rope is joined to the weight. Descartes uses this example with Elisabeth was well to convey the intermingled union of mind and body.
So, Descartes says that the mind is corporeal in so far as it has effects on the body but not corporeal in so far as it is not an extended stuff. This brings to mind the idea that the mind is the form of the body: “in” the body but not made out of the matter. Talk of forms in this way is of course a kind of functionalism.
Let us not forget finally that Descartes was concerned not to upset religious authorities. He blocked publication of his book advancing a heliocentric view of the heavens after Galileo was put under house arrest. He got in trouble for his metaphysics views too. We saw above how Descartes said that talk of substances was talk of principal attributes. You can’t, strictly speaking, separate the substance from its attributes because those properties are just modes of the principal attribute that defines the substance. Now, the Tridentine doctrine of the Eucharist is that the accidental properties of the bread and wine remain whilst the substance is changed into the body and blood of Christ. This is impossible on Descartes’ view. So, Descartes wanted to make room for the immortality of the soul, which is a strong motivation for the separability doctrine.
(A final final note. Descartes was prepared to cede to God some quite remarkable powers. He thought God had the power to make the necessary truths of mathematics other than they are. This is barely comprehensible. So, it might suggest that Descartes didn’t have a clear idea how God could separate mind and body.)
Substance and Substance Dualism – Summary*
On the one hand, we have a way of understanding Descartes as trying to argue that mind and body were distinct kinds of things, where the issue of matter falls into the background. To talk of substances is really nothing more than to talk of principal attributes or key properties. This opens the way for thinking of mental properties as non-physical but without the need for non-physical stuff.
On the other, the separability doctrine and the religious motivations suggest that minds can be genuinely self-standing things without a physical base.
There is no denying that there is a tension here. Let us finish by pointing out:

  • Descartes didn’t have the modern vocabulary to express property or predicate dualism or functionalism.

  • A very modern way of attempting to reconcile the two would be to suggest that a mind is like a computer program. It cannot exist as a working mind without a physical base: to run a program you need a computer. It can however exist without a physical base in a non-functioning state: a program is just an abstract object.

  • Descartes tries very hard to make sure we see the mind as involved with the body.

  • Descartes never talks about the mind as made out of any kind of non-physical stuff.

i To Gassendi, Descartes also replied that he had a much clearer idea of the mind than a blind man has of the sun. But the point Descartes makes in the main text is more important.

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