The Harmonic Void: Descartes’ Extended Substance
Descartes gets a bad rap. His substance dualism is fine first semester undergrad philosophy fodder, to be churned through the “Problem of Interaction”, refuted, discarded. We’re even told by Hatfield on the SEP article on Descartes’ Life and Works that he is remembered for, among other things, “his failed metaphysics” (2014). Descartes is cool in math club, but he’s definitely the kid that doesn’t get invited to the raging Cognitivist Philosopher parties (should such things exist).
Descartes’ thoughts on thinking substance are well known (more or less), his cogito argument is probably the greatest fridge magnet philosophy has ever produced. His views on ‘extended substance’ less so. They usually make an appearance on the periphery as the stuff that thinking substance cannot be. In fact, we find it just easier to omit it entirely when discussing Descartes in broad strokes and just say ‘matter’, or ‘physical substance’. If this ‘physical’ and ‘matter’ are just innocent substitutions, then we’ve thereby learned nothing about extended substance; if they provide some degree of elucidation in their modern character, then they are not necessarily what Descartes had in mind. If we want to know what extended substance is, and what it does, and why thinking substance cannot be it, and why Descartes thought its existence a sure thing, well, we need to go check in on Descartes.
We first need to get a handle on what ‘Substance’ is in general. In the simplest formulation, substance is the thing that properties stick to. We can’t just have ‘reds’ and ‘bigs’ and ‘sitting over theres’ floating around, these properties need to stick in something. We might say they ‘stick to things’. Okay, then substance is ‘things’.
Where Descartes differed from the scholastic, Aristotelian tradition he was going to war with, is that we can actually go further than just saying ‘substance is things’ (or more accurately, ‘things’ are substances). He utilized the subtractive technique for divining the essence of things, but took it to a whole new scale. We should not be content saying ‘here is a substance, there is another’, because we end up with an infinity of substances, which begins to look like that dastardly Atomism of Democritus (the dominant counter view to the scholastics at the time). At base, there should be only one substance, that all things are made of. Thus the properties ‘being a chair’ and ‘being a table’ both stick to one substance to give us two ‘things’. Tables and chairs can bump into each other because deep, deep down, they are both the same ‘stuff’. It’s just that stuff is playing two different ‘roles’ in the drama.
Not only should we not rest until we get it down to one substance, but that one substance should be defined by one property. This property, or ‘principle attribute’ as Descartes refers to it, then dictates what properties can stick to it. Kant would subtly adjust this intuition to get the ‘conditions of possibility’, i.e., his famous transcendental forms. These conditions of possibility form a hierarchy. Chairs, being chairs, can have certain properties and not others. Furniture obviously can have all of those chair properties, and some of the ones that chairs can’t have, but not all of them. Pure Venn diagram stuff.
Now. We know in advance that Descartes, after extending the subtractive method as far as he could, could not reduce the final two ‘principle properties’ to two instances of one substance. Hence the dualism. We know that on the thinking substance side, the radical subtraction (Cartesian Doubt) gets us to ‘Thinking’ as the principle attribute that establishes the conditions of possibility for all of the properties that ‘thinking substance’ can have.
In the case of thinking substance, I realize I can entertain the falsity of a huge number of propositions (I have a body, I am sitting in a café, I am thirty three years old, etc) but realize I cannot entertain the falsity of the proposition that I am entertaining the falsity of this very proposition, without contradiction. This hinges on a liar-paradox-like situation of doubting the proposition “I am doubting”. There’s a self-referential paradox there that demonstrates the ‘principle attribute’ has been discovered, as a kind of genetic root. Thus, Descartes’ mode of divining substances can be seen as moving through the process of a subtraction until uncovering a ‘pure’ contradiction. This pure contradiction, then, concerns the essence of substance: that which cannot be altered without altering what the substance is, and all the properties that inhere in it.
So, how does this work in the case of discovering that the principle attribute of extended substance is extension alone? That’s the heart of the matter (or substance) of this article.
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In the case of extended substance we grant the existence of external objects out there in the world. We then begin the process of subtracting those attributes of which we can entertain the possibility of their falsity (or their actual non-existence) without contradiction (in this case, contradicting our assumption as to the existence of external objects in the world).
But, it could be objected, how can we just grant the existence of external objects out there in the world? By what proof do we ascertain their existence? Well, touché my Kantian comrade. Descartes’ arguments for this premise are notoriously dodgy, but can we please just give him a break and grant the premise and run with it and see what happens, just for fun? I love the conundrum of the problematic nature of so called ‘external reality’ as much as the next metaphysician, but sometimes its nice to take a little break and go back to a more naive time, when tables and chairs were just unproblematicaly there, and not just “empirical intuitions represented through ‘outer sense’ in the transcendentally ideal form of space (as a priori condition of sensibility) who have as their ground the transcendental object = x, of which we can say nothing but for the fact that it is not an object as such but the necessary ground of all appearances such that the manifold may be given to the understanding as possessing a unity vital for the faculty of knowledge, and even the possibility of knowledge as such.” Yes. I agree that’s probably the better way to put it. But for now, let’s just grant Descartes his damned premise. We all secretly believe it anyway.
So, we grant the existence of external objects. Now we want to subtract those properties from them that we can entertain the falsity of without contradicting that initial premise (that external objects exist).
First to go, traditionally, is colour. That is to say we can entertain the possibility that the external world is not coloured in the way it appears to us. It would still be the external world even if we were all colour-blind, regular blind, or tetrachromatic. Besides, a perfectly translucent body/object is not for that property deprived of its designation of being a body/object.
A more pernicious attribute is what Descartes refers to as hardness. We certainly treat hardness as almost co-extensive with our notion of the ‘real, external world’ (as in when we rap on a table or other hard surface while saying ‘reality, the external world’ as if to indicate our reference by ostensis). It might seem impossible to entertain the possibility that hardness does not exist without irreparably altering what the ‘external world’ is, thus indicating we have approached its essence. However, Descartes believes he has a demonstration to the contrary:
“For with respect to hardness, we know nothing of it by sense farther than that the parts of hard bodies resist the motion of our hands on coming into contact with them; but if every time our hands moved towards any part, all the bodies in that place receded as quickly as our hands approached, we should never feel hardness; and yet we have no reason to believe that bodies which might thus recede would on this account lose that which makes them bodies. The nature of body does not, therefore, consist in hardness.” (Principles, Part II, art. 4)
However, in Descartes’ example here it could be said that we could still see and hear hardness without ever feeling it (in witnessing collisions, etc). Let’s try another: Imagine a material that is perfectly plastic such that all force placed upon it is distributed completely by a change of the material’s form. A completely perfect super goo. Now, imagine you and a hunk of this material (say, a spherical body of it) are in free-fall in a void at the same relative velocity. Attempting to grasp the ‘body’ merely changes the form of the material. You experience no hardness in the material whatsoever. Now, on the basis of this, is the material not forming a ‘body’? It seems intuitive that the absence of hardness does not entail that we are not dealing with bodies.
Don’t say “But I’ll feel my own hand grasping”, otherwise I’ll have to add the nightmare-fuel stipulation that you also imagine that your entire body is made from this ‘infinitely plastic super goo’. Having already imagined this extensively to test my intuitions, I’ll save you the body-horror of imagining it yourself and just tell you it’s conceivable, and Descartes’ conclusion, in theory, follows.
So, we are left with extension (volume), and its attendant notion of figure/shape. Here Descartes believes he has discovered the fundamental essence of the external world and bodies. This is easy enough to see if we imagine our perfectly plastic ‘super goo’. Is it possible to extract from this body its shape? That is to say, is it possible to entertain the possibility that it in fact has no shape while maintaining that it is still an existent body? It seems hard to say we can. By denying, or removing, the shape of the body, we’ve in turn removed the body itself. From this Descartes concludes that the essence of the external world is nothing but extension. Or, to put it more accurately, the ‘external world’ is a substance whose essential feature consists wholly in its being extended.
Fair enough. But this is where things get weird.
Enter the Void
There are a number of curious implications of identifying ‘extension’ as the principle attribute of the substance that the external world is made of. Chief among these is the identity of bodies (i.e. objects) and voids (leading to the notion of a ‘true void’ being a contradiction). An empty box and a box full of persimmons contains every bit as much substance as each other, because there is every bit as much extension. If we wanted to ‘empty’ the box of all substance, we would need to make it such that the insides of the box became coextensive. I.e, we would need to remove a spatial dimension from the box entirely and turn it into a two dimensional figure of infinite thinness. Only a geometrist in a fever dream can even conceive of what this ‘infinitely flat’ box would be like to find in the world. Although, I guess, if you have a VR set up, nothing is stopping you from trying it out. You’ll probably give yourself a headache.
Another way of putting all this is that the ‘substance’ that Descartes refers to as the ‘extended substance’ is not best thought of as physical matter populating a space-time container, but is space itself:
“the idea of extension which we conceive in any space whatever is plainly identical with the idea of corporeal substance.” (Principles, Part II, Art.21.)
Spatiality is corporeality. The issue as I see it is Descartes now needs to explain how empty space conceived as a ‘substantial void’ (merely extended substance) can ‘give rise to’ diverse and particular bodies. It would be wrong, if we are to follow Descartes charitably, to ask how ‘substantial bodies’ arise from insubstantial void, because a void is a substantial body: the essence of substance is extension alone. So, extension is enough to constitute a body. So voids are substantial bodies. But we want to know how particular, complex, attribute-laden, heterogeneous bodies, like tables and chairs and puppies and mint-flavored-tooth-paste-in-a-tubes, can arise from a substance that is basically homogenous (mere infinite extension in three dimensions).
Descartes answer? Motion.
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Garber (2006) summarizes nicely the deep role that motion plays in Descartes’ ontology:
“Motion is quite crucial to the Cartesian physics; all there is in body is extension, and the only way that bodies can be individuated from one another for Descartes is through motion. In this way, it is motion that determines the size and shape of individual bodies, and, thus, motion is the central explanatory principle in Descartes’ physics.” (p.303)
A body, then, is composed of a “bubble” of extended substance moving in a congruous way such that it would ‘impact’ other bodies moving in different ways (that is, there would be a conflict of directions of motion, like turbulence). It is perhaps better to say that the molecules that form the parts of the body, (and the parts of these molecules, and their parts and so on, ad infinitum), are moving in a situation of ‘local harmony’ relative to one another to constitute the body. Strictly speaking, there is no absolute motion in space, because space is just another body. For Descartes, as for Leibniz, and Berkeley (and so on) movement was always relative to some other moving thing which was moving relative to… Movement or rest is just a difference of ‘reference frames’.
Descartes uses the example of a watch being held by a man on a ship on the waves (Principles, Part II, art.31). Though every ‘body’ separated out by nouns in that sentence is moving in its own way (and we can separate out further bodies with further names indefinitely), they are moving relative to each other, considering their magnitudes and so on, to create a single ‘aggregate body’ with movement such that from a selected relative point aboard the ship, all seem stationary, or ‘moving as one’ relative to the shore. The bodies ‘hang together’ as one.
“By a body as a part of matter, I understand all that which is transferred together, although it be perhaps composed of several parts, which in themselves have other motions;” (Principles, part 2, art.25)
The interjection of another body external to this harmonic-movement-situation (an iceberg for example), if of sufficient magnitude, could be sufficient to set all of those parts into differing motions relative to each other (the waves suddenly rush forwards relative to the boat, the boat cracking in two different directions, the man tumbling downwards towards the waves, the watch flung into the air, etc). An explosion on the boat could affect just the same ‘dispersal’ of partial bodies at a more granular level (a gear from the watch, a toe, a piece of bannister, a cinder, etc).
How many ‘parts’ does your body have? For Descartes this question has no metaphysical answer. Your body is composed, in theory, of an infinite number of parts (extended substance is infinitely divisible). At the most basic levels of divisibility we would just be dividing void (pure extension). But, your body is a local situation of congruous movement, so its kind of one thing. Your hands have their own dynamics within that general eco-system of movement, as does this this molecule of calcium in your elbow, but their movements, some larger, some smaller, all harmonize at different levels of description such that, for the most part, you hang together and move the whole show around when you walk, or fall down some stairs. Other objects resist insofar as their own little movement situation doesn’t congruously accept the motion we try to impart to it, unless we step up the quantity of motion we apply. A bit like trying to walk through a crowded subway station in a direction perpendicular to the mass of people getting off the train and heading for the exit. Actually, scrap that. It is not a ‘bit like that’, it is exactly like that because there is no difference at all beyond the scale. I cannot stick my hand through the table for the exact same reason I cannot walk down the stairs at XiZhiMen subway station at peak hour when Lines 2 and 13 both dump their passengers down below and they are all now coming up the stairs. Thus, “I was blocked by a wall of x” where ‘x’ is some group of things being likened to a wall is not figurative, it’s literal.
The picture this offers is of a radical arbitrariness of what constitutes a body. Instead we get a local harmonies of movement:
“It ought to be remarked that by superficies [edges] we do not here understand any part of the surrounding body, but only the boundary between the surrounding and surrounded bodies, which is nothing more than a mode;” (Principles, Part II, art. 15)
A mode of a single extended substance. And what comprises that mode? Motion within that substance.
“There is therefore but one kind of matter in the whole universe, and this we know only by its being extended. All the properties we distinctly perceive to belong to it are reducible to its capacity of being divided and moved according to its parts; and accordingly it is capable of all those affections which we perceive can arise from the motion of its parts. For the partition of matter in thought makes no change in it; but all variation of it, or diversity of form, depends on motion.” (Principles, Part II, art. 23)
Okay Descartes. Well played. This is my favorite kind of philosophical madness. But there is still one issue he needs to address in order to have a complete picture. Objects come into being and fall out of being just as a kind of harmonizing and detuning of the relative movements within infinitely divisible void-stuff. But why does it move at all?
Descartes answer in the Principles of Philosophy is that God kick started the movement, and sustains the total quantity of movement in the universe, a precursor to the notion of the conservation of energy. However, earlier Descartes, in The World, just begins (first page) by saying there must have been some quanta of movement in the universe initially. The World, which went unpublished after he finished it, is largely an early version of Principles. There is a theory in the scholarship: Descartes finished The World (a treatise on physics essentially) just before the whole Galileo affair. The theory goes he promptly thought “I should probably wait for this to die down”, and hence deferred publication, ended up writing the more theologically attuned Principles years later, and thus never needed to publish The World. This is just an interesting story. It really doesn’t matter whether God kick started the motion, or the motion was just there. What’s important is what we can infer about the state of this initial motion.
Descartes doesn’t explore this specifically, but it must be the case that he needs something like the Atomist’s Clinamen, or ‘random swerve’, in the beginning of the universe in order for the imparted motion to not itself quickly resolve into a giant, single object.
That is to say, if the universe devoid of all motion is a homogenous, infinitely extended void, this void needs to be put into motion. How much? Well, a single nudge may cause a ripple; crests of relative harmonic movement. But this is a far cry from the diversity of objects we see in the world around us. In order for there to be anything worth calling a universe at all, the motion needs to be:
Catastrophically cacophonic. An entire preponderance of conflicting directions of motion on an absolutely epic scale. And,
This ‘cacophony’ of motion needs to be occurring within the vanishing ‘infinity point’ of the smallest scales of infinite divisibility.
Why? Because when we theorize an atom of hydrogen as a ‘thing’, that is, we say ‘there are atoms of hydrogen’, in Descartes’ picture we see the beginnings of harmonic movement of tiny void-parts. The single atom is in some sense already a local harmony of movement. A pretty shaky harmony, nothing of the scale of the giant harmony of movement between parts that is our earth, with us and everything on it, spinning around the sun, but still, motion has been harmonized even on this tiny scale of the atom. But this harmony could only emerge from the interactions of even smaller parts themselves more or less originally disharmonious among one another, finally resolving into the atom. And these parts themselves, and those parts, and so on and so on unto infinity. And as we go deeper and deeper down, the very fabric of ‘thinghood’ (itself just referring to a local harmony of movement among parts) breaks down further and further into a primordial, chaotic, discordant cacophony. As Žižek would put it: “That there are things at all is evidence that something has gone terribly wrong, a kind of cosmic catastrophe, a cosmic imbalance”.
Another way of putting it is that Descartes’ physics is composed of a kind of musical ontology, where out of a wall of noise, harmonic overtones emerge, themselves harmonizing, and so on and so forth, to compose the attribute laden, heterogenous world of things before us. Think an orchestra tuning before the performance. If you want to feel this ‘deep, chaotic discord in the music of the spheres’, just press your finger into a wall. That resistance you feel is just like you slamming a D and D# together on a piano. Hear/feel the waves of motion, conflicting in a horrible ratio, that ensure you don’t fall straight through.
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Continue reading about Descartes’ substances here.
Descartes, R., Veitch, J., (2002). The Principles of Philosophy, Blackmask Online.
Descartes, R., Haldane, E., Ross, G. and Chávez-Arvizo, E. (1997). Key philosophical writings. Wordsworth.
Garber, D. (2005). Descartes’ Physics. In: J. Cottingham, ed., The Cambridge Companion To Descartes, 2nd ed. New York: Cambridge University Press, pp.286–334.
Hatfield, G. (2014). René Descartes (Stanford Encyclopedia of Philosophy). [online] Plato.stanford.edu. Available at: https://plato.stanford.edu/entries/descartes/ [Accessed 23 Apr. 2018].