Extended Substance

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.