Bernard Williams

Descartes: Meditations on First Philosophy: Fifth Meditation: The essence of material things, and the existence of God considered a second time

There are many enquiries still to be made about God’s attributes, and many about my own nature (that is, the nature of my mind). I may take these up at some time; but right now I have a more pressing task. Now that I have seen how to reach the truth—what to do and what to avoid—I must try to escape from the doubts that beset me a few days ago, and see whether anything can be known for certain about material objects. Before enquiring into whether there are any such things, I should consider the ideas of them in my thought, in order to see which of those ideas are distinct and which confused. I distinctly imagine quantity—that is, the length, breadth and depth of the quantity, or rather of the thing that is quantified. I also enumerate the thing’s parts, to which I attribute various sizes, shapes, positions and movements; and to the movements I attribute various durations, ·that is, I say how long each movement lasts·. Size, shape, position and so on are well known and transparent to me as general kinds of phenomenon, but there are also countless particular facts involving them that I perceive when I attend to them. The truths about all these matters are so open to me, and so much in harmony with my nature, that when I first discover any of them it feels less like •learning something new than like •remembering something I had known before, or •noticing for the first time something that was already in my mind without my having turned my mental gaze onto it. The most important point is that I find in myself countless ideas of things that can’t be called nothing, even if they don’t exist anywhere outside me. For although I am free to think of these ideas or not, as I choose, I didn’t invent them: they have their own true and immutable natures, ·which are not under my control·. Even if there are not and never were any triangles outside my thought, still, when I imagine a triangle ·I am constrained in how I do this, because· there is a determinate nature or essence or form of triangle that is eternal, unchanging, and independent of my mind. Consider the things that I can prove about the triangle—that its three angles equal two right angles, that its longest side is opposite its greatest angle, and so on. I now clearly recognize these properties of the triangle, whether I want to or not, even if I didn’t give them a thought when the triangle first came into my mind. So they can’t have been invented by me. It does not help to point out that I have sometimes seen triangular bodies, so that the idea of the triangle might have come to me from them through my sense organs. I can prove truths about the properties not only of triangles but of countless other shapes that I know I have never encountered through the senses. These properties must be something, not pure nothing: whatever is true is something; and these properties are true because I am clearly aware of them. (I have already proved that everything of which I am clearly aware is true; and even if I hadn’t proved it, my mind is so constituted that I have to assent to these ·geometrical· propositions as long as I perceive them.) I remember, too, that even back in the times when the objects of the senses held my attention, I regarded the clearly apprehended propositions of pure mathematics—including arithmetic and geometry—as the most certain of all.