Now the big thing here, and I mentioned this before, how is Descartes working with a mechanical philosophy gonna safeguard against error? And that is what's his response to puranism? Well there are two things he keeps harping on. One is to have absolutely secure foundations, which to him means they have to be metaphysically based foundations.
His principle follower, Regius, decided to drop all the metaphysics from Theprician and treated all his empirical science and Descartes very quickly disowned him. The foundations have to be grounded in secure metaphysics. Then the second thing is, you don't just theorize about what you're perceiving. You have to give an account of the entire process.
Of the motion, the light leaving it, reaching your eye and reaching your retina. Because at every stage, it's possible for an error to come, possible for you to be mislead. So if you have a theory of the total process, you can then identify every stage at which you can be mislead, and counteract stages one by one.
And one model he had for doing that is Desargues I suspect none of you have heard the name. It's unfortunate, in some ways. Desargues was a contemporary of Descartes. He was on the list I gave you before. He constructed a Euclidean geometry that is a set of axioms, postulates, and propositions derived from them for perspectival geometry.
The geometry of perspective. And it's absolutely beautiful. It's the first projective geometry that we have, but he really worked the whole thing out. Descartes knew it. And it was a perfectly good example that explains away all the optical illusions we have from perspectival elements. You can actually calculate exactly beforehand what the prospectial effect is going to be, etc.
So that's the kind of model but it leads to this thing I said before. A unified, fully comprehensive science with absolutely secure foundations. Not a piecemeal science and that's why. The book, Le Monde, the World, is accompanied by the book The Treatise on Man, because the two are complimentary, you need both.
You've got to give an account of the whole bloody process, until we get out of the physical world and into Descartes' mental world and even there we've got the pinial gland as the transition point, etc. That's also why we have these really elaborate pictures of the eye is part of that.