1. Mind and body are separate substances. "Substance," strictly speaking, for Descartes means "a thing existing in such a manner that it has need of no other thing in order to exist" (Principle LI, The Principles of Philosophy, trans. Anscombe and Geach). In this strict sense, according to Descartes, only God is really a substance. But in a derivative sense "created substances, whether corporeal or thinking, may be conceived under this common concept; for they are things which need only the concurrence of God in order to exist" (Principle LII, trans. Haldane and Ross). Descartes goes on to say that "there is always one principal property of substance which constitutes its nature and essence, and on which all the others depend. Thus extension in length, breadth and depth, constitutes the nature of corporeal substance; and thought constitutes the nature of thinking substance. For all else that may be attributed to body presupposes extension, and is but a mode of this extended thing; as everything that we find in mind is but so many diverse forms of thinking." So the essence of mind is thinking; other mental properties are "modes" of thinking (e.g. sensation, imagination, understanding, . . .). The essence of matter is extension; other physical properties are modes of extension (e.g. mass, volume, shape, movement . . .). Each person is a mind, a mental substance; each person is also attached to a body with which he or she interacts.
This interaction, however, poses a problem for Descartes. How do two substances as radically different as mind and body, two substances which indeed have no properties in common (mind doesnt have extension and body doesnt think, according to Descartes), have any effect on each other? Here is a fragment from a letter from Princess Elizabeth to Descartes (written May 6-16, 1643): "I beg of you to tell me how the human should can determine the movement of the animal spirits in the body so as to perform voluntary acts -- being as it is merely a conscious substance. For the determination of movement seems always to come about from the moving bodys being propelled -- to depend on the kind of impulse it gets from what sets it in motion, or again, on the nature and shape of this latter things surface. Now the first two conditions involve contact, and the third involves that the impelling thing has extension; but you utterly exclude extension from your notion of soul, and contact seems to me incompatible with a things being immaterial." (From Anscombe and Geach, ed., Descartes: Philosophical Writings, Nelson, 1964, pp. 274-75.) Descartes attempts to reply, but the worry seems to many to remain.
2. Freedom of the will. Descartes does not engage in an extended discussion of problems about free will. But he clearly thinks that the will is free: remember that this figures crucially in his explanation in Meditation Four of the possibility of error. We can make mistakes in judgment, despite Gods not being a deceiver, he there argues, because the will extends further than the understanding, so that we sometimes freely assent to propositions which we dont completely understand.
Notice, however, that Descartes thinks that in a sense the will can be completely determined and yet nevertheless be free. Remember the following passage from Meditation IV: "In order for me to be free it is unnecessary for me to be moved in neither direction; on the contrary, the more I am inclined toward one direction . . . the more I choose that direction more freely. . . . The indifference that I observe when no reason moves me more in one direction than in another is the lowest level of freedom; it evinces no perfection in it, but rather a defect in my knowledge, or a certain negation. Were I always to see clearly what is true and good, I would never deliberate about what is to be judged or chosen. Thus, although I may be entirely free, I could never for that reason be indifferent." Elsewhere, Descartes goes so far as to say that "upon a great illumination of the intellect there follows a great inclination of the will; thus, if we see very clearly that a thing is suitable for us, then it is difficult for us (I think, even impossible), so long as we remain in this state of mind, to stay the course of our desire" (Anscombe and Geach, p. 289), and he endorses the Platonic view that no one who acts wrongly clearly understands that what they are doing is wrong: "If we saw clearly that it is bad, we could not possibly sin -- not so long as we did see it in this way" (p. 290).
3. Religion and Science. Notice that Descartes has tried to make theology compatible with natural science by insisting that God, and indeed the spiritual or mental side of human nature, is completely different from the corporeal world and hence need not be subject to the laws of physics, which are the laws of corporeal substance. We will see a radically different attempt to reconcile theology and physics in Spinoza.
4. Skepticism. In the First Meditation, Descartes launches a devastating skeptical attack on our received views. Notice that for Descartes, the gap between what we can be certain of and what, until later in the Meditations, we cannot, coincides with the gap between mental substance and physical substance: we can be certain about the contents of our own minds; the main skeptical problem is how we can ever get from that knowledge to knowledge of the physical world. In the remainder of the Meditations, Descartes tries to win back our certainty about a good many of our beliefs, arguing that we can trust our clear and distinct perceptions, those perceptions made possible by the light of nature, to be true. This theme will virtually disappear in Spinoza and Leibniz, who seem even more sanguine about clear and distinct perception than Descartes. But skepticism will begin to reemerge in Locke, and for Berkeley and Hume it will be a major focus of attention.
5. The source of knowledge. Weve seen Descartes' conviction that sensation and imagination are not reliable sources of knowledge; only understanding or reason can be trusted. This aspect of Descartes' thought will not be questioned by Spinoza or Leibniz, but will come under sharp attack by Locke, Berkeley, and Hume.
6. Subjective and objective. Which of the features we perceive the world to have are objectively present, and which are due simply to the nature of our own perceptual or cognitive apparatus? This is an important question for Descartes, who in the Sixth Meditation concludes that sensory properties -- taste, warmth, colors, and so on -- are not really features of objects, while the properties made use of by mathematical physics are. (You may want to remember the passage on p. 442: "Although I feel heat upon drawing closer to the fire, and I feel pain upon drawing even closer to it, there is indeed no argument that convinces me that there is something in the fire that is similar either to the heat or to the pain, but only that there is something in the fire that causes in us these feelings of heat or pain." We will later see a very similar argument in Locke.