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Descartes's most influential argument for Substance Dualism occurs in a single paragraph in the 6th Meditation.
The first half of the key paragraph runs:
"First, I know that everything which I clearly and distinctly understand is capable of being created by God so as to correspond exactly with my understanding of it. Hence the fact that I can clearly and distinctly understand one thing apart from another is enough to make me certain that the two things are distinct, since they are capable of being separated, at least by God. The question of what kind of power is required to bring about such a separation does not affect the judgment that they are distinct."
Descartes Meditation V, CSM II:54, AT 7:78.
To a first approximation:
We'll see in a moment why we're supposed to think I can clearly and distinctly understand myself apart from my body, and so conclude that I am distinct from my body.
First, let's consider an objection, pressed by Caterus in the First Set of Objections:
Caterus offers another PARODY, aimed at undermining Descartes' claim that X is distinct from Y if I can clearly and distinctly understand X apart from Y:
Descartes will accept 2, but want to resist 3. So he needs to deny 1!
In his Replies to Caterus, Descartes clarifies his position. In order to infer that X is distinct from Y, what we needed is a clear and distinct understanding of X as COMPLETE apart from Y.
And while,
But what exactly does Descartes mean by a clear and distinct understanding of myself as complete apart from my body? And why does he think I can have one?
The second half of the key paragraph runs:
"Thus, simply by knowing that I exist and seeing at the same time that absolutely nothing belongs to my nature or essence except that I am a thinking thing, I can infer correctly that my essence consists solely in the fact that I am a thinking thing. It is true that I may have (or, to anticipate, that I certainly have) a body that is very closely joined to me. But, nevertheless, on the one hand I have a clear and distinct idea of myself, in so far as I am simply a thinking, non-extended thing; and on the other hand I have a distinct idea of body, in so far as this is simply an extended, non-thinking thing. And accordingly, it is certain that I am really distinct from my body, and can exist without it."
Descartes Meditation V, CSM II:54, AT 7:78.
In the Fourth Replies, Arnauld takes the argument to be:
Arnauld points out that this argument is no good. I can be certain that a triangle is right-angled while doubting (owing to ignorance) that it is Pythagorean.
It does not follow that I can clearly and distinctly perceive that being right-angled but not Pythagorean belongs to the triangle's essence!
In his Replies to Arnauld, Descartes clarifies that the argument is rather:
Why does Descartes think I can clearly and distinctly perceive that it is possible for me to exist without my body?
Because I can IMAGINE myself existing as a thinking thing without a body.
The argument in brief:
“Descartes, and others following him, argued that a person or mind is distinct from his body, since the mind could exist without the body. He might equally well have argued the same conclusion from the premise the body could have existed without the mind.”
Kripke Naming and Necessity, p. 144-5.
Kripke's version:
These are both MODAL arguments for dualism.
They move from a claim about what is POSSIBLE (I can exist without my body, or my body can exist without my mind) to the claim that mind and body are somehow distinct.
However, the forms of dualism that they seek to establish are different.
Descartes is arguing for substances just like us except that they lack physical properties, GHOSTS or SPIRITS.