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Source info.
Our translation of Descartes' Meditations on First Philosophy comes from Elizabeth Haldane, The Philosophical Works of Descartes. Vol. II. 1934, pp. 32-3.
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Descartes & the Mind-Body Problem

Descartes: Some Arguments for – and Explanations of – Dualism

"Rene Descartes," by Mitch Francis

Rene Descartes (1596 – 1650) was a philosopher and scientist who probed human knowledge in search of certainty. (Image: “Rene Descartes,” by Mitch Francis.)

Here below are classic excerpts from Descartes’ Meditations in which he argues that the mind and body are distinct substances. His arguments depend on what’s now called Leibniz’s law:
If a = b, then a must have all the properties b has; conversely, if b and a fail to share all properties, then they are not identical.
Be sure you “see” how Leibniz’ law works here.

Meditation II (selection)

My beliefs about external objects are possibly false (as the possibility of the deceiving demon – or The Matrix – shows).

But it’s not possible that I could be deceived about my existence or my nature as a thinking thing.

My mind has the property of being clearly and distinctly known to me, whereas my body lacks that property.

Thus, by Leibniz’ law, my mind is not identical to my body.

The first excerpt is from Meditation II, specifically paragraphs 5-6:

By body I understand all that can be terminated by a certain figure; that can be comprised in a certain place, and so fill a certain space as therefrom to exclude every other body; that can be perceived either by touch, sight, hearing, taste, or smell; that can be moved in different ways, not indeed of itself, but by something foreign to it by which it is touched [and from which it receives the impression]; for the power of self-motion, as likewise that of perceiving and thinking, I held as by no means pertaining to the nature of body; on the contrary, I was somewhat astonished to find such faculties existing in some bodies.

But [as to myself, what can I now say that I am], since I suppose there exists an extremely powerful, and, if I may so speak, malignant being, whose whole endeavors are directed toward deceiving me? Can I affirm that I possess any one of all those attributes of which I have lately spoken as belonging to the nature of body? After attentively considering them in my own mind, I find none of them that can properly be said to belong to myself. To recount them were idle and tedious. Let us pass, then, to the attributes of the soul. The first mentioned were the powers of nutrition and walking; but, if it be true that I have no body, it is true likewise that I am capable neither of walking nor of being nourished. Perception is another attribute of the soul; but perception too is impossible without the body; besides, I have frequently, during sleep, believed that I perceived objects which I afterward observed I did not in reality perceive. Thinking is another attribute of the soul; and here I discover what properly belongs to myself. This alone is inseparable from me. I am–I exist: this is certain; but how often? As often as I think; for perhaps it would even happen, if I should wholly cease to think, that I should at the same time altogether cease to be. I now admit nothing that is not necessarily true. I am therefore, precisely speaking, only a thinking thing, that is, a mind (mens sive animus), understanding, or reason, terms whose signification was before unknown to me. I am, however, a real thing, and really existent; but what thing? The answer was, a thinking thing.

Meditation VI (selection)

A conceivability argument:

If one can clearly-and-distinctly conceive one thing apart from another then they are not identical.

I can clearly-and-distinctly conceive of myself apart from my body.

Therefore, I am not identical with my body.

So I can exist apart from my body.

My mind is not extended.

But my body is extended.

Thus, by Leibniz’ law, my mind and body are distinct.

The second is from Meditation VI, paragraph 9:

[F]irstly, because I know that all which I clearly and distinctly conceive can be produced by God exactly as I conceive it, it is sufficient that I am able clearly and distinctly to conceive one thing apart from another, in order to be certain that the one is different from the other, seeing they may at least be made to exist separately, by the omnipotence of God; and it matters not by what power this separation is made, in order to be compelled to judge them different; and, therefore, merely because I know with certitude that I exist, and because, in the meantime, I do not observe that aught necessarily belongs to my nature or essence beyond my being a thinking thing, I rightly conclude that my essence consists only in my being a thinking thing [or a substance whose whole essence or nature is merely thinking]. And although I may, or rather, as I will shortly say, although I certainly do possess a body with which I am very closely conjoined; nevertheless, because, on the one hand, I have a clear and distinct idea of myself, in as far as I am only a thinking and unextended thing, and as, on the other hand, I possess a distinct idea of body, in as far as it is only an extended and unthinking thing, it is certain that I, [that is, my mind, by which I am what I am], is entirely and truly distinct from my body, and may exist without it.

Reply to Objections (selection)

The last is from his Reply to Objections, II:

[T]hose things are really distinct each of which can exist apart from the other. But once more I ask how you will know that one thing can be apart from the other; this, in order to be a sign of the distinctness, should be known. Perhaps you will say that it is given to you by the senses, since you can see, touch, etc., the one thing while the other is absent. But the trustworthiness of the senses is inferior to that of the intellect, and it is in many ways possible for one and the same thing to appear under various guises or in several places or in different manners, and so to be taken to be two things. And finally if you bear in mind what was said at the end of the Second Meditation about wax, you will see that properly speaking not even are bodies themselves perceived by sense, but that they are perceived by the intellect alone, so that there is no difference between perceiving by sense one thing apart from another, and having an idea of one thing and understanding that that idea is not the same as an idea of something else. Moreover, this knowledge can be drawn from no other source than the fact that the one thing is perceived apart from the other; nor can this be known with certainty unless the ideas in each case are clear and distinct. Hence that sign you offer of real distinctness must be reduced to my criterion in order to be infallible.

But if any people deny that they have distinct ideas of mind and body, I can do nothing further than ask them to give sufficient attention to what is said in the Second Meditation. I beg them to note that the opinion they perchance hold, namely, that the parts of the brain join their forces with the soul to form thoughts, has not arisen from any positive ground, but only from the fact that they have never had experience of separation from the body, and have not seldom been hindered by it in their operations, and that similarly if anyone had from infancy continually worn irons on his legs, he would think that those irons were part of his own body and that he needed them in order to walk.

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