Descartes claims that there are "two highest kinds of things; the first of intellectual things, or such as have the power of thinking, including mind or thinking substance and its properties; the second, of material things, embracing extended substance, or body and its properties." [Principles of Philosophy 1:48]

Extended, or corporeal substance is what we might nowadays call "the physical world": it is what we perceive through our senses. One aspect of extension is location, or "place": an extended object must be positioned somewhere, and occupy some amount of space. Another property of extended substance is that it is divisible. But it doesn't seem that our minds occupy any specific space (although we might imagine them being located somewhere behind our eyes), and "the body is by its very nature divisible, while the mind is utterly indivisible".

But the fundamental difference is that the existence of extended substance can logically be doubted, while thinking substance cannot (because the act of doubting itself demonstrates that thinking is taking place). And since extended and thinking substance are distinct, it must, according to Descartes, be possible for the mind to exist independently of the body.

In his preface, Cottingham takes issue with Descartes' premise that mind is distinct from body simply because one can't be doubted and the other can, saying that this argument could be used to demonstrate that potatoes could exist independently of carbohydrate (assuming I am confident of the existence of potatoes but doubt whether there's such a thing as carbohydrate). In fact, this analogy is not entirely fair: Descartes demonstrates that it is logically possible to doubt the body, but logically impossible to doubt the mind, which is not equivalent to saying "suppose for sake of argument that I doubt that carbohydrate exists but have no doubt in potatoes". Perhaps a more valid objection would be that just because I, an imperfect being, can logically doubt something exists, that doesn't necessarily affect its characteristics.

The issue that bedevils the dualist point of view is that if mind and body are distinct types of substance, then how can it be possible that they can interact with one another? They they plainly do: physical objects cause ideas in us, and our wishes, which are types of thought, can cause actions which change the physical world. Descartes says that his mind is "very closely joined and, as it were, intermingled with [his body]", acknowledging that there is a special relationship, but not really explaining how it can work.