After Descartes has established that he exists and is a thinking thing, he then used Leibniz’s Laws of Identity to prove that he must be something different from his physical body (that his mind and body were not the same thing). His basic strategy is to identify differences between himself (the thinking thing) and his physical body. According to Leibniz’s laws, if two things have different properties, then they cannot be the same thing.
Leibniz’s Laws of Identity. Principle of the Indiscernability of Identicals: If two things are the same then we cannot tell them apart. If two things are the same thing, then they have all the same properties or characteristics. In other words, if two things are identical, then they are indistinguishable. Principle of the Identity of Indiscernables: If it is impossible to tell two things apart, then they must be the same thing. If two things share all the same properties, then they are the same thing. In other words, if I cannot tell the difference between two things, they must in fact be identical.
Descartes uses the first principle (Principle of the Indiscernability of Identicals) to prove that the mind and body are fundamentally different substances or things. Here is a version of Descartes’ Argument for Dualism from Doubt:
1. My body is the kind of thing that I can doubt exists.
2. My mind is not the kind of thing whose existence I can doubt.
3. Since I can doubt my body and not my mind, then I can tell the two apart from one another (I can distinguish one from the other).
4. If two things are distinguishable (because they have different properties), then they are not the same. (Leibniz’s Law)
5. Therefore, mind and body are not identical. They are two different things. Boom. Dualism proved.
Sven notes that the fact that something is able to be doubted is not the kind of property that Leibniz was thinking of when he defined the laws of identity. Just because I can doubt one thing and not another does not mean that they are the same thing. Perhaps I don’t doubt my dad’s existence but then if I see him in a Santa costume I do doubt that he really exists. But this doesn’t mean that my dad is not the same person as the person in the Santa costume. Similarly, I can think that Bruce Wayne is hot but I can think that Batman is fugly. But Bruce Wayne and Batman are the same person.
Here is a version of Descartes’ Argument for Dualism from Conceivability:
1. I can conceive (or think of) myself existing without a physical body existing.
2. Anything I can think of is logically possible.
3. If it is logically possible for something to exist without something else, then the two things are not identical.
4. Therefore my self (the thinking thing) is not identical to my physical body.
Sven notes that this argument presumes that just because something is conceivable then it is also possible. On the one hand, there may be things that are possible that we cannot think of. On the other hand, there may be things that we can think of that are not possible.
Descartes’ Argument from Divisibility: Descartes’ also tries to say that there is another property that physical bodies have that minds do not have. Namely, physical objects like our bodies can be divided. The mental cannot be divided in the same way. Because they do not share this property, they are not the same thing.
1. Physical bodies are divisible.
2. The mind is not divisible.
3. Therefore, no minds are physical.
We can see that Descartes identified three properties that my physical body has that my thinking self does not have. Because of this, he concluded that the two must be distinct from one another.