## Leibniz's Law: Legitimate Uses

Leibniz's Law says that if A and B are one and the same thing, then they have to have all the same properties. If A and B have different properties, then they cannot be one and the same thing. If we find some property that B has but A doesn't, then we can conclude that A and B are not the same thing. Here is an example. We look out the window and see Superman flying by. We wonder who Superman is. Now as Superman flies by outside the window, we see our friend Jimmy Olson standing beside us. We can reason like this:
1. Superman is flying outside the window.
2. Jimmy Olson is not flying outside the window, he's standing right beside me.
3. So Superman has a property that Jimmy Olson doesn't have.
4. So Superman is not Jimmy Olson.
or like this:
1. The person who murdered Mr. Body was left-handed.
2. The butler is not left-handed.
3. So the butler is not the person who murdered Mr. Body.
Makes sense, right?

### Some Arguments for Dualism

Philosophers have tried to use Leibniz's Law to argue for dualism, in a variety of ways. They try to come up with some property that our minds have but our brains and bodies lack, or vice versa. Together with Leibniz's Law, that would enable them to show that our minds can't be the same thing as our brains or bodies.

One such argument uses the property of being divisible. My brain and body can be divided into smaller parts. We then argue that my mind, on the other hand, cannot be divided into smaller parts. If that's right, then my mind can't be the same thing as my brain or my body.

Another argument goes: my brain weighs 5 pounds. My mind doesn't weigh 5 pounds. So my brain and my mind are different things.

What do you think of that argument?

Another argument goes: I am thinking of my Aunt Helen; so I have Aunt Helen in my mind. But Aunt Helen is not in my brain. So my mind and my brain have different properties: one contains Aunt Helen, and the other doesn't. So my mind and my brain are different things.

What do you think of that argument?

A fourth argument goes: my mind is something I have privileged access to. But my brain and body aren't things I have privileged access to. So my mind has do be a different thing from my brain or my body. Let's discuss this argument more closely.