Here's another horribly fallacious argument from Gorgias the Sophist. (See my earlier post for Gorgias' main argument that there is nothing.)
1. If something is, it's either (a) one or (b) many.
2. If it's one, it's either (c) a discrete quantity or (d) a continuum or (e) a magnitude or (f) a body.
3. It's not (c), because a discrete quantity is divisible. Then it's not one.
4. It's not (d), because a continuum can be cut.
5. It's not (e), because a magnitude is divisible.
6. It's not (f), because a body is three - length, breadth, and depth.
7. Therefore, it's not one.
8. If it's many, then it's a compound of things that are each one, and it's impossible to be one.
9. Therefore it's neither one nor many, and thus it isn't. So nothing is.
I don't think the list in the second premise is exhaustive. I can't see how God or souls could fit into one of those four categories, and if there are any sort of universals or real properties they don't seem to fit either.
You'd also have to add a number of premises for this to be logically valid. Here are several:
- Being potentially divisible amounts to being actually many. (This is at least controversial, but I think most people would deny it.I'm having trouble thinking of who in contemporary philosophy might hold such a thing. Maybe people who hold the next claim would think this.)
- Something with many parts can't be something, i.e. nothing is a unified whole unless it has no parts. (For those not up on contemporary metaphysics, views like this are actually held by some very smart people. Peter van Inwagen almost thinks it's true, but he thinks organisms are an exception. At one point in his career, the atoms composing Peter Unger thought it was true, but the ones currently composing him would like to think they're an object and at least would prefer it not to be true. It's certainly a minority view, at any rate.)
- It's impossible for one thing to have three distinct spatial properties or dimensions. (I do think some philosophers would say this. In particular, those who hold what's called a bundle theory of properties would accept something like this. To a bundle theorist, an object is just the bundle of properties that it has. There is no thing that has the properties.