Gorgias: Neither One Nor Many

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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.
You'd be hard pressed to find someone who accepts all three of those who also thinks the list in premise 2 is exhaustive. It would be interesting to see how they'd respond to this argument if they did. I may not have identified all the problems, of course, so there may be other places to get off the boat. Feel free to find any more.


I have problems with "a discrete quantity is divisible." There are two potential problems in my mind. By definition, some people say that a discrete quantity is not divisible. So the definition he is using possibly leaves out the category of indivisible quantities.

Supposing his definition is something along the lines of "a quantity that is not a continuum," I take issue with the assumption that there are no indivisible quantities. Look to modern physics. Quantum mechanics is based off of indivisible quantities.

Eh, just my two cents. Number 3 is either a circular definition or contains an assumption that needs justification.

I took him to mean that if you've got something composed of discrete atoms then it's not a thing but many things masquerading as one thing. This is one of the things (but not the only one) that my first bullet point was about.

The argument as it was presented in the post is a bit sloppy for my taste as well. But I still like to share my thoughts on the 'neither one nor many' argument. I'm (honestly) curious if there are any fallacies in my reasoning as well.

What I think the neither-one-nor-many argument is about: There can't be such thing as an indivisible ("one") particle (as posited by Matt) because a particle should always have a north and south side (and east, etc.). If it were indivisible it wouldn't have these sides and it could not hold position towards another particle. In example, particle P1 cannot be east of P2 because it doesn't have an east side. If you were to claim the particle has only one side--like one direction--all I think you have left is some kind of mathematical abstraction.

Now I'm not sure, but I think one and many are assumed to be an (absolute) dichotomy. I've come to understand that even though they are assumed to be, many is interpreted as being an aggregation of multiple ones. Therefore granted that the one (indivisible particle) doesn't exist, many can't exist either due to it being an aggregation of ones. I'm not so sure about this reasoning.

There is a chance I don't understand this properly, but I think it could be irrelevant:

I think 'neither one nor not-one' would be more accurate a dichotomy. If it's proven that one cannot exist it should still mean not-one can't exist. Like any other dichotomy, e.g., 'white' cannot exist without its opposite 'black'. So you're left with nothing useful (the not-one cannot exist either).

That's the only funny thing about it. If you're trying to map concepts to reality- really precisely like this, trying to name at least something 'one', it's not possible, and you probably end up labeling something purely conceptual (not reality) or otherwise completely arbitrary (an indivisible particle).

The neither-one-nor-many thing is bugging me for about a year, maybe two years every now and then in my head ;)


(p.s. You need to change the action of this form. It yields a CGI error. I changed it using firebug to the action used in your most recent post, that's why I could post this comment. I think the archive uses another (old)template that needs to be updated..)

I can leave comments just fine, so either it's a browser problem (I'm using Google Chrome) or whatever you did fixed it. Someone else has told me about problems leaving comments, but it was on a post that other people were able to comment on. So I'm not sure what's up.

By the way I wasn't referring to Gorgias neither-one-nor-many argument but the one posited in Buddhist literature (like Shantarakshita's Madhyamakalankara).

@Jeremy: I think my post updated the cache somehow, because if I view the source of http://parablemania.ektopos.com/archives/2007/06/i_guess_im_not.html (just selected one at random), the form action is http://movabletype.ektopos.com/cgi-bin/mt-cmt.r120.cgi instead of http://movabletype.ektopos.com/cgi-bin/mt-comments.cgi
I think this is only with archived posts. Maybe everything works fine if you'd copy mt-comments.cgi to mt-cmt.r120.cgi just in case, but I'm not sure.

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