Here's an argument I came up with while being depressed recently. I haven't really thought about this argument at all, but I think there is something to it. I guess I would deny premise 1, 5, and 7.
(1) For any x, if x has finitely many parts, then there must exist something else distinct (non-overlapping) from x which accounts for (or perhaps contrasts) its finitude
(2) If the Universe has finitely many parts, then there must exist something else distinct (non-overlapping) from the Universe which accounts for (or perhaps contrasts) its finitude
(3) there exists nothing else distinct (non-overlapping) from the Universe which accounts for (or contrasts) its finitude (conceptual truth about the Universe)
(4) Hence, the Universe has infinitely many parts
(5) For any xx, if xx are infinite, then xx are "too many" to compose an object (conceptual truth about the infinite? Think of the notion of infinity that was prevelant up until the madman Cantor.)
(6) The parts of the Universe are "too many" to compose an object ((4),(5))
(7) All and only finitely many things compose something
(8) Hence, the Universe is junky ((4),(6),(7))
-Einar
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Einar,
You say:
“(6) The parts of the Universe are ‘too many’ to compose an object”
On (6): Is this premise a bit like stating that all and only my parts don’t compose something? From (1) and (2) I gather that they both have the same funny flaw.
On the argument you say that you “think there is something to it.” What’s that?
I don't understand your comment. Also, identify yourself, coward!
-einar
Einar, I'm having some trouble understanding premise (1). Three possibilities: first, I'm being dense and there is a simple explication of (1) (in which case please tell me); second, there is an argument for premise (1) which is difficult and perhaps controversial, however (1), or something like it, is required by premise (4); third, there is a difficult and controversial argument for premise (1) but premise (4) is independently more plausible than (1).
If the third possibility holds, then you'd be better off just asserting (4) and skipping (1)-(3).
I'm wondering what views about the world would entail that it has finitely many parts. If you believe that the world has point-sized parts, you believe that it has infinitely many parts. If you believe that the world is gunky, you believe that it has infinitely many parts. Does one who thinks that the world has only finitely many parts think that it is neither gunky, nor that it has point-sized parts? What views say this?
Ed
I forgot to add that being an extended simple doesn't count as a plausible thesis about the world.
I'm with Ed on being confused about (1), but I want to talk about (5) and (7) -- why can't an infinite number of things compose something? We have intuitive examples of this (geometric points composing a line segment or figure, domains, sets, gunky models [and, hey, what would this argument do to theories of mereology that allow for composition from gunk?]...), and I'm having trouble grasping reasons not to accept this (though maybe I'm just poisoned by being a post-Cantorite). Many mereological formalizations provide a way to represent fusion from infinite parts, so why not take it?
Dearest confused Einar,
I take it from (1) and (2) that you are treating ‘the Universe’ (whatever the definite article refers to) as a singular referring expression with the underlying logic guaranteeing that this term is as such. Otherwise, it seems you need to go learn how first order quantifier logic works. But, if that’s true, then you’re referring to a single thing. From (4), I take that the Universe has parts. From (6), I take it that it is denied that all and only these parts compose something.
But that’s a rather embarrassing admission, isn’t it?
Archi
Dear Archi,
I took it to be obvious that 'the universe' functions as a plural term for junky worlds, given that junky worlds are pluralities. Many people accept this use of 'the universe' and 'world', e.g. Jonathan Schaffer, Peter Simons, van Fraassen, and Varzi. Surface grammar is not always the road to the correct logical form.
Truly,
-Einar
Barak,
I agree, but the idea was that there is a distinction between metaphysical/ontological/actual infinity and pure formal/mathematical/potential infinity. Pre-Cantorians (e.g. Aristotle and Leibniz) had, for example, great trouble accepting actual infinity in the sense of, say, there being an entity of infinite extension, though they had no trouble accepting that there is no end to how many entities of finite extension there are. The idea behind (7) was that maybe someone would accept this notion of the infinite. If so, then there could only actually exist fusions of finitely many parts.
As a compositional universalist I myself would reject this notion of the infinite, I think.
You say: “I took it to be obvious that 'the universe' functions as a plural term for junky worlds, given that junky worlds are pluralities.”
Thank you for giving such a clear response. On a more serious note,
The term you employ in your argument is the funny expression ‘the Universe’ (whatever that refers to), not the common expression ‘the universe’ (look at the argument). And in any case, if ‘the Universe’ is a plural referring expression, then (to put it loosely) it seems that (1) does not provide support for (2) since (2) certainly doesn’t follow the logical structure of (1). But then it looks as though (1) plays no role in your argument.
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