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Physics I.4 The number of kinds of things must be finite since the infinite is unknowable and a finite body cannot be composed of an infinite number of finite bodies.
Again Aristotle is arguing against someone to prove his point. In this case, Anaxagoras. Aristotle presents this as since "it is impossible for something to come into being from non-being," so everything that exists is made up of smaller constituents. And if everything comes from smaller constituents, then there cannot be a smallest object -- it, itself, would need to be composed of even smaller things. Aristotle, disagrees. Although there must be more than one thing, or even one kind of thing, there cannot be an infinite number of things, let alone an infinite number of kinds of things that the finite things we see are composed of.
It is a little difficult to keep track of things here, because sometimes Aristotle seems to be talking about the number of things that exist; at other times, he seems to being talking about the the number of kinds of things that exist; and at still other times, he seems to be arguing about the number of different properties that a thing can hold.
Aristotle's argument that there cannot be an infinite number of things has five parts, of different quality:
(1) The infinite is unknowable.
(2) If an object has a finite size, then its parts must also be finite.
(3) That some of every constituent is present in every object is inconsistent.
(4) Nothing material can be extracted from the smallest instance of a substance.
(5) An infinite collection must be both divided and connected simultaneously.
Now that I try to explain them, I don't think any of them are very good. I think many of the reasons he discussed earlier are much better than his discussion here, but the conculsions he came to were wrong. And ironically, on this one Aristotle is right.
Nothing is composed of an infinite number of things, to our knowledge. It seems like there are a finite number of kinds of things that something can be composed of at the smallest level (standard model) and even a finite number of possible elements something can be made of (periodic table). So although a copper ball has an impossible number of atoms in it (maybe 1025 or so), it is still a finite number, and although the atoms that make up the ball have constituents, they have a small number of constituents (say, around 250).
 Although, as philosophers, they do continue to find value in them. See Salmon, Zeno's Paradoxes and Sainsbury, Pardoxes. [Amazon]
 But there could be preons inside of quarks (but probably not). And if there are preons inside of quarks, then what's inside the preon?
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