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Aristotle said in Metaphysics about the Pythagoreans?

the "limited" (the odd numbers) and the "unlimited" (the even numbers) are not entities of a different order, but that the "unlimited" and unity-as-such are the subject of whatever is predicated. Which is why they consider number to be the substance of all things."

What did he mean by, and unity-as-such are the subject of whatever is predicated?

  • What translation of the Metaphysics are you taking this quote from? Where exactly is it in the Metaphysics? – Geremia Jun 2 '17 at 21:29
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    Hi Geremia, the quotation can be found in Metaphysics (987a) – Michael Lee Jun 2 '17 at 22:57
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This is how Ross's translation of Metaphysics bk. 1 §5 reads:

the Pythagoreans … thought that finitude [= odd numbers?] and infinity [= even numbers?] were not attributes of certain other things…, but that infinity itself and unity itself were the substance of the things of which they are predicated. This is why number was the substance of all things.

St. Thomas Aquinas explains this in Sententia Metaphysicæ, lib. 1 l. 9 n. 14-17 [147-150]:

  1. Here he summarizes the opinions expressed by the Pythagoreans, both what they held in common with the foregoing philosophers, and what was peculiar to themselves. Now the opinion common to some of the foregoing philosophers and to the Pythagoreans was this that they posited, in a sense, two principles in the same way as the foregoing philosophers did. For Empedocles held that there are two contrary principles, one being the principle of good things, and the other the principle of evil things, and the Pythagoreans did the same thing, as is clear from the co-ordination of contrary principles which they posited.

  2. However, they did not do this in the same way; because Empedocles placed these contrary principles in the class of material cause, as was stated above (111), whereas the Pythagoreans added their own opinion to that of the other thinkers. The first thing that they added is this: they said that what I call the one, the limited and the unlimited are not (~) accidents of any other natures, such as fire or earth or the like, but claimed that what I call the one, the limited and the unlimited constitute the (+) substance of the same things of which they are predicated. From this they concluded that number, which is constituted of units, is the substance of all things. But while the other philosophers of nature posited the one, the limited and the unlimited, they nevertheless attributed these to another nature, as accidents are attributed to a subject, for example, to fire or water or something of this kind.

  3. The second addition which they made to the views of the other philosophers is this: they began to discuss and to define “the whatness itself,” i.e., the substance and quiddity of things, although they treated this far too simply by defining things superficially. For in giving definitions they paid attention only to one thing; because they said that, if any given definition were to apply primarily to some thing, this would be the substance of that thing; just as if one were to suppose that the ratio “double” is the substance of the number two, because such a ratio is found first in the number two. And since being was found first in the one rather than in the many (for the many is composed of ones), they therefore said that being is the substance itself of the one.

    But this conclusion of theirs is not acceptable; for although the number two is double, the essence of twoness is not the same as that of the double in such a way that they are the same conceptually, as the definition and the thing defined. But even if their statements were true, it would follow that the many would be one. For some plurality can belong primarily to something one; for example, evenness and the ratio double belong first to the number two. Hence [according to them] it would follow that the even and the double are the same. And it would likewise follow that that to which the double belongs is the same as the number two, so long as the double is the substance of the number two. This, indeed, is also the conclusion which the Pythagoreans drew; for they attributed plurality and diversity to things as if they were one, just as they said that the properties of numbers are the same as the properties of natural beings.

  4. Hence, Aristotle concludes that it is possible to learn this much from the early philosophers, who posited only one material principle, and from the later philosophers, who posited many principles.

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