I'm having trouble with the following part of Aristotle's physics (185b17-185b18):

But to proceed: If their One is one as indivisible, nothing will have quantity or quality, and so what exists will not be infinite, as Melissus says—nor, indeed, limited, as Parmenides says; for though the limit is indivisible, the limited is not.

  1. Why if it is not divisible it will not have quantity or quality?
  2. Why if it is not divisible it will not be limited?

Can you clear it up?

  • If it is indivisible it cannot be extended and cannot be measurable as quantity or quality. If it is indivisible it cannot have boundaries. I feel Aristotle gets this right. Leibnitz notes that a Unity has no parts, which implies what Aristotle notes here. It would be why a Unity is inconceivable, it does not conform to the categories of thought. Thus Kant places it prior to the categories as the basis of the intellect. You would need to think hard about the meaning of 'Unity' even though technically it is unthinkable, or read relevant areas of the Wisdom literature. – user20253 Apr 26 '18 at 11:52
  • Great! Thanks. Do you have any source worth reading? Also, can you edit the title of my question? I wasn’t sure how it should be labeled. @PeterJ – César D. Vázquez Apr 26 '18 at 13:19
  • The topic runs through the literature but I don't know of a book that focuses on it. You might like to google Hermann Weyl and read what he has to say about the Continuum (which is a Unity). His book on the continuum is mostly maths but there are other writings. There is a good essay on him by John Bell which might show up. Your question would be right at home in the foundations of maths. The question title seems okay to me, perhaps because I share A's view that an extended object cannot be indivisible. . – user20253 Apr 27 '18 at 10:51

St. Thomas Aquinas's commentary (lib. 1, lect. 6) says:

  1. He [Aristotle] says first that just as being is said in many ways, so also is one. And so we must consider in what way they say that all things are one.

    For ‘one’ is used in three ways: either as the continuous is one, such as a line or a body, or as the indivisible is one[Melissus's sense of "one"], such as a point, or as those things are said to be one whose nature [ratio] or definition is one, as drink and wine are said to be one.

  1. Next where he says, ‘But to proceed ...’ (185 b 18), he shows that it is impossible for all to be one as the indivisible is one[refutes Melissus]. For that which is indivisible cannot be a quantity, since every quantity is divisible.[answer to your question #1] As a result of this it cannot be a quality, if it is understood that we are speaking of a quality which is founded upon quantity. And if it is not a quantity, it cannot be finite as Parmenides has said, nor can it be infinite as Melissus has said. For an indivisible terminus, such as a point, is an end and is not finite. For the finite and the infinite are found in quantity.
  • Here we see why the sages say we cannot say 'God is One' or 'All is One' where it would imply a numerical quantity. 'Unity' may be the most difficult word in all of philosophy. . . – user20253 Apr 26 '18 at 11:57
  • I think I got the idea that an indivisible object has no quantity and thus cannot be either limited or unlimited. But, I still have trouble with "..though the limit is indivisible..." What does "The limit" means? I would understand if it says the limited or the unlimited, but the limit? – César D. Vázquez Apr 26 '18 at 13:32

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