2 Answers

  1. Well, I haven't touched Aristotle yet, so I'll just give you my opinion.

    Quantity. In my understanding, quantity is a bill. In order to count, we use natural numbers, i.e. from one onwards, not negative in any way, and not even zero. Accordingly, when it comes to quantity, we cannot, for example, remove 4 books out of two from the table to get the “opposite” – minus two books.�

    In addition, we count items. Instead of an object, we cannot remove some part of matter, space (what else is there?) to get a “negative amount”.�

    To sum up, I don't know if I'm right or wrong, but it's hard for me to disagree with him.

    1. “1” and ” -1 ” are not opposite quantities, but opposite numbers that measure and express the quantitative characteristics of things. Some of these characteristics can be described as opposite, but opposite to each other, not to quantity. I.e. your example does not refute Aristotle.�

    2. What does Aristotle mean when he says in the sixth book of Categories that “nothing is the opposite of quantity”? Categories here are types of what can be said about existing things and the relationships between them.

    The quality (“caloric content”) of a thing does not need another thing for its definiteness: a lemon is sour by itself, and not because a watermelon is sweet or a cucumber is fresh (let's take the latter for clarity). But in comparison with the sweetness of watermelon, relative to which the sourness of lemon is only different, the freshness of cucumber is the opposite of the sourness of lemon. I.e., there is always some quality that is different from it or opposite to it.�

    But it is impossible to quantify a thing without comparing it with another thing: a lemon is small in size only relative to a watermelon that is large in size, or it is (approximately) equal in size to a small cucumber. And in the case of quantity, only a difference in the quantitative parameters of things is possible, but not the opposite. There are no things (material) with zero or negative value, so to speak, “non-quantitative” or “non-qualitative” things -nothing is the opposite of quantity.�

    1. But for mathematical objects not considered by Aristotle (he lived much earlier than modern mathematics), which “exist” in imaginary, postulatively defined spaces, the same thing is true – their qualitative characteristics are different up to the opposite, and their quantitative descriptions are different, but not opposite.

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