Aristotle, Metaphysics

[1061a] [1] and each is used in this way because it has a reference, one to the science of medicine, and another to health, and another to something else; but each refers always to the same concept. A diagnosis and a scalpel are both called medical, because the one proceeds from medical science and the other is useful to it.The same is true of "healthy"; one thing is so called because it is indicative, and another because it is productive, of health; and the same applies to all other cases. Now it is in this same way that everything which exists is said to be ; each thing is said to be because it is a modification or permanent or temporary state or motion or some other such affection of Being qua Being.And since everything that is can be referred to some one common concept, each of the contrarieties too can be referred to the primary differentiae and contrarieties of Being—whether the primary differentiae of Being are plurality and unity, or similarity and dissimilarity, or something else; for we may take them as already discussed.¹ It makes no difference whether that which is is referred to Being or Unity; for even if they are not the same but different, they are in any case convertible, since that which is one also in a sense is , and that which is is one.

Now since the study of contraries pertains to one and the same science, [20] and each contrary is so called in virtue of privation (although indeed one might wonder in what sense they can be called contraries in virtue of privation when they admit of a middle term—e.g. "unjust" and "just"), in all such cases we must regard the privation as being not of the whole definition but of the ultimate species. E.g., if the just man is "one who is obedient to the laws in virtue of some volitional state," the unjust man will not be entirely deprived of the whole definition, but will be "one who is in some respect deficient in obedience to the laws"; and it is in this respect that the privation of justice will apply to him (and the same holds good in all other cases).And just as the mathematician makes a study of abstractions (for in his investigations he first abstracts everything that is sensible, such as weight and lightness, hardness and its contrary, and also heat and cold and all other sensible contrarieties, leaving only quantity and continuity—sometimes in one, sometimes in two and sometimes in three dimensions—and their affections qua quantitative and continuous, and does not study them with respect to any other thing; and in some cases investigates the relative positions of things and the properties of these,