Questions on Aristotle's Categories

Question Twenty-Four

201 [QUESTION TWENTY-FOUR Whether there is Something Contrary to Quantity] t is asked whether anything is contrary to quantity. 1. It seems that there is: Primarily, through general arguments (rationes). Some quantity is more distant from another ; another quantity is less . Therefore, some is extremely distant from another . But the greatest distance in the same genus is contrariety, according to Aristotle in Bk. X of the Metaphysics.1 Therefore, some quantity is contrary to another. The first implication is shown previously, by the authorities and the reason above.2 2. Second, in this genus and in every other , there is a differentia according to the species;3 and this is contrariety, according to Aristotle in Bk. X of the Metaphysics;4 therefore, etc. 3. Third, this is argued through specific arguments (rationes). Since, according to Aristotle in Bk. V of the Physics,5 every motion is from a contrary to a contrary or from an intermediate to an intermediate. But motion is said to exist properly in the genus of quantity, according to the same author in the same place.6 Therefore, there are contraries or intermediates there between 1. Metaphysics, Bk. X, Ch. 4 (1055a 9–10). 2. Cf. supra, q. 14, n. 13; q. 16–17, nn. 13–22. 3. Cf. supra, q. 18–19, n. 7. 4. Metaphysics, Bk. X, Ch. 4 (1055a 16–33). 5. Physics, Bk. V, Ch. 5 (229b 11–22). 6. Physics, Bk. V, Ch. 5 (229b 15–17). 202 JOHN DUNS SCOTUS contraries, and if intermediates, then there are also contraries. 4. Fourth, to undertake more and less and to receive contraries are convertible properties with respect to any genus; but quantity undertakes more and less; therefore, also contraries . The major is evident inductively. Proof of the minor: great and small are essential (per se) attributes (passiones) of quantity and of it alone; but more and less do not happen except where great and small ; and somewhere, then only in the genus of quantity.—Similarly, “every whole is greater than its part”;7 but some quantity is essentially (per se) part of another quantity; therefore, more and less is essentially in quantity.—Similarly, equal and unequal are essential (per se) inhering ;8 but unequal is more or less; therefore, etc. 5. Fifth, great and small seem to be contrary quantities.9 6. Similarly, up and down ;10 therefore, etc. 7. To the opposite is Aristotle.11 [I. The Response To The Question] 8. To the question, it must be said that contrariety is taken equivocally; namely, it can be taken properly or in a transferred sense. In a transferred sense, it expresses the absolute greatest distance in a genus, and it is extended to privative opposition, as in Bk. I of the Physics,12 it is said that principles are contrary for form and privation, which, it is manifest, are opposed privatively. Contrariety exists in this way in every genus, since every division of a genus is through opposite differentiae contrary in this way. properly, contrariety is the greatest distance of forms, which are apt by nature to exist mutually in the same susceptive . This is denied 7. Cf. Euclid, Elements (ed. H. Busard, p. 33). 8. Categories, Ch. 6 (6a 35). 9. Categories, Ch. 6 (5b 13–16). 10. Categories, Ch. 6 (6a 13–14). 11. Categories, Ch. 6 (5b 13). 12. Physics, Bk. I, Ch. 5 (188a 26–30). QUESTION 24 203 about substance and quantity; and it must be understood in definite , that is, in the species of quantity, as Aristotle says,13 perhaps not in its attributes (passiones ). Similarly, it must be understood of quantity in itself, not as it exists naturally, since perhaps in that way it has a contrary, as will be said in responding to the arguments. [II. To The Principal Arguments] 9. To the first ,14 it is said that in quantity there is not any greatest distance, since the division of a continuum proceeds to infinity, and so an infinity in continuums and in numbers resulting from their division. 10. Against this is what Porphyry says,15 that the most specific species are finite according to nature, although not with respect to us. This also seems through its nature (rationem ), since every species is an essential part of the universe, and in these parts an infinity does not seem possible, since this is repugnant to the order which is the...