Question Twenty-Four
[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 <quantity>; another quantity is less <distant from another quantity>. Therefore, some <quantity> is extremely distant from another <quantity>. 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 <given> above.2
2. Second, in this genus and in every other <genus>, 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).
JOHN DUNS SCOTUS
contraries, and if <there are> 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, <there are> also contraries <in this genus>. 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 <happen>; and <if they exist> somewhere, then <they exist> 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) <properties> inhering
<in it>;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 <seem to be contrary quantities>;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 <where> 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
<which are> contrary in this way. <As it is said> properly, contrariety is the greatest distance of forms, which are apt by nature to exist mutually in the same susceptive <thing>. 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
about substance and quantity; and it must be understood <to be denied> in definite <things>, that is, in the species of quantity, as Aristotle says,13 <although> 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 <argument>,14 it is said that in quantity there is not any greatest distance, since the division of a continuum proceeds to infinity, and so <there is> 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 <to be the case> 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 good of the universe.
11. Therefore, one can say that even though there are infinite species in potency to quantity, although not any of the infinites is contrary to another <infinite>—since it is not maximally distant—nevertheless, an intermediate species common to these
<things> can be maximally distant from another intermediate species common to those, as a continuum is maximally distant according to the form of continuity from the discrete, although continuums are infinite, and discrete <quantities> are similarly infinite. Therefore, it can be said that the first two arguments
(rationes)16 lead to a true <conclusion> concerning contrariety as it was said in the first way, namely, in its transferred sense, since each authoritative quotation of Aristotle in Bk. X of the Metaphysics17 is only to be understood of that <sense>.
13. Categories, Ch. 6 (5b 13–150).
14. Cf. supra, n. 1.
15. Porphyry, Isagoge, Ch. "On Species" (AL I6 12; ed. Busse, 6.12–14).
16. Cf. supra, nn. 1–2.
17. Cf. supra, n. 8.
JOHN DUNS SCOTUS
12. To the third <argument>,18 I say that motion is not toward quantity in itself, but as it is under <something> natural.
And in this way it has contrariety, as imperfect quantity to perfect <quantity>, to which <things> and of which <things> are augmentation and diminution. For those differentiae are not of quantity in itself, but of natural quantity. For "imperfect," which is not necessary to the species, is said according to its natural form; "perfect" <is said> through the opposite. For, as it is said in Bk. II of On the Soul:19 "Of all constant things, nature is the determinate account (ratio) of magnitude and augmentation."
For some imperfect quantity is not absolutely in the genus of quantity, but an imperfect <quantity> is in a natural being; and according to this, something is moved from imperfect to perfect quantity or vice versa.
13. Against this <reply>: Motion is toward a thing of some genus, not to an accidental being; according to Aristotle in Bk. III of the Physics:20 "There are as many species of motion as there are of being"; <and> the Commentator adds "having been acquired through motion."21 But quantity under natural existence is not a species of a genus, but is an accidental being, since it is composed from two <things>, of which one happens to another.
Therefore, motion is not toward quantity in this way, but motion is toward that which is essentially (per se) in the genus of quantity; therefore, something is contrary to that.
14. One can say here that motion is toward quantity, in the way that <something> acquired, as an end, is essentially (per se) in the genus of quantity through motion. But <that thing> is not acquired as it is a quantity, but under such a mode of being, and it has a contrary under such a mode of being. Then one ought to say that it is not necessary that something is properly contrary to that form, which is essentially (per se) the end of motion, but only to it as it is acquired through motion. Then
<regarding> the form, if one <thing> is understood to be com18. Cf. supra, n. 3.
19. On the Soul, Bk. II, Ch. 4 (416a 16–17).
20. Physics, Bk. III, Ch. 1 (201a 8–9).
21. Averroës, Physics, Bk. III, Com 5 (ed. Iuntina, IV f. 41va ).
QUESTION 24
posed from these, I say that quantity under natural existence is an accidental being; but <that thing> is not a quantity, although it is taken under such a mode of being, when the mode is not understood to be part of the being composed from two things; and in this way motion is toward quantity.
15. To the fourth argument,22 I say that it is one thing to receive greater and less, and another thing to receive more and less, since greater and less are said according to quantity; but more and less express the intension and remission in the form to which they are added. It must be conceded then that quantity receives greater and less, but not more <and less>.
16. To the fifth <argument>23 about great and small, Aristotle24 responds that they are not quantities, since they are said only in respect to another <thing>; otherwise, "a mountain would never be said to be small, and a grain of sand <would never be said to be> large."25
17. Otherwise,26 one can respond that if they are quantities, they are not contraries. First, since nothing is contrary to that which is said only in respect to another; great and small are also of this kind. Second, since then contraries would be said of the same thing, since the same thing is great <in comparison> to this and small <in comparison> to that; therefore, it is great and small.
18. Against the first response.27 According to Aristotle in Bk.
V of the Metaphysics,28 magnitude is posited as an essential (per se) species of quantity; and a concrete <term> is not in another genus than the abstract <term>.
19. Likewise, in the same place in Bk. V,29 great and small are said to be essential (per se) quantities.
20. Against the second response30 proving in two ways that 22. Cf. supra, n. 4.
23. Cf. supra, n. 5.
24. Categories, Ch. 6 (5b 27–28).
25. Categories, Ch. 6 (5b 20–22).
26. Cf. Categories, Ch. 6 (5b 30–37).
27. Cf. supra, n. 16.
28. Metaphysics, Bk. V, Ch. 13 (1020a 19–22).
29. Metaphysics, Bk. V, Ch. 13 (1020a 24–25).
30. Cf. supra, n. 17.
JOHN DUNS SCOTUS
these are not contraries. The first proof does not seem valid, since something is contrary to a relation, as Aristotle31 says a little lower, for example, as virtue is <contrary> to vice, and knowledge to ignorance.
21. The second proof does not seem valid, since all opposites imply contradictory <things>; therefore, to those <opposites>, to which contradictory <things> do not follow, other opposites do not follow. But to the premises, in which there is a relation to diverse <things>, contradictory <things> do not follow, but there is an ignorance of the refutation (ignorantia elenchi): for example, it is the double to this and not-double to that; therefore, it is double and not-double. Therefore, neither do some opposites follow such premises.
22. To the first of these <counter-arguments>,32 one can say that "magnitude" is taken equivocally: as it is a species of quantity, and as it is an attribute. In the second way "great" is said denominatively from magnitude seeing that Aristotle denies that magnitude is a quantity.
23. To the <second counter-argument>,33 I say that they are essential (per se) quantities in the second way; that is, they are attributes (passiones) of quantity, not essential (per se) <quantities> in the first way, as species.
24. To the <third counter-argument>,34 I say that nothing expresses its contrary of which it is a relative, since "contraries" and "relative opposites" are distinguished in many <ways>.
Great, however, is said relatively to small; therefore, it is not its contrary; Aristotle understands it thus. Nevertheless, a contrary to one <thing> can be a relative to another <thing>, as knowledge is relative to the knowable, and it is not contrary to it, but to ignorance. And so <it is to be taken> in the others.
25. To the <fourth counter-argument>,35 I say that relatives can be predicated of the same thing and of one another, but not relative opposites. And so relatives can be inferred absolutely from themselves <when they are> taken with respect to diverse <things>. Therefore, great and small can be inferred ab31. Categories, Ch. 7 (6b 15–16).
32. Cf. supra, n. 18.
33. Cf. supra, n. 19.
34. Cf. supra, n. 20.
35. Cf. supra, n. 21.
QUESTION 24
solutely from themselves <when they are> taken with respect to diverse <things>, and by hypothesis, they are contraries; therefore, they are contraries of the same thing. I also concede that opposites cannot be inferred relatively from themselves taken with respect to diverse <things>, but great and small can <be inferred>; and by hypothesis, these are contraries; therefore, they are contraries of the same thing.
26. To the sixth <principal argument>36—about up and down —I say that either "up" is taken absolutely for the circumference of heaven, and "down" is taken for the center of the earth; or it is taken generally, as anything is said to be up with respect to <something> lower. In the first way they are not contraries, since they do not naturally come into existence concerning the same thing; nor perhaps are they the most distant in nature, although they may be the most distant according to place. In the second way they are relatives (ad aliquid). And each response is about them <taken in this second way>, which is about great and small.
27. Nevertheless—whether they are contraries or not—one can say that <this means> nothing to the question at hand.
Since if they are species or differentiae of place, <then> they are not in the genus of quantity, since place is not <a species of quantity>, as was said earlier.37
36. Cf. supra, n. 6.
37. Cf. supra, qq. 20–23, nn. 20, 24–25.