Questions Twenty through Twenty-Three
<QUESTIONS TWENTY THROUGH
TWENTY-THREE>
[QUESTION TWENTY
Whether Aristotle Sufficiently Enumerates the Species of Quantity]1
t is asked whether Aristotle sufficiently enumerates
the species of quantity.
1. It seems that he does not:
According to Aristotle in Bk. V of the Metaphysics:2 time is a quantum through an accident; but genus is predicated accidentally of no species; therefore, time is not a species.
2. Second, according to the same author in the same place:3 time is a quantum through motion; therefore, all the more is motion a quantum: "that is more <of a certain thing>, on account of which every <thing else> is such a thing."4 Therefore, there are more species than those that are enumerated here.
3. Third, time is number, according to Aristotle in Bk. IV of the Physics;5 therefore, it is not another species.
4. Fourth, place is not enumerated among the species of quantity, in Bk. V of the Metaphysics; therefore, either it is insufficiently <enumerated> there, or place is not a quantity.—Similarly, the Commentator there <in his commentary>6 assigns the cause why Aristotle omits place there, saying that place is not 1. Questions 20–23 will all be answered in the negative; cf. infra, nn. 20–23.
2. Metaphysics, Bk. V, Ch. 13 (1020a 26–29).
3. Metaphysics, Bk. V, Ch. 13 (1020a 32).
4. Posterior Analytics, Bk. I, Ch. 2 (72a 29–30): Omne enim propter quod unumquodque tale, et illud magis.
5. Physics, Bk. IV, Ch. 11 (219b 1–2).
6. Averroës, Metaphysics, Bk. V, com. 19 (ed. R. Ponzalli, p. 161).
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a quantity according to the opinion of Aristotle, but it is only commonly <thought to be a quantity>.
5. Fifth, place does not seem to be another species other than a surface, since <a surface> is posited primarily in the definition of place in the abstract;7 and when an accident in the abstract is defined, what is posited primarily in its definition is of its essence.
6. To the opposite is Aristotle, etc.
[QUESTION TWENTY-ONE
Whether Place is a Quantity]
long with this it is asked whether place is a quan-
tity.
7. It seems that it is not:
Since everything posited in the definition of an accident is its subject or is of its essence; "the limit of the containing body"8 is posited in the definition of place, and it is not of its essence, since then it would be the same species with surface; therefore,
"limit" is the subject of place. But it is impossible that a subject and an attribute be the species of the same genus. Therefore, place is not a species of quantity. And this reason is confirmed through the Commentator <in his commentary> on Bk. V of the Metaphysics,9 who says that place is an attribute in the limit, as <it has> the condition of being immobile.
8. Second, nothing is moved naturally to a "quantum" insofar as it is "quantum"; but something is moved naturally to its own proper place, according to Aristotle in Bk. IV of the Physics.10 Proof of the major: nothing is moved to another except on account of a suitability in its nature; but "quantum" insofar
7. Physics, Bk. IV, Ch. 2 (209a 31–b 2).
8. Cf. supra, n. 5.
9. Cf. supra, n. 4; Averroës, Metaphysics, Bk. IV, com. 41 (ed. Iuntina, IV f.
65rb–va).
10. Physics, Bk. IV, Ch. 4 (210b 22–211a 12).
QUESTIONS 20–23
as it is "quantum" is suitable with no thing in its nature, but it is nature that is "the principle of motion and rest,"11 since it is naturally prior to those <things which> inhere in a substance.
9. Third, "quantum" insofar as it is "quantum" does not preserve anything naturally, since it is not suitable to anything in nature, but place insofar as it is place preserves <something> placed, according to Aristotle in Bk. IV of the Physics.12
10. Fourth, place is said essentially (per se) of <something> placed; therefore, it is in the genus of relation.
11. To the opposite is Aristotle.13
12. First, place is essentially (per se) a measure; therefore, it is a quantity. The antecedent is evident; the implication is also
<evident> according to Aristotle, who argues in the <same> way about speech.14
13. Second, a peculiar property is not found beyond that of which it is a <property>. But "it is a peculiar property of quantity that something is said to be equal or unequal according to it";15 however, this pertains to place. Therefore, it is a quantity.
14. Third, place is essentially (per se) divisible; therefore, it is a quantity.
[QUESTION TWENTY-TWO
Whether Place is a Continuous Quantity]
long with this, it is asked whether <place> is a
continuous quantity.
15. It seems that it is not:
Let some continuous rod be fastened into the earth, a part of which is in the earth and a part in the air. Then I argue in this way: "place is the limit of a containing body";16 but the limit of the air and the limit of the earth, which holds (locant) the 11. Physics, Bk. II, Ch. 1 (192b 21–23).
12. Physics, Bk. IV, Ch. 2 (209a 31–b 2).
13. Categories, Ch. 6 (5a 6–7).
14. Cf. supra, q. 18–19, n. 3.
15. Categories, Ch. 6 (6a 26–27).
16. Physics, Bk. IV, Ch. 2 (209b 1–4).
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<rod> which was placed (locatum) <there>, are not continuous but only contiguous;17 therefore, the place of this rod is not continuous.
16. To the opposite is Aristotle.18
[QUESTION TWENTY-THREE
Whether the Particles of a Body and of a Place are Joined Together at the Same End]
ext, it is asked whether the particles of a body and
of a place are joined together at the same end <or ter-
minus>.
17. It seems that they are not:
Since the particles of a body are joined to the surface; the particles of place are not. Since place is a surface, and the particles of a surface are not joined to the surface but to a line.
18. Second, place is divided by <that which is> placed, according to Aristotle in Bk. IV of the Physics;19 therefore, the same thing does not end and continue the parts of each. The implication is evident, since an end is not divided from that of which it is
<an end>; therefore, it is not the same <end> of two divided <things>.
19. To the opposite is Aristotle.20
[I. The Response To Questions Twenty through Twenty-Three] 20. To the second question,21 it must be said that place is not a species of quantity, on account of the first reason there,22 and 17. Physics, Bk. V, Ch. 3 (227a 11–13; 227a 6–7).
18. Categories, Ch. 6 (5a 9).
19. Physics, Bk. IV, Ch. 4 (212a 15–21).
20. Cf. Categories, Ch. 6 (5a 9–13).
21. Namely, to q. 21.
22. Cf. supra, n. 7.
QUESTIONS 20–23
on account of the saying of the Commentator, in the statement above in the preceding question.23
21. Similarly, on behalf of the first reason to the third question;24 <it must be said> that place is not necessarily continuous.
But nothing would be different <with regard> to its unity <if> its surface is a contiguity (contiguatas)—if the same <object> is surrounded (locetur) by diverse contiguous bodies—or <if> the surface of one <thing> is continuous, when the <thing that is> placed is held in one <thing> holding <it>.25
22. Similarly to the fourth <question>:26 <it must be said> that the parts of place can in no way be joined to the same end in number to which the parts of the body <are joined>, since place is divided from <the thing that is> placed. For place is that from which or to which the <thing that is> placed is moved, and <place> is not moved when the <thing that is> placed <is moved> nor <is it moved> to the same end in species. Since that end <or boundary> of a body is its surface, which is not the end
<or boundary> of a place, unless place were a body. To be more precise, it is not necessary for these to be joined to the same end <or boundary>, since it is not necessary for these to be continuous.
23. The solution to the first question follows from this, since he does not sufficiently enumerate the species of quantity, at least with respect to the species "place."
[II. The Response To The Authority Of Aristotle] 24. To the authority of Aristotle to the opposite to all the questions, it must be said that he does not speak here of place according to his own opinion, but according to the opinion <of those who> posit place to be the space equal to <the thing having been> placed; and according to that <opinion>, all these
<claims> would be true of place.
23. Cf. supra, n. 4.
24. Cf. supra, n. 15.
25. The Latin is as follows: quando locatum locatur in uno locante.
26. Namely, to question 23; cf. supra, n. 17.
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25. But that opinion is disproved by Aristotle in Bk. IV of the Physics.27 Thus, frequently, when <something> is said of something <else>, where the place is not proper for determining the truth, he uses the common opinion of others about it, <and> even elsewhere, when the place <is proper for> determining the truth about it, <he often uses the common opinion of others>, provided that the knowledge (ars) can be given according to the opinions of others just as <it could> also <be given> according to the proper truth. This is the way it is in almost all the examples in logic; since he does not care if it is thus or not, as long as that knowledge (ars) is true in those <examples>, if these <opinions> are such. Just as here it is sufficiently manifested that quantity is a genus, since it has many intermediate species and most specific <species> under it; whether place is any of those species or not.
[III. To The Principal Arguments Of The Twentieth Question] 26. To the first argument of the first question,28 one can say that <the statement,> "something is a quantum through an accident or through another <thing>" is twofold: effectively or formally. Formally, time is not a quantity through another; that is, nothing is <a quantity> through another which receives the predication of quantity; but <something is a quantity if quantity> is predicated of it in the first way of essential (per se) <predication>.29 Effectively, in a certain measure, one can say that time is a quantum through another, since effectively it has its own essence and its own quantity, which is its own essence, from another as from motion; nevertheless something does not make it
<such> that time is a quantity.
27. To the second <argument>,30 I say that the proposition of Aristotle is only true when something univocal is said of a cause and of its effect, which by nature receives more and less, and 27. Physics, Bk. IV, Ch. 4 (211a 25–b 5).
28. Cf. supra, n. 1.
29. The Latin is as follows: per se primo modo.
30. Cf. supra, n. 2.
QUESTIONS 20–23
when the cause is essential (per se) and of the whole. The first condition is absent here, and the second is similarly <absent>.
First, since time is a quantity, motion is not a quantity, since its whole nature (ratio) can be understood to be suitable to an indivisible. Nor are they univocally designated (univocantur) in "quantum," since <quantum> is said of motion essentially (per se) in the second mode; <and quantum is> in no way <essentially said> of time, so that time is a species of quantity.
28. To the third <argument>,31 I say that "number" is sometimes taken from one <species> to another <species>, as it is generally taken for measure, perhaps on account of the fact that the nature (ratio) of measure in quantities pertains primarily to number, and in this way <number> is posited in the definition of time,32 not, however, as it is a discrete quantity. And <here> there is equivocation according to the second mode.
29. The other <arguments> about place must be conceded except the last.33 To that <argument> it must be said that this predication is only material: "place is the limit <of a containing body>"; and formally the proposition is false. But formally place is the immobility of the limit, according to the Commentator.34
Nevertheless, perhaps in the definition of place "limit" is posited first, since that is more known by the immobility of place.
[IV. To The Opposing Arguments Of The Twenty-First Question] 30. To the arguments to the opposite of the second question,
<the following> must be said.
To the first <argument>,35 one can say that place is not an essential (per se) measure, but <it is a measure> through the nature of its material, which is its surface; therefore, it measures the same dimension as the surface.
31. Cf. supra, n. 3.
32. Physics, Bk. IV, Ch. 11 (220a 25–26).
33. Cf. supra, n. 15. The editors of the critical edition identify the last argument as n. 5, which is the last argument of the first question. In my judgment, however, the last argument referred to is n. 15, which is the last argument of the three questions that posit place as a species of quantity.
34. Cf. supra, n. 7.
35. Cf. supra, n. 12.
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31. And if it is argued against this: because <place> has another nature (ratio) of measure than the surface; for it is an extrinsic measure, and a surface is an intrinsic <measure>:
32. One can say that extrinsic and intrinsic do not essentially (per se) vary the nature (rationem) of measure. Therefore, place does not essentially (per se) have another nature (rationem) of measure than the surface; for this reason, <the nature> is extrinsic, since materially it is "the limit of a containing body" and it is the limit of the <thing> contained, which nevertheless is measured by place.
33. To the second <argument>,36 I say that something is not said formally to be essentially (per se) equal to another according to place, but perhaps <it is said> materially <to be essentially equal to another> according to the surface of that which contains <it>; rather, to be more precise, place is said <to be> equal to <the thing> placed, according to Aristotle in Bk. IV of the Physics,37 and not insofar as other <things> are said to be equal.38
34. To the third <argument>,39 I say that place is accidentally divisible through the nature of its material, just as other forms essentially (per se) based in quantity are accidentally divisible through the nature of quantity; and perhaps place is more <divisible> than the others in that it is the proper attribute of a surface.
36. Cf. supra, n. 13.
37. Cf. supra, n. 18.
38. The Latin is as follows: et non illud secundum quod alia dicuntur aequalia.
39. Cf. supra, n. 14.