1052715. év tots wept Tod mooaxds, A.6. The classification of the senses of ‘one’ there given is as follows:
(1) 70 kard cvp,B_Byxds, e. g. the unity of ‘Coriscus and musical ’, &e.
(2) 16 Kal aro ev,
(a) 76 ovvexés civan (e. g. a bundle),
(4) 7@ 70 broxeipevov TO cider eivar ddidopov (e. g. all wine is one) or dv 70 yevos ev diadéepov Tals avrixepevars Siapopais (e.g. horse, man, dog are all one),
(c) dowy 6 ddyos 6 76 Ti_ Hv elvar éywv adiatperos mpos GAXov Tov Sndotvra [ri fv ctvar] ro mpayya (e.g. that which increases and diminishes is still one if its definition does not change).
(These three senses are summed up in 1016P9 pia i) ovvexeta } cider 7) AOyw, cf. 1017% 3-6),
(d) The essence of ‘one’ is dpyj tut dpibyod etvar.
17. téttapes. These are given in |. 34—r0 ovvexés, 76 dAov, 75 Kal? éxagrov, TO kabodov. The first answers to (2 @) above, the third to (2 c), the fourth to (2). The second appears as a species of (2 a), the con- tinuous which has a single form, e. g. a shoe as opposed to the same materials when not arranged to serve a purpose (1016 11-17). (1) is expressly excluded in this chapter (1052* 18); (2d) is introduced as the primary meaning in 1052) 18.
27. cit... mpdtqv. Grammar requires us to translate ‘if anything
282 Commentary
by nature has a principle of movement which is the primary principle of the primary movement’. But it is hard to assign any definite mean- ing to ‘the primary principle’. It seems clear that rHs zpérys is explained by dopas and points to the fact that locomotion is the primary kind of movement, and that rjv_mpwryv is explained by KukAogopiav and points to the fact that circular‘motion is the primary kind of Zocomotion. I. e. tis tpaérns and rv mpwryy are used in the sense which they would properly have if xivyow, not Kwyoews apxny, had preceded. jl ;
tis mpéryns. Locomotion is prior to the other kinds of change— change of size, of quality, of substance (generation and destruction), since a subject can have it without having the others (PAys. 260% 20— 261%26). Cf. Z. 1036’ gn.
thy mpdéryv. Circular motion is prior to other kinds of motion because (on Aristotle’s view) it does not involve change of direction. This is equally true of motion in a straight line, but the latter is exposed to the objection that if it is to go on it ultimately requires infinite space (which Aristotle does not believe in); circular motion returns on itself and does not need infinite space (PAys. vili. 7).
28. toito mpAtov péyelos ey, i. e. a celestial sphere is the best instance of what is one by continuity.
29. Just as the continuous and the whole are akin, so are the other two main kinds of unity, 76 xa6’ exacrov and 76 xafodov; they are introduced as subdivisions of ra dv av 6 Adyos cis 7. The first two are one because their movement is indivisible, the last two because the thought of them is indivisible (1. 36).
33. 16 Tals ovclais aitvoy Tod évds, i.e. the essence.
35. It is rather surprising to find the fourth kind of unity described as ro xaOdAov; what Aristotle has said about it (1. 31) suggests only the infima species, the least universal of universals. A genus is one object of thought in the sense that it has a single definite nature ; it is not one in the sense that it is logically indivisible, and Aristotle seems here rather to confuse the two things. But he is right in recognizing the unity of a universal, whether genus or species, as one kind of unity.
bz, Aristotle now introduces the distinction expressed in modern logic as that between extension and intension, or denotation and connotation. He has named four kinds of thing that are one; he now proposes to state the single connotation of the word ‘one’. This is ‘nearer to the word’, while the others are ‘nearer to its application’ (1. 6). |The connotation of ‘ one’ is ‘ indivisible’ (1. 16), or ‘ whole and indivisible’ (1. 17), or ‘first measure of a class, and primarily of quantity’ (1. 18).
7. TH Suvdpe 8 éxetva, Alexander takes this to mean ‘but the others are only potentially one’. It seems clear, however, that waAAov éyyvs is to be understood and that the meaning is ‘while they are nearer to the force (or application) of the word’. For this meaning of dvvapus cf. Lys. 10. 7, Pl. Crat, 394 B3.
Hy ty 1O5 2725. 10539 23 283
10. 76 daerpov, Anaximander’s ‘ indeterminate’.
27. Kowviy év tots évaytiors, i. e. each of the terms is common to each of two contraries.
1053° 12. BSieots, cf. A. 1016” 22n.
15. at dvécerg SU0o. There can be little doubt that this refers to the two distinguished by Aristotle’s pupil Aristoxenus (i. 21), the enhar- monic, which was a quarter-tone, and the chromatic, which was one- third ofa tone. Aristotle ignores the hemiolian déec1s, mentioned in Aristox. ii. 51, which was three-eighths of a tone.
Bz. thinks that the two diéces were the major semitone (éorop:)) and the minor semitone (Aciypa) recognized by Philolaus. But Philolaus seems to have used d/eous simply in the sense of ‘minor semitone ’ (Boethius, Inst. Mus. wi. 5, 8, pp. 277, 278 Friedl.).
17. at dwvat mrelous ats petpodpev, i.e. there is no one letter which is the measure of speech more than the others. A, @, 2, 0, w, and again J, c, d, &c., are equally units of speech and not necessarily of equal length.
Kal 7 Sidperpos Suct petpetrar Kat 4 wAeupd. It is difficult in view of the order of the words to translate this ‘the diagonal and the side of the square are measured by two different measures’. It may be that the diagonal itself is said to be measured by two measures, i.e. that it is conceived as consisting of two parts, a part equal to the side, and a part which represents its excess over the side, and that these parts being incommensurate are said to be measured by different units. Cf. A. 10218 3 TO 0 dmepéxov Tpos TO dmepexopevov dAws adpurrov Kar’ apiOpov' 6 Yop, dpi pos ov ppeTpos, KaTo pn UPpeTpoV 8 api pos ov A€yerau, 70 oe & brrepexov Tpos 70 brrepexopevov Tog obrov Te €oTL Kab erL, rovto 6 dopuroy. If this interpretation be right, xat 7 mAevpa is the gloss of an over-zealous copyist.
18. kal 7a peyeOn mdvta. Bz, takes this to refer to quite a different point, that the areas of all plane figures are measured by multiplying together two numbers which express the Jength of the sides of a rectangle equal to the given figure. But (1) it is difficult to interpret Ta peyeOn rayra as referring only to plane figures. peyéOy covers all lines, surfaces, and solids. (2) The two factors of the area are not at all analogous to the two dieces, the various letters of the alphabet, the two different units required for the measurement of incommensurate lines, They are not two units used to measure different things ; both are used to measure any one plane figure.
No suitable meaning for ra. weye0n wavra presents itself, unless it be the rather vague one ‘and in all kinds of spatial magnitudes similar incommensurabilities can be found’. There is something to be said for Ab’s reading 7 dudpetpos . . . Kal 7 wevpa, peyeOn Twa Ovta. Ondov Oy, which seems to have been read by Alexander (610. 6, 7): In that case dru should be inserted after 67. But peyéOy twa ovra appears pointless. Goebel’s kal peyéOy twa ofov 76 AjAvoy. ovrw is more ingenious than convincing.
23. Geréov is Professor E. S. Forster’s conjecture. For ribévas eis
284 Commentary
‘to class among’, cf. Phys. 201% 24, L. NV. 1156" 30, &c. Ar’s Gere represents the first stage in the corruption. This emendation gives a better sentence than Bz.’s eivar ddvatperov (for eis ddvaipera), in which the position of efvac is unnatural. -
Gotep eipytar 79n, |. 5. 4
30. 68 dprOpds TAHO0s povddur, cf. Z. 103912 n.
32. érel petpodvtar paAXov 7 petpodow, ‘although really they are measured rather than measure’. The scope and variety of reality is not measured by knowledge and perception, since there are real things which we do not know or perceive ; but the scope of our knowledge and perception is measured by the things we know or perceive, as, when something of known length (e.g. a cubit-rule) is affixed to our body, our body is measured by the cubit-rule and not the cubit-rule by our body. On the priority of the object of knowledge (or perception) to knowledge (or perception) cf. 10572 7-12, I. roro 30—r1o114 2, A. 10218 29—-) 2, @, 1051” 6-9.
35. émi tooodrov, It seems difficult to take this as = rooavraxis as Alexander does, and probably the reading ézi tocotrov jv, ‘ over such and such a fraction of ourselves’, is preferable to AP Al.’s éxt TOTOVTOV Hiv.
Unity not a substance but a predicate coextensive with being (ch. 2).
1053" g. Is the one a substance, as the Pythagoreans and Plato say, or does some nature underlie it, e. g. (as the natural philosophers say) friendship, air, or the indefinite ?
16, (1) If, as we have said, no universal is a substance, and being is not an independent substance but a predicate merely, the same is true of the one; being and unity are the most universal of all predicated terms. Thus genera are not separately existing substances, and unity is not a genus, any more than being or substance is so,
24. (2) Since in qualities and in quantities ‘one’ is the attribute of something that underlies it, we must similarly in all the categories ask what the one is; it is never the whole nature of a thing to be or to be one. In colour the one is a colour (e. g. white), so that if the world consisted of colours, it would be a number, indeed, but a number of colours, and the one would be one something,
34. So too if the world consisted of tunes, articulate sounds, or rectilinear figures, it would be a number of quarter-tones, letters, or figures, and the one would be the quarter-tone, the vowel, or the triangle.
1054" 4. If this is true of the other categories, it must be true of substance ; the one itself must be one substance,
I. I. 1053%30— 2. 1053) 32 285
13. That unity in a sense means the same as being is clear (1) because it is found in all the categories ; (2) because it adds nothing to the meaning of a term, any more than ‘existing’ does; (3) because for a thing to be one is to be the particular thing it is,
1053? 10. év tots Stamophpacw, B. 10012 4-24.
14. Bz. sees that the question w&s Set yywptpwrtépws AexOfvar should not be answered at the same moment that it is asked, by the words xai padXov dorep ktX. In view of this, and of Alexander’s dpa do7ep oi rept pucews, he proposes 7 padAov (interrogative) for kai waAXov. But this does not remove all difficulties: as de? yrwpywrépws exOjvac remains a very curious phrase. The order is much against Schwegler’s aos for ras. The best solution is to excise 7@s as an emblema from kat was det, |, 11.
15-16. 6 pév tts, Empedocles; 6 8’, Anaximenes; 6 $é, Anaximander.
17. év tots wept ovcias, Z. 13.
avro Todo refers to ro ov (zepl Tov dvros, 1. 17). avrd Todro is sub- ject, ovciay predicate ; this is preferable to making airéd rotro, otciay, subject, as Bz. does.
23. For the reason why being and unity cannot be genera cf. B. 998» 23.
24-28. ‘The question whether unity is self-subsistent or requires a subject must be answered for all the categories alike. Now in the category of quality unity is the attribute of some subject or other (e.g. a colour); therefore it must be so in all the cate- gories.’
29. éort Td Ev xpOya. Alexander (613. 12) seems to have read éori ru 70 €v, and Bz. thinks the right reading is that of EJT, éoré 70 €v xpopa, ‘the one is some colour’, But the order is strange ; either te Or xp@pa is probably an excrescence, and it seems better to read xpaua with all the manuscripts and to omit 7 with A>. ru has come in by dittography or by the influence of |. 26.
29. The true reading seems to have been preserved by JT, who have eira. Al.’s commentary (613. 13) suggests efra rather than ¢i, which has no doubt been produced by haplography.
31-32. todtro...wrtds. Jaeger is probably right in treating this as
286 Commentary
a gloss; for glosses somewhat of this form cf. A. 984> 11, T. roog* 26, A, 1073* 33.