35. Prof. Shorey in Class. Phil. vii. go—g2 holds that et py here and in], 36 means not ‘unless’ but ‘ but only that’. He argues that in 1. 33 knowledge is said to be ‘of’ universals, i.e. to have universal con- clusions as well as universal premises (cf. Phys. 1892 5-7, Z. 1039” 27), and that singular propositions never occur as conclusions in Aristotle’s logical writings. This use of ei py is found, e.g., in Ar, Zy. 186, Av. 1681, Lys. 943, Thesm. 898, and Alexander so interprets the words here (790. 1)—There are, however, occasional references in Aristotle to the occurrence of singular propositions as the minor premise or conclusion of syllogisms (e.g. Az. Pr. 43° 37-40), and in the absence of any evidence of this idiomatic use of ei jm in Aristotle, it seems preferable to suppose that Aristotle has in mind a syllogism of the form :
All triangles have their angles = two right angles,
This figure is a triangle.
. This figure has its angles = two right angles.
Cf. An. Post. 71* 19-29 (where the same example occurs).
36. 6p0ai is as much in accordance with Aristotelian usage as dp6ais, and it is better to keep the better attested reading.
37—1087* 4. GANG piv... éotw. According to the manuscript reading the argument is: ‘But if the principles are universal, or for that matter if the substances composed of them are universal, non- substance will be prior to substance; for the universal is not sub-
Mate btdbes td se welt we ful
stance, and the element or principle is universal, and an element or principle is prior to the things of which it is principle and element’. There is manifestly no argument here; the second clause makes nonsense of the passage. All that is needed is to insert 4 before gorau in 1087%1. ‘But if the principles are universal, either the substances composed of them are also universal or non-substance will be prior to substance.’ Cf. 10879 21 ézel ei dvdyKy Tas dpxas KabdAov Elva, ava-yKn kal ta éx TovTwv KaGodov. When the first 7 once came to be mis- understood as ‘or’, the second was bound to drop out. Syrianus (164. 36) treats the clause beginning 7% xai as apodosis, and therefore probably read the second 7.
Aristotle has already (ll. 20-37) shown the difficulties that arise if the elements of substances be taken to be numerically single. He has now (1086 37—1087* 4) shown that if the elements are universal, either non-substance will be prior to substance (which is absurd) or the substances will be universals ; but this contradicts the very notion of substances, which is that they are xeywpiopevat, Kal Tov TpdTov TovTOV ds A€yerau 7a Kal?’ Exacta TOV dvtwv (1086) £7).
Jaeger treats 37 7)... 10872 1 xaOddov as a gloss intended origin- ally to have come after ovoias in 108741. But the clause goes back to Alexander (790. 9), and the insertion of 4 cures the passage more simply.
108724-10, in spite of wdvra, refer especially to the difficulty expressed in rtocatr’ éora Ta dvta doamep TA oToLyeia (1086? 21, cf. 108729, 10); ll. ro—25 deal with the other difficulty, od« émurryra 7a. ororxeia (1086? 22).
5-6. kal .. . kexwptopevov has given much trouble. Alexander has two interpretations. (1) ‘And when they claim that there is a single separate avroeidos distinct from the substances which are sensible and have in them the Ideas’ (791. 2). The Greek evidently will not bear this meaning. (2) ‘And when they claim that there is a single abroeioos separate from the substances, i. e. from the Ideas, which have in them the dpyixov & or avrocidos’ (791. 5). Besides misreading 76 ard eldos aS TO avToEtoos, this introduces a notion which the context does not warrant, the notion of a hierarchy among the Ideas. The passage is concerned solely- with the relation between separately existing substances and their elements. In view of the failure of Alexander’s interpretations Bz. proposed to omit xa} i8éas, but there is another interpretation which removes the difficulty. ‘When they claim that apart from the substances which have the same form there are Ideas, which are each of them a single separate entity.’ So interpreted, the two clauses dependent on dray answer exactly to the original statement of the question, ay dé tis 09 Tas otoias (here = the Ideas) ywpurrds, rs Onoe Ta. crorxELa Kal Tas dpyas adrdyv ; (1086 19).
4-10. Aristotle here states his own mode of escape from the difficulty raised in 1086 22-32, just as in ll. 13-25 he states his mode of escape from the difficulty raised in 1086) 3 2-37.
y. Aristotle says domwep as if he were afterwards going on to state
2573 2 Hh
bili ded
466 Commentary
the true view about the elements of substances, of which the true view about the elements of syllables is an illustration ; but the dozep clause gives his meaning sufficiently and the principal clause never appears. Cf. B. 1000 r n.
17. Bz.’s excision of tod is, in spite of Alexander’s attempt at an interpretation, absolutely necessary.
22. domep emt Tov dmodetEewv, because dzddevéis must be in the first figure (Az. Post. i. 14), and in that figure universal premises always give a universal conclusion.
Book N
(B) The tdeal theory treats contrartes as first principles (ch, 1. 1087 29-33).
1087? 29. All philosophers make the first principles contraries, the first principles of unchangeable substances as well as those of the objects of physics. Now, since there cannot be anything prior to the first principle of all things, the first principle cannot be an attribute of something else, for then that other would be prior to it. But
M, Yo! 1087" 13-22 467
all generation from contraries implies a substratum, so that all con- traries are attributes of a subject and none is self-subsistent ; therefore no contrary is strictly a first principle. .
b4. Now the Platonists make one of the contraries—viz. the unequal (the dyad of the great and small) or plurality—the material principle, and its contrary, ‘the One’, the formal principle.
12. Further, they state the first principles badly, whether they describe the material principle (a) as the great and small, or (6) as the many and few, or (c) as the exceeding and the exceeded. These diversities make no difference to any but the verbal objections.
21. If you treat the exceeding and the exceeded in general as the principle rather than the great and small, you should say that number in general is derived from the elements previously to the number two ; but they do not say this.
26. Others oppose (¢) ‘the other’, or (e) plurality, to the One. If the One has any contrary, it is plurality; but even this antithesis is wrong, because it would follow that the One is few.
Objections (ch. 1. 1087> 33-2. 1088 35). (1) Objection relative /o the formal principle.
33. ‘The one’ evidently means a measure. It always has a sub- stratum, in harmony the semitone, in length the finger, &c., and generally in qualities a quality indivisible in kind, in quantities a quantity indivisible to the senses; there is no substantial ‘One itself’.
1088%4. This is natural, for ‘one’ means a measure of some plurality, and number a measured plurality or a plurality of measures (so that one is not a number).
8. A measure must be something common to the things measured ; ‘horse’ is the measure of horses, ‘living being’ is the measure of a man, a horse, and a god, ‘class’ is perhaps the measure of ‘man’, ‘white’, and ‘ walking’.
(2) Objections relative to the material principle.
15. Those who make the dyad an indefinite something composed of great and small say what is neither plausible nor possible. For (a) these are, like odd and even, &c., attributes rather than the sub- stratum of numbers and magnitudes.
21. (4) Great and small are relative terms, and therefore belong to the least substantial of all the categories. Relation is an accident of quantity, and always implies a substratum.
Hh 2
468 Commentary
2g. Its unsubstantiality is shown by this, that of it alone there is no generation, destruction, nor change, as there is increase and diminution in respect of quantity, alteration in respect of quality, motion in respect of place, generation and destruction in respect of substance; a thing becomes greater or smaller without itself changing, if its correlative becomes-smaller or greater.
by. (c) The matter of a thing is what is potentially that thing; but relation is neither potentially nor actually substance. Non-substance cannot be an element in substance.
4. (d) Elements are not predicated of their compounds, but many and few are predicable of number, long and short of line, &c.
8. If there is a plurality (e.g. two) which is simply ‘few’, there must be one which is simply ‘many’ (e.g. 10 or 10,000), But if the many and few are elements in number, either both or neither should be predicable of it.
(3) Odjection to regarding eternal entities as composed of elements.
14. Can eternal things be composed of elements? If they were, they would have matter. That which is composite is generated from its elements, but that from which a thing is generated is that which is potentially it. Now that which is potential need not become actual. Therefore that which has matter, however long it lasts, is capable of not being and is therefore not eternal.
28. Those who make an indefinite dyad the material principle, but avoid calling it the unequal, avoid only the objections incidental to making the unequal (a relative term) an element.
The mistake on which the theory rests (ch. 2. 1088> 35-10908 2).
35. The chief reason why the Platonists turned to such causes was their archaic statement of the problem. They thought all things would be one, viz. ‘being itself’, if they did not oppose Parmenides’ dogma and prove that not-being is; they thought that if things are many, they: must be composed of being and something else.
1089* 7. But (r) if ‘ being ’ has many senses (substance, quality, &c.), what sort of unity will all things be if not-being does not exist? Will all substances be one, all qualities, &c., or all things in whatever category they are? It is impossible that one thing (not-being) should cause the diversity between the different categories.
15. (2) What sort of not-being combines with being to make things ? Not-being has different senses answering to the categories.
20. Plato means by ‘not-being’ the false; whence it was said that
we must presuppose something false, as geometers assume the line which is not a foot long to be a foot long; but in fact geometers assume nothing false, and this sort of not-being will not account for the generation or destruction of anything.
26. It is from not-being in another sense, viz. the potential, that generation takes place.
gi. The inquiry seems to be how being in the sense of substance is many; for what these thinkers generate is numbers, lines, and bodies. But it is absurd to ask how there are many substances and not how there are many qualities or quantities. The indefinite dyad cannot be the cause of there being many colours, for instance; for then colours would have been numbers and units.
bg. If they had considered this, they would have seen the cause of the plurality of substances also; for it must be at least analogous. This error is also the cause of their treating as the material principle a relative term (viz. the unequal) which is not really opposed to being or to the One but is one kind of being.
8. They ought to have asked how relations are many; but while they ask how there are many units besides the One, they do not ask how there are many unequals besides the Unequal. Yet they use many unequals—great and small, many and few, long and short, &c.
15. It is necessary to presuppose for each thing that which was potentially it; the author of this theory indicated what in his view is potentially substance, viz. the relative—he might as well have said quality—which is neither potentially the One or being nor the con- tradiction of them, but a kind of being.
20. Much more, if he was asking how things are many, was it necessary not to confine himself to substances or to qualities.
24. In the categories other than substance there is another problem as to how things are many ; no doubt, since they do not exist apart, they are many through the substratum taking on many qualities, &c.; but there must be a matter for each category, only it cannot be one existing apart from substances.
28. But in the case of substance we can see how the individual is many things, if we avoid the mistake of treating the same thing both as an individual and as a nature; the real difficulty here is how there are many actually existing substances.