32. domep obd€ xpapa tadtov kat dpatdv. Cf. De An, 418) 2 didrep oby dparov dvev pwrds, GAA TaV TO Exdorov XpHua ev puri dpardy. It is xpaua that is visible, but it needs a further condition, viz. light, before it becomes visible. I.e. visibility is a cvpBeByxds which under a certain condition belongs to the subject colour.
34. oT pev is answered by ori dé, 10662.7. ~~
10663. Simplicius interprets ToOto as 76 oixodopyrov, i. e. the raw materials of a house, but this is plainly wrong. The alternatives, as the following lines show, are the act of building and the house. The most probable reading is that given in the text. ‘ The actuality is either this which has just been mentioned, viz. the act of building, or the house.’ 3Bz.’s rovrov for rotro is improbable.
8. wept adris, i.e. about movement, referring back to 1065» 33.
g. There seems to be no clause responding to oltre ydp kth. Neither 4 re kivnows xrA., 1. 20, nor Kat 8a rodro xrA., 1. 22, will quite serve the purpose. The parenthesis proving that movement cannot be classed as anything but an évépyeua seems to have made Aristotle forget what the second main member of the sentence was to have been. What logic would require as the sccond member would be ‘nor, if movement is an évépyeia, can it be any évépyea other than that of the duvaréy as such’.
II. ot pev yap... 7d ph ov. Hs 8 érépas cvororyias KrX., 1. 14, in- dicates that the Pythagoreans are referred to; cf. A. 986% 25, where movement occurs in the cverouxia of the indefinite. But the reference to the other, the unequal, the non-existent suggests rather the Platonic view. We may compare such passages as Soph. 256d, Zim. 57 Eff. Simplicius is doubtless right in supposing that both the Pythagoreans and Plato are referred to. ;
11-13. If movement be identified with otherness, inequality, or not- being, this can only (Aristotle argues) be a loose way of saying either that these are the subjects of movement or that they are the termini of movement. But (1) it would be untrue (or rather it would be non- sense) to say that they are necessarily moved, and (2) if they are ter- mini of movement, then since movement is between contraries, their contraries are equally termini of movement, and have as much claim to be mentioned in the definition of movement.
19-20. oltre yap ... woody. ‘That which has the potentiality of attaining a certain size does not necessarily undergo the change to that size, so that xivyovs cannot be identified with dvvayus. Nor, again, does that which actually has a certain size change to that size, so that kivnows cannot be identified with évepyeua.
20. H Te Klynots evépyera pev etvat Soxet tis, dreds S€, cf. @. 1048) 18-36.
25. The reading kat évépyevay kal évépyevay thy eipnpevny, ‘both an actuality and the kind of actuality we have described’, answers to the text of the Physics (2024 1), évépyevay pév twa. etvat, Tovavrny 8 evepyevay olay etrowev. EJT read xat pa évepyeay in place of the second xat évépyevav ; but movement has been described not as pa) évépyera but as
évépyewa dreys, and further the reading we have adopted accounts better for A>’s reading simply kat evepyevay THY €ipnpevny.
27. €v TO KWITA, SC. OdK ev TO KI TIKO.
28. 7% Tod KwytiKod évépyera odx Ady éotiy, i.e. the actual moving of the one thing and the actual being moved of the other are insepar- able aspects of the same event, as the same interval looked at in one way is the interval from 1 to 2 and looked at in another way the in- terval from 2 to 1.
29. det pev yap elvar evrehdxerav dpdotv, ‘for it must be the com- plete reality of both’. The xwyri«éy must have an actuality, viz. 7d xwveiv, and in this very act it actualizes the xwnrdv, so that one and the same event is on the one hand the actualization of the xuvyrixdv and on the other the actualization of the xuwyrév.
péev in de? pev ydp xrA. seems to point forward to éyeu 8 dzopiar, which follows in the Physzcs (202% 21) but not in the Aetaphysics— another indication that this part of K is not notes preparatory to the Physics but excerpts from it.
31-34. Spolws... domep ... Spotws is a good instance of Riddell’s ‘binary structure ’ (Apology of Plato, 198, § 209). Cf. A. 983>16n.
Non-existence of an actual infinite (ch. 10).
1066? 35. The infinite is either that which cannot be traversed be- cause it is not its nature to be traversed, or that which is traversed with difficulty, or that which cannot be traversed though it is its nature to be traversed; again, it is infinite by addition or by subtraction or in both ways. (A) A separate entity it cannot be; for (1) if it is neither a magnitude nor a multitude but infinity is its whole nature, it is indivisible, and if so it is not infinite except in the sense in which the voice is invisible, which is not the sense in question.
b7. (2) How can infinity exist per se if number and spatial magni- tude, whose attribute it is, do not so exist?
8. (3) If on the other hand it exists per acczdens, it is not gua in- finite an element in things, any more than the invisible is of speech, though the voice is invisible.
11. (4) That it cannot exist actually is clear. For any part of it must be infinite (since the infinite and infiniteness are the same thing, if the infinite is a substance), so that it must be either indivisible or divisible into infinites ; but the same thing cannot be many infinites, so that it must be indivisible. But that which is actually infinite cannot be indivisible, for it must have a certain quantity. The in- finite must therefore exist only per accidens, and therefore not it but that of which it is an attribute will be the first principle.
330 Commentary
21. The above discussion is general; () that the infinite does not exist 7 sensible things follows from the facts (1) that if the definition of body is ‘that which is limited by planes’, there can be no infinite body whether sensible or intelligible, and (2) that since number is numerable, there can be no separately existinginfinite number.
26. The same fact is clear from the following physical considera- tions: (3) the infinite cannot (2) be composite, since the elements are limited in number; for ome of the elements cannot be infinite, the other finite, else the former would destroy the latter, and al/ cannot be infinite, since an infinite body must be infinite in all directions.
34. Nor (4) can the infinite be a simple body, either (i) as some- thing distinct from the elements from which the physicists generate the world (for there is no such body apart from the elements ; if there were such an element in things, they would be seen to be dissolved into it); or (ii) as one of the elements ; for apart from the difficulty of supposing one of them infinite, the universe, even if it is finite, cannot be or become any one of the elements, The same argument applies as in case (i); everything actually changes from contrary into con- trary.
1067* 7. (4) The sensible body is somewhere, and whole and part have the same proper place, so that if (a) the infinite body is homo- geneous, it will be unmoving or else always moving, but this is im- possible ; for why should it rest or move in one place rather than another? Where will any part of it move or rest? The place of the cognate body is infinite ; will it, then, occupy the whole place? How could it? It will either rest everywhere and nowhere be in motion, or move everywhere and nowhere be at rest.
15. If on the other hand (6) the all is not like throughout, the places will be unlike and (i) the body of the all will not be one save by con- tact ; (ii) the parts will be either finite or infinite in the number of their kinds.
18. (a) Finite they cannot be, for if the all is infinite, some parts will be infinite in size and will destroy the finite. parts; while (() if they are infinite and simple, the places will be infinite and there will be an infinite number of elements. If this is impossible and the places must be finite, the all also must be finite.
23. (5) In general, it is impossible that there should be an infinite body and at the same time a place for bodies; for if every sensible body is either heavy or light it will move either towards the centre or upwards, but neither the whole nor the half of an infinite body can behave thus; for how can you divide it?
28. (6) Every sensible body is in a place, and there are six varieties of place; but these cannot exist in an infinite body. And generally, if there cannot be an infinite place there cannot be an infinite body; for what is in place is up or down, &c., and each of these is a boundary.
33. The infinite is not the same thing in magnitude, motion, and time; motion, if it is infinite, is infinite in virtue of the distance traversed, and time is infinite in virtue of the motion that occupies it.
This chapter consists of extracts from Phys. iii. 4, 5, 7 on the infinite.
1066* 35-)1. 16 8 dmeipov...mépas. On the various meanings of a privative cf. A. 1022) 32.
DT. ér mpoobécer 4 apaipécer 4 dppw. The infinite may be in- finite in the sense that it may be added to indefinitely (the sense in which number is infinite, according to Aristotle), or in the sense that it can be subtracted from (or divided—®dvaipeois is more usual than d@afpeors in this connexion, cf. Phys. 204% 7) indefinitely (the sense in which space is infinite, on Aristotle’s view), or in both senses (as time is, according to Aristotle).
Gude, i.e. xpoabere. TE diretpov Kal datpeoes dmerpov.
Xwpiorov pev 8 adto tu dv. Aristotle considers first the view of the infinite held by the Pythagoreans and Plato (cf. Phys. 2034). In the vulgate reading, xwpictov pev 81 adro te dv, aicOyrov & ovx otov 7 etvat, the words aicOyrov 8 are irrelevant to the argument, since the question whether the infinite can exist as an object of perception is not discussed until]. 22. Christ’s emendation aic@yrév 7 does not remove this difficulty, and it seems better to regard the words as an unintelligent gloss. The alternative is to read aic@yrov 3 ov, which would be a fair enough paraphrase of the reading of the Physzcs ywpu- orov Tov aicOnrav. ‘That the infinite should exist as a thing separate and existent by itself but not perceptible, is impossible.” The sort of infinite treated of in the argument in ll. 2-21, which is pyre peyeOos payre 7AO0s, is in fact an insensible infinite.
8. That number and extension do not exist apart from actual con- crete things has already been argued in A. ggt" 9 ff.
18. GAG advvatoy 7d évTedeXeEla Sv GaeLpoy, Sc. apepioToV Kal GdLaipe- TOV Elva.
20. cipy ran, Os
QI. Tov dépa. The allusion is to Anaximenes and to Diogenes of Apollonia, 716 dptvoy alludes to the Pythagoreans (cf. 203% Io).
25-26. dpiWyntov yap... dprOydv. ‘For number, or that which has number, is numerable and therefore not infinite.
26. duorkds, i.e. taking account of the physical nature of the infinite body, viz. the question whether it is simple or compound, as opposed to the purely abstract consideration in Il. 22-26.
337 Commentary
28. ci memépaytar TH TWANPEL Ta oToLXeta. This has been proved in Phys. i. 6. :
33. mwdvTn €otat amerpoy, sc..and therefore there can be no second body alongside of it.
34. For od8€ év 8€ cf. De An. 427? 11, ZL. NV. 1120731.
35. Gs éyouct twes. The reference is to Anaximander.
37—1067°1. od dalverar .. . odpata, ‘we do not see things resolved into anything beyond, more ultimate than, the four ele- ments’.