8. maca Suvapis dpa tis dvtipdceds éotw. It is the peculiarity of rational faculties to be able to produce either of two confraries (10465); a knowledge of medicine enables a man either to cure or to kill. But all potentialities are potentialities for either of two contradictory results. ‘That which can under certain circumstances become or do something can also, if those circumstances be absent, not become or do it.
Q-II. Td pev... od0evi is merely preparatory; 16 Suvatdv .. . évep- yetv is the emphatic clause.
11. On the difference between 8uvardy and évdexduevov cf. 1047? 26 n.
14. $9aptév, dwAds 7 TodTo adtd & AdyeTar evBéxeoOar ph eivar. ‘ Perishable either in the unqualified sense or in that precise respect in which it is said to be capable of not being.’ A thing is ‘ perishable’ if it can lose its essence ; ‘locally perishable’ if it can change its place; ‘quantitatively perishable’ if it can change its size; ‘ qualitatively perishable’ if it can change its quality.
IQ. Kaito tadta mpdta is the minor premise of the syllogism:
Things existing of necessity do not exist potentially.
The primary things are the things that exist of necessity.
(Therefore the primary things do not exist potentially.
Therefore actuality is prior to potentiality.)
21. obk €or. ... mot. Ie. it is necessarily moved, but while moving from A to B it may be capable of moving from B to C.
23. & hoBodvrar ot wept pucews. Alexander says the reference is to Empedocles, and this is confirmed by De Caelo 284% 24 otre di) Totrov Tov tTpdrov troAnrTéov, ote Sia Tiv Sivnow OdtToves TvyxavovTa (Tov ovpavov) hopas Tis oikeias poris ere cdlecbar tocodrov xpdvov, Kabdzrep *Byredoxdyjs pyoiv. Aristotle compares Empedocles’ view to the traditional belief in the necessity of an Atlas to hold up the heavens. There is nothing about this in the remaining fragments of Empe- docles.
30. KaQ aird...xivqow. It is doubtful whether this refers to the natural movement of fire upwards, and of earth downwards, or to the
ie ©
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constant tendency of the elements to change into one another, by virtue of which Aristotle says (De Gen. et Corr. 337% 1-7) they imitate the circular movement of the heavenly bodies.
30-33. Aristotle repeats here the general statement (cf. 1. 8) that all potentialities are potentialities for either of two contradictories. He then subdivides. (1) Things which in virtue of a Aéyos can act in one way can also act in the contrary way (2 68/ = ‘to move not thus’, not ‘not to move thus’). (2) Irrational potentialities are potentiali- ties for either of two contradictories according as they are present or not.
Thus under (2) Aristotle is not referring to the sense explained above (ll. 8-12) in which potentialities are potentialities for either of two contradictories according as certain conditions are present or not (Alexander interprets it so, but the Greek will not bear this interpre- tation), but is saying that they are potentialities for either of two con- tradictory results according as they themselves are present or not. This at first sight seems pointless. But in PAys. 251231 Aristotle says that there is something in physical things akin to the con- trary actualizations of a ‘rational power’, 7d yap wWuxpdv Oeppatver otpapév mws kat dmeAOov. That which is cold is capable of be- coming hot, and shen of heating other things. This seems to be the meaning here.
30. ai dé Gddar Suvdpers, because Aristotle has been speaking of things which are in some respect tainted with dvvapus, e. g.in respect of their position in space (cf. Il. 17, 18), though in other respects existing in actuality.
gl. é§ dv Sidpiotar. The statement is a general one about ai aAdau dvvdpes aca, so that the reference is probably not to the distinction of rational from irrational powers as being rév évavtiwy ai avrat (1046” 4, 104848), but to the discussion of potentialities in ro50? 8-12.
35. ot év Tots Adyots, ‘the people who occupy themselves with verbal discussions’. Cf. A, 987» 31 n.
36—1051° 2. atts émorypy is the faculty of knowledge itself, apart from particular manifestations, and as such inferior to the activity of knowledge.
I05I° 3. Kal Suvdpews Kal mdons dpxfs petaBAntiis, cf. 1049 6.
Miscellaneous remarks about potency and actuality (ch. 9).
105124. A good actuality is better than the good potency. For capacity for one thing is always capacity for the opposite, and is so at the same time (though the opposites cannot exist at the same time), and therefore is both good and bad, or neither.
15. Similarly a bad actuality is worse than the potency, and posterior to it, and therefore evil cannot be an actual substance existing apart from bad things. Therefore among eternal things there is nothing evil,
21, Geometrical relations are discovered by actualization, i.e. by dividing the given figures by lines that before existed potentially. Cf. the proof that the angles of a triangle = two right angles, or that the angle in a semicircle is a right angle. What exists potentially is dis- covered by being actualized. The reason is that the geometer’s thinking is an actuality. Thus potency comes from actuality (and therefore the knowledge comes by action), though the actuality is later in genesis than its own potency.
7. Bz.’s conjecture in the Odservaizones, kat rs vooelv (sc. Sivacbax Aeyopevov), is obviously better than his actual reading, cat vooeiv.
II, 12. ‘But contraries cannot belong to a thing at the same time, and (therefore) the actualizations also cannot belong to it at the same time.’ | 13-15. dot dvdyxn ...Bedtiwy. The reasoning is not very clearly expressed but seems to be as follows: ‘To be capable of A is to be also capable of its contrary B. Therefore, while what is good (in the sphere of a particular dvvapus and the corresponding évépyevor) must be one of the contrary évépyeo, the dvvayis must be said either to be both good and bad or to be neither ; therefore the good actuality must be better than the dvvayis’. rtovtwv Odrepov <ivar téyaGov is in sense sub- ordinate ; 70 dvvacGau xrd. is what follows from the protasis.
Bz. complains that Aristotle suggests that of any two contraries one must be good, and thus introduces good and evil into regions where they are inappropriate. But Aristotle does not make this mistake. He takes only the dvvames which would be called good (I. 4), and shows that they are really neutral, and are called good only because we forget the bad actualizations of which they are capable; and that
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therefore the good actualization is better than the potentiality. His only mistake is in calling one thing better than another when the other is strictly speaking not good at all but neutral.
The reasoning implied in Jl. 17-19 seems to be as follows:
What exists apart from its, particular manifestations must exist actually.
Actuality is prior in nature to potentiality.
Potentiality is prior to the bad.
Therefore what exists apart from its particular manifestations is prior to the bad.
Therefore the bad does not exist apart from its particular manifesta- tions.
From the fact that the bad is posterior to potentiality it also follows (Aristotle adds in ll. 19-21) that there is nothing bad among the original and eternal entities. If we placed a full stop after zpaypara anda colon after duvdpews we might suppose ovx dpa ... duepOappévov to be a repetition in other words of djAov. . . mpaéypara (which Bz. apparently takes it to be); but this hardly does justice to ovdé.
The reasoning in ll. 17-19 involves, as Bz. shows, a fallacy of equi- vocation, For actuality is prior to potentiality, according to Aristotle’s view, in realzty or substantiality (this was what was argued in 10502 4— 1051 3), while potentiality is prior to the bad in worth (this was what was argued in 1051" 15-17). When the bad is shown to be posterior to the potentiality (in worth), it is treated as one of the contrary actualizations of the potentiality. But then it must be prior to the potentiality in reality, according to the argument of 1050% 4 —10514 3.
21-33. In the attempt to interpret this difficult passage I owe much to the late Professor Cook Wilson, who discussed it with me. The passage is evidently out of place. It belongs in principle to the argument for the temporal priority of actuality to potentiality (1049 17—1050% 3).
22. Siaypdppara is taken by Bz. to mean ‘geometrical proofs’, and the word sometimes occurs in this sense, cf. B. 998% 25 n. But ec & hv Siypnpéva, pavepa av jv' viv & evyrdpyer duvdpe seems to show that the word has its ordinary meaning of ‘geometrical construc- tions’, (To make the construction intelligently, however, is to see the proof, and Aristotle at once passes to this (87Aov Sa ti, 1, 26).) What he says, then, is that ‘ geometrical constructions are dis-
covered by an activity ; for we find them by dividing’. The activity is later (I. 30) described as vénois, and this may seem inconsistent with the description of it as division. But it is not really so, for division here does not mean the drawing of lines with chalk or pen but the apprehension that the geometrical figures with which we are dealing are divisible in certain ways. The geometer is dealing with figures which are voyra (Z. 1036% 3), and his essential activity is véyous, not the construction of anything aicOyrév; the latter is merely an aid to the former. 24-26. The proposition is Euc. i. 32. The given figure is
We have only to ‘ divide’ (in this case to divide the space surrounding the triangle) in order to see the reason why the interior angles of the triangle must be equal to two right angles.
A Je
Produce BC to D and draw CZ upwards (dvjjxro) parallel to BA, Then the angle CAB = ACE and ABC = ECD (Euc. i. 29).
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Therefore BCA+CAB+ABC = BCA+ACE+ECD,
which = BCA + ACD,
which = two right angles (i. 13).
Therefore the interior angles of the triangle two right angles.
Of the two supplementary-lines-which had to be drawn, Aristotle mentions only CZ. In Euclid this theorem is the second part of a proposition of which the first part is that ‘in every triangle, if one of the sides be produced, the external angle is equal to the two interior and opposite angles’, so that CD is supposed to be already drawn ; and Aristotle probably knew the proposition in its Euclidean form.
25, et oly dvikto } mapa thy wAeupdv (sc. ypappn). The use of avayew for the drawing of a line is not recognized in L. and S., and Bz. gives only one other instance of it, viz. AZefeor. 376% 1. Aristotle seems not to be using technical language (cf. ll. 27-29 n.). He uses dvdyew in the natural sense of ‘ draw upwards’ ; the parallel line must be drawn on the same side of the base as the triangle.
27-29. The proposition is Euc. iii. 31. The construction contem- plated seems to be as follows:
BAC is an angle in a semicircle. From the centre D draw DL perpendicular to BC ( ék pécov éeriortabeioa dp6y) and meeting the semicircle at Z. Join BL, CL.
Then DH = DB. Therefore the angle DEB = DBE,
Di = DC. Pheretore DEC = DCL.
Therefore DEB4+DEC=DBE+ DCE, i.e. BEC = CBE+ BCE.
But BLC+ CBE + BCE = two right angles (i. 32)
Therefore BEC is a right angle.
But BAC = BEC (iii. 21).
Therefore BAC is a right angle.
29-33. The interpretation of this passage is complicated by two
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(2) The manuscript reading airiov 8& ori vonow 4 évépyera is diffi- cult. ‘The potentially existing constructions are discovered by being brought into actuality; the reason is that the actuality is an act of thought.’ This identifies the actuality of the figure with the actuality of thought, while ll. 32, 33 seem to distinguish them. Aristotle has committed himself to the view that vdénous actualizes the figures, but it is doubtful whether he would identify the actuality of the figures with the vonots. True, ro voovpevov and 6 voids are identical in the case of dca ph tAnv exer (A. 107573, cf. De An. 43073). But mathematical objects do contain vA, even if it be vont vAyn (Z. 103611, » 35, K. 105915). They are not the pure forms which alone Aristotle identifies with the apprehension of them.