1 Even as Lovejoy's ideas have stimulated a great amount of subsequent studies and inquiries in the history of ideas, Lovejoy's general approach to the problem, as well as many of his original findings, have come under heavy criticism. For materials and studies collected under a representative title see Knuuttila (ed.) 1981.

2 For Lovejoy's original formulations, cf. Lovejoy 1936, 52-55. For an adequate assessment of

Lovejoy's approach and the shortcomings inherent in the notion of a "unit idea", cf. J.Hintikka, "Gaps in the Great Chain of Being", in Knuuttila (ed.) 1981, 1-17.

3 Excellent accounts of the infinite power argument's history are offered in Davidson 1987 (a résumé with references on pp. 409-411) and Sorabji 1988 (ch. 15, 249-285, and cf. also ch. 13).

4 For the Arabic original see Averroes, Tafslr mâ d 3Î*tabt d»B0ok Lâm, c. 41; 3:1628.10—

1638.8, Bouyges. (In this instance, Charles Genequand's English translation cannot be recommended, because of inconsistencies in the translation of key terms; those wishing to consult the Latin will find the passage in Aristotelis Opera cum Averrois Cordubensis in eius Commentariis [henceforth abbr. AOACC] 8:324B-325M.) Averroes discusses the infinite power problem in so many of his works that it would be impractical to try and cover all the ground here. I will content myself with mentioning a few vital points in connection with the Metaphysics commentary text. For other original passages see the Long Commentary on the Physics 8, c. 79 (in AOACC 4:425H-427I); the Long Commentary on De Caelo, 2, c. 71 (AOACC 5:145H-146H) ; the Middle Commentary on De Caelo '

(Taikhts m-samâ' Wd-al-'àlam, 178.10 183.17. al-'Àlawîand also AOACC5:293G-

295B); De substantia orbis, chs. 1, 3, 5, 6 (in Hyman's Hebrew-English edition of 1986 and in AOACC 9) & 7 (only in AOACC 9:13H-14M, and in a Hebrew manuscript, for which see Davidson 1987, 329-331); Averroes' Questions in Physics, q. 7 (27-28, Goldstein) & 9 (3336, Goldstein). Sorabji (1988, 265) and Davidson (1987, 322) also mention a passage in the Middle Commentary on the Metaphysics which I have not had the opportunity to consult.

5 Tafsîr 3:1627.10-12, Bouyges (cf. Aristotle's summary of the proof in Metaphysics 1071b6-

12, continued at 1073a3-12). In character, Averroes presents the argument as a "syllogism" (1627.10, Bouyges), even pointing out that it is "of the second figure" (1627.12, Bouyges). It is important to note that this is Averroes' interpretation. If one examines closely Aristotle's own argument in Physics 8, ch. 10, it quickly becomes apparent that something quite different may in fact be going on from what most of the interpretative tradition would have us believe. As this is a study of that interpretative history and not of Aristotle, I shall not pursue the matter further here; but cf. Ross' commentary in Physics; 452-455, Ross.

6 Tafsîr 3:1628.10-15, Bouyges. The intended length of the quotation is debatable, as

Philoponus never puts the latter point in exactly these words in his preserved writings. I have chosen to end the quotation where I have because the text then continues with the juxtapository: "and we say." (1629.1, Bouyges; added emphasis). Part of the point made in this chapter is that Philoponus utilized the conceptual framework of De caelo 1, ch.12 to its fullest, even if he did not explicitly allude to the work itself.

7 See the still excellent reconstruction by H.A. Wolfson in Wolfson 1976, 374-382 (cf. also

Davidson 1987, 89-93; Sorabji 1988, 254-257).

8 In the subsequent discussion it may be assumed in orthodox Aristotelian fashion that whenever perishability (end or possibility of ending) is mentioned generability (creation or possibility of beginning) follows, and vice versa. Aristotle took perishability and generability, and correspondingly imperishability and ungenerability, to be mutually implicative: the point forms the main focus of De Caelo 1, ch.12 and was widely accepted in both its modal and non-modal (factitive) forms. Proclus (412-485), referring to the Phaedrus (245D) and the Republic (546A), made the influential claim that already Plato had held the same opinion (In Tim 1:295.27-296.6, Diehl): still, on the question of the correct interpretation of Plato's cosmology opinion remained divided. (Ostensibly the Timaeus describes a generated, perishable, but never-perishing universe: but cf. e.g. Proclus' remarks in favor of an allegorical interpretation, op. cit. 1:286.20-21, 296.6-12, Diehl.)

9 For Philoponus' criticism of the eternalist arguments in Physics 8 see C. Wildberg's reconstruction, Philoponus 1987. Simplicius reprimands Philoponus for assigning these and other inconsistencies to Aristotelian doctrine: but of course, the post-529 Philoponus is interested only in preserving and presenting those parts of Aristotle he finds congenial to his own evolving creationist philosophical worldview.

10 Aristotle, De caelo 281b20-23; English translation based on J.L.Stocks's (1:466-467, Barnes's ed.).

11 De caelo 281b23-25 (the last clause reading haplos in the original Greek). The approach, which is to verify the hypothetical possibility of the world's destruction by way of searching for any incongruities arising from its assumption, markedly resembles Aristotle's famous "test" for possibility in the Prior Analytics (32a18-20), as noted by Averroes in De substantia orbis 6 (Hebrew 11. 20-23/English pp. 125-126, Hyman). Its application here seems to indicate that this compossibility is tested only across a single world history, without a notion of possibilities as synchronous alternatives.

12 Of the various attempts at articulating what exactly is wrong with Aristotle's argument see Van Rijen 1989, 73-87; cf. also Knuuttila 1993, 9-10.

13 The notion is clearly presupposed in Aristotle's argument from necessary coincidence, De Caelo 281bl8-20: "But if a thing has for an infinite time more than one capacity, another time is impossible and the times must coincide." (Stocks's translation, my italics.) On the significance of the infinity of time in the argumentation of De caelo see Waterlow 1982, 6578.

14 Physics 203b30; cf. also De generatione et corruptione 338al-3; Metaphysics 1050b6-34. Aristotle seems to have held that the temporal-frequency model also applies in the case of generic possibilities: if something is genuinely possible for a given species, then it will be instantiated at least once. For an overview of the debate regarding Aristotle's adherence to a statistical modal theory (with extensive bibliographical references) see Knuuttila 1993, 1-18.

15 On Alexander of Aphrodisias' views on the modal status of the heavens see Staples 1983a and b; on Aquinas and Buridan and the same De caelo passage, Williams 1965. Both articles point to the complexity of the question about the role of temporalized Plenitude in ancient and medieval philosophy: even if many thinkers took the principle to apply to Aristotle's thought in some way, few were willing to interpret the idea as literally as Averroes did and most attempted to qualify it in some way. For the history of the idea in the Latin West see Knuuttila 1993, passim.

16 Some have taken Philoponus to argue backwards here, from perishability to finite capacity (cf. e.g. Davidson 1987, 93), but I do not believe this to be the case. What Philoponus does is rather refer to his more general argument from finite power.

17 Philoponus, quoted by Simplicius, In Phys. 1333.24-30, Diels (English translation taken from 121, Wildberg).

18 Christian Wildberg (in Simplicius 1991; 121, n. 43 Wildberg) expresses his dismay at how only a possibility of perishing seems to be argued for in the passage: but this of course is enough if and only if something like temporal Plenitude is already presupposed. Simplicius, meanwhile, quite intentionally plays down the point made in the argument: he accuses Philoponus of believing that the limits of his imagination are the limits of possibility. (In

Phys. 1334.26-39, Diels.) This, too, misses the point, because for Philoponus the envisioned logos of destruction is no fanciful exercise in imagination, but an objective feature of physical reality.

19 The last point curiously highlights the parallels between Philoponus' and Aristotle's argumentation. Aristotle's argument in De caelo 1, ch. 12 was directed squarely against the Timaeus account of a generated and perishable but never-perishing world. So Aristotle maintains that an eternal world cannot be destructible even in potentia, while Philoponus claims that a destructible world cannot ever be eternal in actu; and both continue by extrapolating from end to beginning. Both utilize a statistical interpretation of Plenitude to reach their conclusions, and both foreclose any divine overriding of the naturally appointed and mutually exclusive categories of generable-destructible and ungenerable-indestructible.

20 R.M.Dancy offers an interesting piece of "fuzzy logic" for this on the lines of "nature doing nothing in vain": the explanation involves the utter super-fluousness of both such a potentiality and the eternal hindering factors. Cf. R.M.Dancy, "Aristotle and the Priority of Actuality", in Knuuttila (ed.) 1981, 79-80; and for an almost exact parallel, Averroes, Long Commentary on the Physics 2, c. 48; AOACC 4:66M-67A.

21 Aristotle's proof from motion was in late Antiquity in subsequent stages moulded into a proof from the varying levels of existential power on a Neoplatonist ontological model. Proclus (cf. also below) argued that Aristotle's infinite power argument should be extended to cover the fact of the heavenly spheres' very existence; while Proclus' pupil Ammonius, who was also teacher to Philoponus, claimed that Aristotle's argument was actually meant in this way. For an overview of the history, cf. Davidson 1987, 281-282; Sorabji 1988, 249254.

22 There runs a curious parallel between Proclus' (in late Antiquity) and Waterlow's and Van Rijen's (in our time) analyses of the role of matter in Aristotle's modal metaphysics, one that seems to me to merit further investigation.

23 Averroes' most complete exposition on the subject is the first chapter of De substantia orbis, which serves as an almost point-by-point refutation of Philoponus' first five books against Aristotle. (Averroes ostensibly targets Avicenna rather than Philoponus: but cp. with Philoponus 1987, passim.) Cf. also e.g. Tahafut al-tahafut 4; 270-271, Bouyges.

24 See Aristotle, Metaphysics 1069b24-27; and for Averroes' comments, Tafsir, book Lam, c. 10; 3:1447, Bouyges. The point is argued already in Aristotle's early anti-Platonic De caelo 1, chs. 2-4, and is enough to make short shrift of the Platonist scare of the heavens ever dissolving (which was purportedly due to their inherent instability as material and composite entities).

25 Cf. Metaphysics 12, chs. 6-7; also Physics 8, chs. 8-9 and De Caelo 1, ch. 4. On one interpretation the heavenly motion, because it is at root an intellectual activity, is of the energeia rather than the kinesis type; that is, it has no outside goal but has perfection in its own execution. Cf. Metaphysics 1048bl8-35 and the tenth book of the Nicomachean Ethics (esp. 1073a29-33, 1074b9-13, 1177a20-27) for the roots of the distinction in Aristotle; and cf. Kogan 1985, 50-51, 211-212, 232-233 for Averroes' take on this. (Cf. Kogan 1985, 277, n. 64 for references to the literature on Aristotle.)

26 See e.g. Metaphysics 1046a19-26. Given the presence of both complementary potencies, and the absence of any relevant external hindrances, the change takes place out of necessity: cf. Metaphysics 1048a5-7, 1048a13-21, 1048b37-1049a14.

27 If it can be said that the heavens' motion is essential to them (even more so, to the sublunar world), then perhaps celestial rest can amount to the same as celestial dissolution. Cf. Averroes, De substantia orbis 4 (ll. 34-38 Hebrew/ p.117 English, Hyman; Latin in AOACC 9:10I); also Tahafut al-tahafut 1 (46-47, Bouyges), 3 (172, Bouyges).

28 On the breakthrough of the "kinetical" explanation of Aristotle's infinite power argument cf. the now indispensable Lettinck 1994, 661-664; cf. also Sorabji 1988, 281-285. Averroes in one treatise asserts that "rest is only privation and not a potentiality": depriving the heavens of rest does not then offset any genuine potentiality and represents no breach with nature. Cf. De substantia orbis 5 (l 21 Hebrew/p. 122 English, Hyman; Latin in AOACC 9:11B). The solution is as far as I know unique to the passage; it could be another, and possibly a complementary way around the difficulty posed by the heavens' possibility of resting.

29 Cf. Averroes, Long Commentary on the Physics 8, c. 79 (AOACC 4:427D-G); Long Commentary on De caelo 2, c. 71 (AOACC 5:146C-F); Questions in Physics 7 (27-28, Goldstein), 9 (35, Goldstein); De substantia orbis 3 (ll. 63-94 Hebrew/107-110 English, Hyman; Latin in AOACC 9:9F-10A). The Physics commentary professes to return to the words of Aristotle on the question (AOACC 4:427G), and this seems indeed to be correct.

30 The reason repeatedly cited for the impossibility of this is that such a potentiality might fail, with the apparent gap in Aristotle's reasoning again implying one conclusion: might in this context equals will, sooner or later. The notion of temporal Plenitude is again discernible.

31 See the excellent "Aristotle and the Priority of Actuality", in Knuuttila (ed.) 1981, 74-80.

32 The necessitarian view, however inadmissible from a Theist viewpoint, would be wholly in line with the general tenor of Aristotle's inquiries into the matter. What Aristotle wanted to do was preclude any possibility of a cataclysm ever occurring. The lack of a beginning for the world was in this context more a happy side-effect (witness e.g. the structure of De caelo 1, chs. 9-12), though in the Physics admittedly the eternity of motion is considered equally both from the side of its being necessary a parte ante and a parte post. At any rate, postulating any contingency in the world's perpetual superstructure would have been far from Aristotle's mind. On the statistical interpretation in Averroes' modal theory see the brief remarks in Knuuttila 1977, 79-87 (a proper study on the subject remains to be done).

33 For statistical explanations of the modal terms in Averroes see e.g. the short logical treatise edited in Dunlop 1962 (translated into English in Rescher 1963, 91-105), and The Long Commentary on De caelo 1, c. 123 (AOACC 5:84A-E). The latter is significant for our purposes for its context alone: Aristotle's reasoning in De caelo 1, ch. 12 is explained by aid of a diagram, in which "being eternal" equals "being necessary", while the contradictory "that for which it is possible not to be" equals "not eternal".

34 I tend to concur with Helen Tunik Goldstein in that this was not necessarily due to ignorance. Averroes does not strictly speaking aim at reproducing Avicenna's thought, as many have seen him to do and fail: "what Averroes does do is to continue to use terms, such as possibility and necessity, in the sense he thought was truly Aristotelian, rather than in the sense Avicenna intended" (in Goldstein's notes to Averroes' Questions in Physics; 150, Goldstein).

35 On the basis of the Metaphysics commentary text it seems that Averroes may have held hopes for the Aristotelian definition of kinesis as the actuality of a potentiality qua potentiality to be a way out of the problem of determinism—as Aristotle himself apparently did. (On the latter point, and on why the solution would not ultimately have worked, see Hintikka et al. 1977, 59-77.) Cf. also Tahafut al-tahäfut 3 (172, Bouyges), where the world is said to be describable as created on account of its mobile nature.

36 Several presentations of Avicenna's modal metaphysics have been made recently available: see e.g. Goodman 1992, 49-122, whose notes offer an overview to the literature. For a study of Avicenna's remarks on modal logic, cf. Bäck 1992.

37 Avicenna, commenting on Metaphysics, Book Läm, in Badawi 1947, 26.8-12. Sorabji (1988, 260-263) is to my knowledge the first to discuss this passage in the context of infinite power.

38 For Plotinus see e.g. the Enneads, II.3.18, II.9.3, II.9.6, II.9.8, II.9.17, III.2.14-7, III.8.8, VI.7.12; for the origins of the idea of Plenitude in Plato, Timaeus 29e-30a, 39e, 41b-c.

39 See Proclus, In Tim. 1:437.11-24; 1:438.13-15; 1:443.5-8; 3:90.15-27; 3:93.5-14; 3:175.15-176.10; 3:224.17-22, Diehl (Plotinus, Enneads III.7.11 partially foreshadows the idea on "Proclus on Plenitude" cf. further Kukkonen 2000).

40 See Siorvanes 1996, 175-179.

41 It is noteworthy (and indicative of the continued pressures exerted by the naturalistic model) that Proclus feels it necessary to point out that the heavens are not potentially perishable (dynamei phthartori), all appearances to the contrary, nor are they adapted for destruction (epitedeios eis phthoran). What is meant by their having limited potency is only that they are of themselves incapable of forever sustaining their existence (In Tim. 1:293.14-294.8, Diehl). Proclus' assurances would seem superfluous, were there not still a place in his scheme for the supposition that every potentiality is sometime realized: so even as he takes steps to counter just that kind of approach, Proclus in fact confirms the continued tenacity of a naturalist interpretation of the potencies of bodies.

42 On the interplay of dynamis and energeia in Plotinus' modal metaphysics see Buchner 1970. Peter Adamson in this volume has adduced fascinating examples about potencies higher than acts garnering a mention in the Arabic Plotinian tradition; in the light of what has been said, it is quite understandable that these ideas were apt to produce confusion, insofar as they were culled from something which was ostensibly the "Theology of Aristotle".

43 For the roots of the idea see Timaeus 29e-30a.

44 Simplicius, In AristotelisDe caelo commentaria (361.10-15, Heiberg): English translation taken from Sorabji 1988, 259.

45 As detailed by Davidson 1987, 311-335.


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