1 An. Post. 2.12.98b1-2, in Aristotelis Organon Graece, ed. Waitz, T. (Leipzig: Hahn 1846)Google Scholar

2 95a10-15

3 Phys. 7.1.242a57-62, in Aristotelis Physica, ed. Ross, W.D. (Oxford: Clarendon Press 1950)Google Scholar

4 See, for example, An. Post. 1.6 and 2.16-17.

5 Alexander of Aphrodisias, Quaestio 3.5 in Supplementum Aristotelicum, 2:2, ed. Bruns, I. (Berlin: G. Reimer 1892),Google Scholar 88.24-6, 88.28-9

6 De Gen. et. Cor. 2.11.337b14-25. However, in Metaphysics 6.3 Aristotle discusses what appears to be a tergo necessitation in such a way that there is no evident sign of this ‘peculiar’ Peripatetic doctrine. Meta. 6.3 has come to be considered a locus classicus of Aristotle on the ‘determinism’ issue because his approach there seems a particularly modem one.

7 See Alexander's Quaestio 2.22 in Sup. Arist., 2:2, 71-2; Quaestio 3.5, ibid., 87-9. For a recent helpful study of these passages, see R. W. Sharples,’ “If What is Earlier, then of Necessity What is Later“?: Some Ancient Discussions of Aristotle, De Generatione et Corruptione 2.11,’ University of London Institute of Classical Studies Bulletin (BICS), 26 (1979) 27-44.

8 The use of ‘coeval’ to translate ‘homogonon’ is due to Barnes, J., Aristotle's Posterior Analytics (Oxford: Clarendon Press 1975), 68.Google Scholar

9 For extensive accounts of the Greek perfect aspect, see Wackernagel, J., ‘Studien zum griechischen Perfectum,’ Programm zur akademischen Preisverteilung (Goettingen: W.F. Kaestner 1904);Google ScholarChantraine, P., Histoire du parfait grec (Paris: H. Champion 1927);Google ScholarMcKay, K. L., The Use of the Ancient Greek Perfect Down to the Second Century A.D.; BICS, 12 (1965) 1–21.Google Scholar The example in the text comes from Plato's Crito, 46a4-5, discussed in White, M.J., 'Aristotle's Concept of Thēoria and the Energeia-Kinēsis Distinction,’ Journal of the History of Philosophy, 18 (1980) 255-6.Google Scholar

10 In at least two places (De Gen. et Cor. 2.11.337b6-10 and De Divinatione per Somnum 2.463b28-33), Aristotle does seem to treat the ‘future’ formed by the verb ‘mellein’ as an essentially present form with ‘some import as to the future.' Of course, originally, it simply connoted a present ‘intention’ (which may or may not come to fruition). But in the latter passage referred to above, Aristotle seems to understand it as connoting any ‘beginning’ of something which may later come to fruition. In both passages, however, Aristotle stresses that, although such forms connote ‘something present’ which is ‘directed toward the future,’ we cannot infer anything about the future from what now ‘mellei the case.’ So, the most we can infer from the truth of a proposition formed with this verb is the ‘tendency’ of the future to be such-and-such. The ‘regular’ Greek future Aristotle, in places at least, seems to interpret as implying that the event/state of affairs it connotes is necessary, relative to the present. The fact that Aristotle regards such a tergo necessitation with suspicion seems to be related to the constraints he may want to put on the circumstances in which a use of the future tense results in a true proposition. See Michael J. White. 'Fatalism and Causal Determinism: An Aristotelian Essay,’ Philosophical Quarterly 31 (1981) 231-41; ‘Necessity and Unactualized Possibilities in Aristotle,' Philosophical Studies 38 (1980) 287-98.

11 95b32-35

12 Barnes, 224

13 An exception, for Aristotle, seems to be those cases (to be further discussed) in which the ‘future’ event/state of affairs that is inferred is itself haplōs necessary. Cf. An. Post. 2.12.95b38-96a2. Here Aristotle has in mind the following sort of cyclical configuration: B is a necessary condition of A; Cis a necessary condition of B; A is a necessary condition of C. As R. Sharples remarks, ‘according to the most plausible interpretation, [Aristotle] mentions only the a fronte necessity at each stage of the cycle...‘('“If What is Earlier, …,’ 34). So, if we suppose that at least one event/state of affairs, say A, is at some time instantiated, we produce an infinite series of cycles of A-type events/states, preceded by B-type events/states, preceded by those of type C, preceded by those of type A. Aristotle's doctrine that such infinite cycles cannot extend in only one temporal direction apparently then yields the ‘bonus' consequence that, in this special circumstance, the a tergo inference from a present A to an ‘upcoming’ C is possible. See note 28.

14 Hintikka, J., Time and Necessity: Studies in Aristotle's Theory of Modality (Oxford: Clarendon Press 1973), 183Google Scholar

15 283b13-14

16 It seems likely that there is at least a psychological connection between this asymmetrical conception of time and Aristotle's (and our) ‘homely’ conception of necessary conditions as sometimes a fronte but virtually never a tergo.

17 32b10-13.

18 The Cement of the Universe: A Study of Causation (Oxford: Clarendon Press 1980), Ch. 7. See especially Mackie's discussion of ‘fixity’ and ‘unfixity,’ 179ff. 'If events have preceding sufficient causes in the strong, counterfactual, sense then they are fixed as soon as these causes have occurred’ (181). But, an event/state of affairs also apparently becomes ‘fixed’ by its temporal instantiation.

19 Hintikka, 103 et passim

20 Actually, ‘p’ need not denote a unique event/state of affairs: a condition sufficient for making the two modal wffs true is that, if there is a temporally first instantiation of ‘q’ that instantiation not be contemporaneous with or preceded by an instantiation of ‘p'.

21 Arthur Prior encounters this sort of difficulty in his attempt to represent a premise of causal a tergo necessitation in terms of a modal-tense logic postulate in a discussion of ancient ‘Master-like’ arguments. The strategy of such arguments is to ‘transmit’ the necessity of the antecedent of a necessary conditional to the consequent of the conditional. A premise of the form LCPFpFp, e.g., ‘Necessarily, if God knew that it would be the case, then it will be the case,’ ‘is false, i.e. as a law, simply because by the time of utterance what was going to happen, or what God knew would happen, may have already happened, and it may not be going to happen again.’ Prior resolves the problem by moving to a ‘metric tense-logic’ formulation of the argument, which involves a sort of quantification over temporal intervals. See Prior, Past, Present and Future (Oxford: Clarendon Press 1967), 113-21.

22 Temporal density posits the existence of a distinct temporal ‘point’ or ‘instant' between any two distinct points/instants. von Wright's discussion of causation in terms of modal-tense logic assumes, as he notes, that time is discrete. He then can appeal to a dual pair of operators: ‘perhaps it is the case at the next time’ and ‘certainly it is the case at the next time.’ See Georg Henrik von Wright, Causality and Determinism (New York and London: Columbia University Press 1974), 13-35.

23 For Aristotle on temporal density, see Physics 6.1. Aristotle's view seems to be that time is continuous as well as dense. That is, if a temporal interval is partitioned into two subintervals such that each point in the first temporally precedes all points in the second, there must be either a 1ast’ point in the first or an initial point in the second, but not both. Cf. Sorabji, Richard, ‘Aristotle on the Instant of Change,’ Aristotelian Society Supplementary Volume, 50 (1976) 69–89.CrossRefGoogle Scholar

24 Russell, Bertrand, ‘On the Notion of a Cause,’ reprinted in his Mysticism and Logic (New York: Barnes and Noble 1957), 181.Google Scholar Russell's argument has been criticized by Mackie, 143-7. For another discussion of the topic, not dissimilar to Russell's, see Dummett, M.A.E., ‘Can an Effect Precede its Cause?,’ in his Truth and Other Enigmas (Cambridge, MA: Harvard University Press 1978), 32Q-1.Google Scholar

25 For Russell, the events/states of affairs that are the ‘terms’ of the causal relation must be ‘universals’ of some sort: ‘an “event”, in the statement of the law, is obviously intended to be something that is likely to recur since otherwise the law becomes trivial’ (Russell, 180). Russell evidently implicitly identifies ‘causal relation’ with ‘law-exemplifying relation’ and comes to the same conclusion with respect to the former's ‘repeatability.’ von Wright points out another problem posed by the assumption of a temporal gap between cause and effect for a Laplacean form of determinism: ‘then it is not enough to know just one pair of successive states (and the laws) in order to be able to predict all future changes. For some of the changes which take place may be the effects of changes which were anterior to the given pair of successive states’ (von Wright, 118-19).

26 See note 21.

27 Sup. Arist. 2:2, 88.12-15. The translation is that of Sharples, ‘“If What is Earlier, …,’ 30.

28 Part of the problem is that Aristotle does not have at his disposal the various sophisticated set-theoretic concepts that figure in the contemporary, Cantorian analysis of infinity, e.g., the distinction between being properly contained or a proper subset of and having a smaller cardinality. For a detailed, enlightening study of De Caelo 1.12, including the role that Aristotle's interpretation of ‘for an infinite time’ plays in that chapter, see Waterlow, Sarah, Passage and Possibility: A Study of Aristotle's Modal Concepts (Oxford: Oxford University Press 1982),CrossRefGoogle Scholar Ch. IV, particularly 65ff.

29 See, for example, De Caelo 1.12.283a7-10: ‘Everything is capable of acting or undergoing, being or not being, either for an infinite (apeiron) or some bounded extent of time - and for an infinite time insofar as “infinite time” is defined in this way: as that of which there is no greater. So the “infinite in one direction” (to pē apeiron) is neither infinite or bounded.'

30 338a3-4

31 Insofar as Aristotle himself argues for this entailment, he seems to do so in An. Post. 2.12 in terms of his ‘inferability’ conception of conditional necessity or necessitation. We can infer in the a tergo direction only if the future ‘consequent' is necessary for the present ‘antecedent.’ But such a situation occurs only where we find a circular configuration of necessary conditions. See note 13.

32 See Long, A.A., ‘Freedom and Determinism in the Stoic Theory of Action,’ in Problems in Stoicism, ed. Long, A.A. (London: Athlone Press 1971),Google Scholar especially 170-1.

33 Alexander, De fato 8, Sup. Arist. 2:2, 173.16-19

34 De fato 22, 192.22-4

35 There is a species of ‘anti-compatibilist’ argument, quite common in postAristotelian philosophy up through the Medieval period, according to which the necessity of the past will be transmitted to ‘all the future’ by means of ‘conditional necessity’ linking the past to the future (if, that is, ‘all the future’ can be thus 1inked’ to ‘what has already happened’). It is apparent that this is the essential structure of the the ‘Master’ argument of the Megarian logician Diodorus Cronus. And versions of it are found in sources extending from Cicero (De fato 7) to the fifteenth-century scholastic Peter de Rivo ('A Quodlibetal Question on Future Contingents,’ in ms. translation by N. Kretzmann) and beyond. The necessary conditionals transmitting past necessity to the future may be either ‘semantic’ (e.g., the tense-logical axioms used by A. Prior in his reconstruction of the Master) or ‘causal,’ as in Cicero's version of the argument. But, for such arguments to be valid, the necessity of the conditional must ‘distribute’ over antecedent and consequent in the manner represented by what is usually referred to as the distinctive axiom ‘K’ of normal modal logics: L(p ﬤ q) ﬤ (Lp ﬤ Lq). Recently, some incompatibilists have rediscovered this form of argument. In an interesting recent paper, Michael Slote has provided a counterargument which is, in essence, the following: any sense of the modalities which validates the ‘necessity of the past’ will not validated axiom K (or its logical equivalents). See his ‘Selective Necessity and the Free-Will Problem,’ The Journal of Philosophy, 79 (1982) 5-24.

36 The principle that a necessary a tergo conditional implies the ‘absolute’ necessity of its consequent helps to explain the fact - which rightly puzzles Sharples - that Alexander sometimes seems to argue against Stoic determinism (i.e., universal a tergo necessitation) by arguing for the existence of some variability in the cosmos. See Sharples, R.W., ‘Aristotelian and Stoic Conceptions of Necessity in the De fato of Alexander of Aphrodisias,’ Phronesis, 20 (1975) 247-74.CrossRefGoogle Scholar

37 Quaestio 3.5, 88.13-16.

38 At places, however, in the corpus attributed to Alexander, the author seems not to regard ‘accidental causes’ as really being causes at all. For a discussion of this issue, see Sharples, ‘Responsibility, Chance, and Not-Being (Alexander of Aphrodisias mantissa 169-172),’ BICS, 22 (1975) 37-64.

39 As Dr. Sharples has pointed out to me, it seems unlikely that even the Epicureans should want to deny that an event/state of affairs has some necessary conditions of ‘instantiatin': a parengklisis, for example, will have as a necessary condition of its occurrence the existence of an atom to serve as the ‘subject’ of the event. Perhaps the disagreement between Alexander and the Epicureans could be described in the following way: while Alexander posits the existence of a temporally prior change/event as a necessary condition for the occurrence of every event, the Epicureans deny this for ‘chance’ events such as the ‘swerve.'

40 De fato 24, 193.30-194.17

41 Mackie, 34

42 Ibid.

43 Cf. note 39.

44 Philoponus, In Aristotelis de generatione et corruptione, in Commentaria in Aristotelem Graeca (CIAG) 14:2, ed. H. Vitelli (Berlin: G. Reimer 1897), 308.25-8. The passage is noted by Sharples in’ “If What Is Earlier, … ; 41, note 85.

45 Of course, with sufficient imagination, one might be able to come up with a conception of ‘foundationless houses’ that falsifies this claim. But the idea that the existence of a house requires the existence of a foundation and, in fact, the foundation's prior completion does seem to be one of those ‘homely’ conceptions of kinēseis and their effects from which Aristotle's notion of necessary conditions appears to be derived.

46 Even if we consider the matter in terms of contemporary genetics, assuming that it is necessary that Socrates have exactly the same ‘genetic structure’ he actually has, it does not seem necessary that he should have had the father he actually had. His father and mother might have had different genetic structures but have passed on to Socrates the same combination that he, in fact, received (each parent supplying a part of that structure different from the part he/she in fact supplied).

47 Certainly, if a given type of event/state of affairs, no matter how ‘finely’ it or the ‘surrounding circumstances’ are described, can have different causes, the actual cause of a given event/state of affairs would not always be necessary in the circumstances in terms of the ‘inferability’ model of conditional necessity.

48 See note 20.

49 Hume, An Inquiry concerning Human Understanding, Sect. VII, Part II, in Enquiries concerning Human Understanding and concerning the Principles of Morals, 3rd. edn., rev. Nidditch, P.H. (Oxford: Clarendon Press 1975), 76Google Scholar. See Lewis, David, ‘Causation,’ in Sosa, E., ed., Causation and Conditionals, (Oxford: Oxford University Press 1975), 180.Google Scholar

50 Mackie, Ch. 2, ‘The Concept of Causation - Conditional Analyses'

51 Ibid., 47-8

52 Ibid., 37

53 Ibid.

54 Of course, it is not clear that an effect can contiguously succeed its cause. See the references to Russell and Dummett in note 24. Mackie's own formulation is complicated to allow for the possibility of an effect which temporally precedes its cause. See Mackie, 52-3.

55 Ibid., 53

56 Stalnaker, R. and Thomason, R., ‘A Semantic Analysis of Conditional Logic,' Theoria, 36 (1970) 23–42CrossRefGoogle Scholar

57 See D. Lewis, ‘Causation,’ 183-5. Lewis, D., Counterfactuals (Cambridge, MA: Harvard University Press 1973).Google Scholar

58 See, e.g., Mackie, 31, 52-3.

59 The criticism does not depend on any particular metaphysical conception of possible worlds: any ‘semantically useful’ conception will view possible worlds as ‘determinate’ in the sense required by the argument. The same sort of criticism seems to apply to Lewis’ concept of causal dependence, developed in 'Causation.'

60 Of course, the import of such a possible-worlds analysis is not always obvious. Mackie evidently believes that ‘Y would not have occurred if X had not occurred' is equivalent to ‘Y would not have occurred if X had not but the laws of nature remained the same,’ while Lewis denies that such an equivalence universally holds.

61 See, e.g., Mackie, Ch. 2.

62 G.E.M. Anscombe, ‘Causality and Determination,’ in Causation and Conditionals, 63-81. This paper is Prof. Anscombe's Inaugural Lecture delivered at Cambridge and was originally published by Cambridge University Press (1971).

63 Cf. Mackie, 267, footnote 19: ‘all that a law could demonstrate as being necessary for the effect is that an event of a certain sort should have occurred, not that this one in all its concrete detail should have done so.’ Vid. also, 265: 'our earlier difficulty arose from the fact that the concrete event was not necessary in the sense in which the fact was; the event could have been a bit different without altering the result...’ However, the ‘straightforward’ counterfactual interpretation of ‘Event X was necessary in the circumstances for event Y' (i.e., ‘Y would not have occurred it X should not have occurred’) does not seem to allow that the cause X could have been different at all, relative to the occurrence of effect Y.

There is another problem with Mackie's analysis, which is equivalent to a problem discussed by Dr. Pollard in his comments on my paper. It pertains to cases where X caused Y and the cause X is itself a causally necessitated consequence of antecedent circumstances, and its upshot is that Mackie's analysis becomes trivial in such cases. In such cases, as in all others, Mackie's analysis maintains that the counterfactual ‘If, in the circumstances X had not occurred, Y would not have occurred’ obtains. If we expand ‘in the circumstances’ here as the conjunction ‘(a) all actual events up to the time of the occurrence of X remain unchanged and (b) the 1aws of nature’ governing the actual world remain unchanged and (c) these laws are ‘deterministic’ with respect to the antecedents of X causing, in the circumstances, X,’ then we have the counterfactual, If it should have been the case that ((a) and (b) and (c) and X does not occur), then Y would not have occurred.’ But the antecedent specifies an impossible state of affairs. Hence, according to standard counterfactual logic, any consequent could be substituted for ‘Y would not have occurred,’ and the resulting counterfactual would still be true. lewis’ analysis of causation avoids such a criticism by not assuming that a world at which the antecedent of a counterfactual is true that is characterized by the same ‘natural laws’ governing the actual world need be more similar to the actual world than a world at which the antecedent is true but at which the laws governing the actual world do not obtain. While he provides some intuitively plausible reasons for his position, part of the price he must pay is what seems to be the rather ad hoc divergence of his concepts of causation, causal dependence, and nomic dependence (Lewis, ‘Causation’).

64 Another path is that of moral or legal responsibility or accountability. This is perhaps the path that Aristotle is traveling in Nicomachean Ethics 7. Even here, however, he tends to conflate the relational concepts of explanation and moral/legal responsibility.

65 As Ernest Sosa comments, ‘the view that a certain concept (e.g., causation) cannot be analysed is difficult to refute except by producing an analysis. So far as I know no one has published a successful analysis of causation by reference to conditionality or lawfulness’ (Introduction,’ Causation and Conditionals, 5).