Abstract
One of the great “dialecticians” (i.e., logicians) of antiquity was Diodorus Cronus, who flourished in the latter part of the fourth and very early part of the third century B.C. His life seems to have slightly overlapped that of Aristotle (who died in 322); but it is questionable whether Diodorus could have had any philosophical influence on the Philosopher.1 Until very recently, Diodorus was considered to have been an adherent of the Megarian school, which originated with Euclides of Megara, a pupil of Socrates, in the early fourth century.2 Diogenes Laertius comments that
those who followed him [Euclides] were called Megarics [or Megarians], then Eristics, and later Dialecticians, Dionysius of Chalcedon having first thus named them on account of their formulating their arguments by question and answer.3
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References
Sedley is of the opinion that the most commonly accepted date for Diodorus’ death, ca 307 B.C., is about twenty years too early, that 334 is “the earliest possible date at which his influence might have been felt,” but that “even this is against the odds” (D. Sedley, ’Diodorus Cronus and Hellenistic Philosophy’, Proceedings of the Cambridge Philological Society 207 [1977], p. 280).
See D.L., 2.106ff
D.L., 2.106.
Sedley, p. 75.
Ibid p. 77
Ibid
Ibid
D.L.,2.113.
Sedley, p. 75.
D.L., 2.107.
Ibid.
Ibid., 2.113.
Ibid., 2.111–112
Ibid., 2.106.
See Sedley, p. 74.
D.L., 2.106.
Parmenides D/K 28 B2.
I am here, of course, adopting the interpretation of Zeno’s work set forth by Plato at the beginning of the Parmenides.
Meta. 9.3.1036b29–33.
Sextus Empiricus, Adversiis mathematicos (hereafter, M) 1.311.
Cf. Sextus, M 10.85–87, Hypotyposeis (Outlines [of Pyrrhonism], hereafter cited as “PH”) 2.242-245, 3.71. While the argument attributed by Aristotle to Zeno involves time (specifically, the claim that, since in a given “now,” a body is occupying a space equal to itself, it cannot be moving in the “now”), the analogous argument attributed by Sextus to Diodorus involves space (specifically, the premise that a body cannot move in the space where it is [for that space, being equal to itself, does not afford it space for motion]). Diodorus’ argument is spelled out in a way that connects it with time at M 10.119-120: “if something is moving, it is moving now; if it is moving now, it is moving in the present time; if it is moving in the present time, it is moving, therefore, in an indivisible time. (For if the present time is divided, it will certainly be divided into the past and the future, and thus will no longer be present.) If something is moving in an indivisible time, it is traversing indivisible places. If it is traversing indivisible places, it is not moving. For when it is in the first indivisible place, it is not moving: for it is still in the first indivisible place. When it is in the second indivisible place, again it is not moving, but it has moved. Therefore, it is not the case that anything is moving.” If, as Sorabji believes, the “now” in which Zeno’s arrow occupies a space equal to itself and, therefore, is not moving is an “instant” (temporal “point”) rather than an indivisible time atom, there is perhaps less in common between Zeno’s “Arrow” and the arguments of Diodorus than at first seems to be the case (R. Sorabji, ‘Atoms and Time Atoms’, in Infinity and Continuity in Ancient and Medieval Thought, ed. N. Kretzmann [Ithaca and London, 1982], pp. 43–44). However, as the discussion in the following section indicates, it is certainly the case that Diodorus did not regard his “denial of motion” as entailing that the world cannot be “different” at different times. It is far from certain that Zeno would have been willing to go this far with Diodorus.
This is not to say, of course, that there are not other philosophical influences to be discerned in the succession as well.
2:5 Meta. 9.3.1046b–32.
1047a 12–13. M = “it is possible that...”;F=“it will, at least once, be the case that...”
1047a14–17.
Hintikka, T&N, pp. 199–200.
Hintikka makes essentially the same point in his discussion of the passage (T&N, pp. 197–199). However, far from being a “rather peculiar concept of possibility” (ibid., p. 197), the concept being exploited in the passage by Aristotle strikes me as a very commonly encountered concept.
Sextus, M 1.311–312.
I agree with Sedley that Sextus’ explanation is exceedingly problematic (Sedley, p. 108, Note 35). The correct interpretation, I suspect, is that “authi” is to be understood as the contracted form of “autothi,” here an adverb of place. The crows are asking “how shall we come to be there?” or “how shall we get over there?” in allusion to Diodorus’ denial that anything is ever moving (kineisthai).
Sextus, M 9.363.
M 10.85–86.
M 10.91–92.
M 10.101.
Cf. Hintikka et al., Aristotle on Modality, p. 79: “According to what was said above in Section 24, a potentiality which gives rise to an energeia — and which in the sense explained coincides with this energeia — cannot be a contingency, for such a potentiality is necessarily realized, unlike a dynamis which gives rise to an outcome to be reached through a kinesis. In the latter case, a potentiality exists only while the change toward the goal is taking place, and then the potentiality has not yet been realized. Hence in the case of a potential energeia, the only situation in which we can truly say that it possibly exists is one in which we can say that it in fact exists, whereas a potentiality which is realized through a kinesis obtains only when it is true to say that in certain circumstances it would be realized.”
Dr. R. W. Sharpies suggests (in private communication) the possibility, however, that “our evidence is distorted by the desire to use Diodorus as a stick with which to beat the determinist Stoics.”
Cicero, De fato 7.13.
Other terms are sometimes used: e.g., Waterlow (Passage and Possibility, pp. 111ff) uses the term “dated propositions.” The idea, as was pointed out in the preceding chapter, is that such propositions are “Ceternally (or atemporally) bound” to a particular time and, hence, can connote only an event/state of affairs obtaining at that time.
Boethius, In lib. Arist. PH, ed. Meiser, editio secunda, 234. The conjunction “cum” in the clauses “cumfalsum sit” and “cum verum sit” is normally translated as “when” and the logical import of the resulting accounts of impossibility and necessity consequently interpreted as a simple conjunction: the impossible=that which, when it is false, will not be true=that which is false and will always remain false; the necessary=that which, when it is true, will not be false=that which is true and will always remain true. However, one would, I think, expect the indicative mood rather than the subjunctive if the sense of “cum” were the straightforwardly temporal “when” or “whenever.” I suggest that “cum” has a causal or quasi-causal sense here — hence, my translation of it as “since.” The point is that since a temporally determinate proposition or the event/state of affairs it connotes is false (true), it cannot become true (false) with the passage of time. Diodorus is, therefore, implicitly appealing to a doctrine of the eternal fixity of truth values (of temporally determinate propositions or events/states of affairs) in his “definition” of impossibility and necessity.
JW In the normal semantic interpretation of tense logic, prepositional variables or “sentence letters” are (arbitrarily) assigned a set of “times” or “possible times” at which they are understood to be “instantiated” or “made true.”
This assumption is clearly made, e.g., by Waterlow: “The dated propositions cannot change in truth-value” (Passage and Possibility, p. 111). However, the assumption can be consistently and rigorously denied, as I did in my “Aristotelian” treatment of unactualized possibilities (“Aristotle and Unactualized Possibilities”).
I consider such a collapse in my “An S5 Diodorean Modal System”, Logique et Analyse 88 (December, 1979), pp. 477–487. I now believe, however, that the assumption underlying the article, that “Diodorean modalities” should be interpreted as applying to temporally indeterminate or indefinite propositions, is seriously mistaken.
In the Logique et Analyse article cited in the preceding note, as well as in ‘Facets of Megarian Fatalism: Aristotelian Criticisms and the Stoic Doctrine of Eternal Recurrence’, Canadian Journal of Philosophy 10/2 (June, 1980), pp. 189–206, 1 suggest that the first of the entailments in the text (Fp⊃GFp) could! be saved for temporally indeterminate propositions by the added postulate of the eternal recurrence of cosmic history (or the logically equivalent postulate of circular time). We have no evidence that Diodorus subscribed to a doctrine of eternal recurrence or circular time, however; and I now think that it is extremely unlikely that he would have interpreted his definition of the modalities “tense-logically” (i.e., as applying to temporally indeterminate propositions) and, consequently, that it is unlikely that he would have attempted to “save” the deterministic thesis (Fp ⊃ GFp) by appeal to the doctrine of eternal recurrence.
De fato 10, SA 2/2, p. 177.20–21.
Boethius, In lib. Arist. PH, ed. Meiser, editio secunda, 246–247.
Cf. note 38 supra.
Cf. Paul C. Plass, ‘Timeless Time in Neoplatonism’, The Modern Schoolman 60 (November, 1977), pp. 1–19; Michael J. White, ‘Time and Determinism in the Hellenistic Philosophical Schools’, Archiv fur Geschichte der Philosophie 65/1 (1983), pp. 40–62.
De fato 1.13.
This is, of course, a version of the (“first-order”) principle of plenitude.
Epictetus, Dissertationes ab Arriano digestae, ed. H. Schenkl (Leipzig, 1898 ), 2. 19.
In view of the context of Epictetus’ report — the discussion-of “unprofitable” scholarly pedantry in philosophy — it seems most likely that Epictetus did not care.
Hintikka, T&N, pp. 188–189.
Cf. F. S. Michael, ‘What is the Master Argument of Diodorus Cronus?’, American Philosophical Quarterly 13 (1976), p. 234. I have previously (‘Diodorus’ “Master” Argument: A Semantic Interpretation’, Erkenntnis 15 [1980], pp. 69ff) expressed some reservations concerning this interpretation of the second0 premise, but now agree completely with Michael.
Actually, (all substitution instances of) K are also theorems of all regular modal logics, which are weaker than the minimal normal modal logic K, which (unlike regular logics) has as a rule of inference ⊢ p⇒ ⊢Lp.
Alexander, In Arist. an pr. lib, I, CIAG 2/1, pp. 177ff. I shall examine Chrysippus’ view in detail in the following chapter. His example of an impossible proposition that follows from a possible one is “That man is dead” (Dion being pointed to) and “Dion is dead,” respectively.
Sorabji, NC&B p. 108, Note 16.
M. A. E. Dummett, ‘The Reality of the Past’, reprinted in Truth and Other Enigmas (Cambridge, Mass., 1978), pp. 358–374. “If I now (2.45 p.m. 12 February 1969) say, ‘I am in my College room’, I make a present-tense statement which is, as I say it, true: let us call this statement A. Suppose now that exactly one year later someone makes the statement (call it B) ‘A year ago Dummett was in his College room’. Then it is a consequence of the truth-value link that, since the statement A is now true, the statement B, made in one year’s time, is likewise true” (p. 363).
For a summary of Prior’s work on the Master, see A. Prior, Past, Present and Future (Oxford, 1967), pp. 32–34. I have, I think, shown that issue of the logical role of Diodorus’ doctrines concerning the discreteness of time in the Master is a red herring raised by Prior’s syntactic tense-logical approach to the reconstruction of the argument: Michael J. White, ‘The Necessity of the Past and Modal-Tense Logic Incompleteness’, Notre Dame Journal of Formal Logic 25/1 (January, 1984 ), pp. 59–71.
Hintikka, T&N pp. 179–180, note 3.
In terms of Prior’s tense logic, this interpretation amounts to allowing unrestricted substitution (including wffs prefaced by the tense-logic “simple future” operator ‘F’) for the propositional variable ‘p’ in the tense-logical version of premise (1): Pp ⊃ LPp.
In ‘Aristotle and the “Master Argument” of Diodorus’, reprinted as Ch. nine of T&N, pp. 179–213. Sorabji (NC&B, pp. 107-109) distinguishes two principal classes of interpretations of the Master in much the same way that I do.
Ibid., p. 108, note 16.
This conclusion does not apply straightforwardly to modal-tense logic because of its implicit interpretation of propositional variables as temporally indeterminate. But there are modal-tense logic analogues of this fact: for example, in a modal-tense logic in which the modal component is the minimal normal modal logic K plus premise (1) of the Master and the tense component is some tense logic for linear, backwards serial time, from FPp it follows that L(Pp Vp VFp). See my ‘The Necessity of the Past’, p. 60.
In Arist. an pr., CIAG 2/1, p. 184.5–6.
Ibid., p. 184.2–5.
Sharpies comments (in a private communication) that “I feel it would be quite in character for Alexander simply to recognise that the argument involved assumptions which he would regard as false (i.e.: un-Aristotelian); though one might have expected him to point this out rather than just to pass over it.”
Cicero, for example, indicates the reluctance of Chrysippus to embrace Diodorus’ fatalism in De fato 6–8.
Epictetus (loc. cit) reports that Cleanthes denied the first, necessity-of-the-past premise, while Chrysippus denied that the second, reductio-ad-impossibile premise holds universally. Cf., Cicero, De fato 7.14. Chrysippus’ response, which seems so strange and unsatisfactory from the contemporary perspective, will be further discussed in the next chapter.
Cicero, De fato 7.14.
The distinction here refers to the difference between the “Middle Platonist” and Stoic conceptions of fate, to be discussed in greater detail in Chapter Six. Cf. the opinion expressed by Quintus in Cicero’s De divinatione: after defining “heimarmenf” as “ordinem seriemque causarum, cum causae causa nexa rem ex se gignat,” he remarks that “Ita fit, ut et observatione notari possit, quae res quamque causam plerumque consequatur, etiamsi non semper (nam id quidem affirmare difficile est), easdemque causas veri simile est re rum futurarum cerni ab eis, qui aut per furorem eas aut in quiete videant” (De divinatione 1.55.125–126). The standard contemporary work on ancient conceptions of fate, especially as they relate to divination, is that of David Armand (E. Armand de Mendieta), Fatalismeet Liberte dans I’Antiquite Grecque (Louvain, 1945).
De fato 7.14.
Ibid. 10.20–21.
Ibid. 10.21–22, for Epicurus. The case of Aristotle is less certain, although he was certainly interpreted by Ammonius and Boethius as holding that the aphorismene truth of future events/states of affairs is dependent on the causal or logical necessitation of those events/states of affairs. Cf. my ‘Fatalism and Causal Determinism: An Aristotelian Essay’.
See my ‘Time and Determinism in the Hellenistic Philosophical Schools’ for more on this; also Chapters Two and Six of the present work.
P.-M. Schuhl, Le Dominateuret Les Possibles (Paris, 1960), p. 28, Note 2.
Theodicy (p. 470 b, ed. Erdmann), as quoted by Schuhl, ibid.
Chrysippus’ identification of fate and providence will be further discussed in the follow-ing chapter.
In other words, Diodorus would have in some sense accepted the ontological priority of McTaggart’s B-series temporal relations and, to quote Sorabji (who is not speaking of Diodorus), “McTaggart’s point that the relations of earlier, simultaneous, and later apply changelessly, when they apply at all (R. Sorabji, Time, Creation and the Continuum [London, 1983], p. 390). Although this conception of time bears some resemblance to the “timeless time” of Neoplatonism, it may be, as Sorabji suggests (ibid.), a mistake to overemphasize the similarities.
For example, pseudo-Plutarch’s distinction between what is “in fate” (en heimarmene) and what is “according to or in conformity with fate” (kath’ heimarmenen) in his De fato seems to be a working-out of the idea that although all events/states of affairs that are “ever actual” have a changeless place in the linear time series constituting a annus magnus, this fact does not entail that each is a necessitated consequence of temporally antecedent events/states of affairs. See my ‘Time and Determinism in the Hellenistic Schools’ and Chapter Six below.
In the following chapter, I distinguish between two versions of Chrysippean compatibilism one of which distinguishes between universal a tergo causal determinism and universal a tergo necessitation and one of which does not. For another discussion see Ch. Four, ‘Stoic Embarrassment over Necessity’, of Sorabji’s NC&B, pp. 70”88.
R. Sorabji, Time, Creation, and the Continuum(TC&C) (London, 1983 ), p. 17.
Weierstrass completed the rigorous development of the concept of the limit of a covergent sequence by means of the so-called “delta-epsilon method,” thus showing that the mathematics of the calculus did not require the postulation of infinitesimals.
B. Russell, ‘Mathematics and the Metaphysicians’, reprinted in Mysticism and Logic (London, 1917), p. 76.
“A Quodlibetal Question on Future Contingents,” in manuscript translation by N. Kretzmann.
P. van Inwagen, ‘Reply to Narveson’, Philosophical Studies 32/1 (1977), p. 96. Van Inwagen’s original paper was ‘The Incompatibility of Free Will and Determinism’, Philosophical Studies 27 (1975), pp. 185–199. Cf. J. Narveson, ‘Compatibilism Defended’, Philosophical Studies 32/1 (1977), pp. 83–87; A. Gallois, ‘Van Inwagen on Free Will and Determinism’, ibid., pp. 99–105; van Inwagen, ‘Reply to Gallois’, ibid., pp. 107–111.
In a recent interesting 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” thesis (premise 1 of the original Master) will not validate the distributive thesis K or its logical equivalents (premise 2 of the Master). See his ‘Selective Necessity and the Free-Will Problem’, The Journal of Philosophy 19 (1982), pp. 5–24.
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White, M.J. (1985). Diodorean Fatalism. In: White, M.J. (eds) Agency and Integrality. Philosophical Studies Series in Philosophy, vol 32. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5339-0_3
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