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Published online by Cambridge University Press: 11 February 2009
A well-known epigram by Callimachus on the philosopher Diodorus Cronus (fr. 393 Pfeiffer) reads as follows:
The question of the third line, while perhaps recondite from a contemporary perspective, was clear in antiquity. The crows are asking ‘What follows (from what)?’, in allusion to the Hellenistic disputes concerning the truth conditions of conditional propositions (συνημμ⋯να), disputes in which the views of Diodorus figured prominently.
I agree with Sedley that the question of the last line is ‘much more problematic’. The common interpretation has been to read the αὖθι as a form of αὖθις and to interpret it temporally. The result, in Pfeiffer's estimation, is ‘quomodo posthac erimus?’.
This interpretation derives from Sextus Empiricus' discussion at M. 1.309–12 of the last two lines of the epigram. After crediting the grammarian with the ability to understand the allusion in the crows' first question (M. 1.310: κα⋯ μ⋯χρι τούτου συνήσει τ⋯ κα⋯ παιδίοις γνώριμον), he proceeds to argue that the philosopher has a better chance than the grammarian of understanding the second question. But, to quote Sedley, Sextus ‘makes a ghastly mess of it’ when he attempts his own elucidation. According to an argument of Diodorus, a living thing does not die in the time in which it lives nor in a time in which it does not live. Hence, Sextus concludes, it must be the case that it never dies and, ‘if this is the case, we are always living and, according to him, we shall come to be hereafter (αὖθις γενησόμεθα)’ (M. 1.312).
1 See Empiricus, Sextus, PH 2.110–12Google Scholar and the discussion in Mates, B., Stoic Logic (Berkeley and Los Angeles, 1961), pp. 45–7Google Scholar.
2 Sedley, D., ‘Diodorus Cronus and Hellenistic Philosophy’, Proceedings of the Cambridge Philological Society 20 (1977), 108 n. 35Google Scholar.
3 Pfeiffer, , Callimachus (Oxford, 1949), i.35Google Scholar.
4 Sedley, loc. cit.
5 See Pfeiffer's apparatus, op. cit. i.247.
6 Cf. M. 10.119–20.
7 Diogenes Laertius 9.72.
8 Vlastos, G., ‘Zeno of Elea’, The Encyclopedia of Philosophy, ed. Edwards, P. (New York and London, 1967), viii. 375Google Scholar.
9 The technical import of this phrase is that a crow moves through a potentially infinite number of places where it might stop in moving from place X to place Y. These ‘potential places’ can be linearly ordered: for any two distinct potential places U and W between X and Y, either U is between X and W while W is between U and Y or W is between X and U while U is between W and Y. However, these potential places cannot be discretely ordered, that is, ordered ⋯ɸεξ⋯ς, in Aristotle's sense: no such potential place could be the immediate successor or predecessor of another potential place. I should like to thank the anonymous reader for drawing this matter to my attention, and for suggesting the phrase ‘continuously traversing’.
10 Although the development of the calculus facilitated the formation of a conception of ‘instantaneous velocity’, it is open to the defender of Aristotle's resolution of the Arrow to claim that this term involves a πρòς ἕν homonymous use of ‘velocity’: instantaneous velocity is not velocity in the primary or focal sense, i.e. distance traversed divided by the time during which it is being traversed, but the limit of an infinite sequence of velocities in this primary sense. Hence, the concept of instantaneous velocity need not imply that a body is either moving or at rest at an instant in the way that the concept of velocity in a primary sense implies that a body is either moving or at rest during a (non-zero) interval or ‘stretch’ of time.
