From the Beginning to Plato

154 PYTHAGOREANS AND ELEATICS
Parmenides or Zeno). On these as possibly Zeno’s: see Vlastos [4.64], 371–2 and
Makin [4.66].
38 On their possible interdependence, see section (e).
39 Compare the assumption needed in (e) above, that anything having size can be
divided into two things each having size.
40 Sometimes known as the ‘Dichotomy’. Aristotle’s own solution is at Physics VIII
8, 263a4–b9.
41 Aristotle’s phrase corresponding to ‘at a moment’ is ‘in the now’, i.e. ‘in the present
understood as an indivisible instant’. This excludes periods of time, even
supposedly indivisible ones. It is possible that Zeno’s argument somehow depended
crucially on the instant’s being taken as present (as suggested by Lear [4.67]).
42 Diogenes Laertius (Lives IX.72, DK 29 B 4), using a source independent of
Aristotle, gives a summary of an argument which may possibly descend from
Zeno’s formulation of step (2): ‘that which moves does not move either in the place
in which it is, or in the place in which it is not’.
43 The long illustrative example (240a4–17), implying a lettered diagram, is given as
Aristotle’s own contribution; there is no reason to attribute it to Zeno.
44 Attempts to reconstruct a more satisfactory argument include those of Furley [4.63]
and Owen [4.68].
45 In some interpretations, the arguments have been seen as systematically exhausting
the theoretical possibilities for pluralism. The idea goes back to the nineteenth
century; notable in this connection is the theory of Owen [4.68]. On such a view,
time and the track of the moving thing are considered in the ‘Stadium’ and the
‘Achilles’ as divisible ad infinitum; but in the ‘Arrow’ and the ‘Moving Rows’ as
‘atomized’, i.e. as consisting ultimately of indivisible units of extension.
46 On the indications connecting Zeno’s arguments with ‘Pythagoreans’ see Caveing
[4.62], 163–80.
47 This is not to deny that modern mathematics enables us to give sharper formulations
both of the arguments and of the possibilities for meeting them: see especially
Grünbaum [4.75].
48 See above pp. 145–7.
49 On Aristotle’s description and criticism of this programme, see Huffman [4.78], 57–
64; and Kahn [4.2].
50 The surviving fragments attributed to Philolaus are due to various late sources
(Diogenes Laertius, some Neoplatonists, and the anthology of Stobaeus). Their
authenticity is controversial; on this question, see Burkert [2.25], 238–68; [4.78],
The reading of Philolaus given here is indebted to Burkert [2.25] and particularly
to Nussbaum [4.79],
51 See DK 44 B 1, 2, 4, 5, 6.
52 Nussbaum [4.79], 102.
53 Aristotle Metaphysics I.5, 986b25–7 (‘rather crude’); Physics I 2, 185a10–11 (‘lowgrade’).
One purported source, the pseudo-Aristotelian essay On Melissus
Xenophanes Gorgias (MXG), is an exercise in ‘philosophical reconstruction’, from
which it is not possible to disentangle with confidence any further information
about Melissus. MXG is not drawn on here. The most noteworthy modern attempt
to rehabilitate Melissus as a philosopher is that of Barnes [2.8], chs. 10, 11, 14.
54 This is a conjectural interpretation of Simplicius’ paraphrase, Physics 103.15: ‘if
nothing is, what would one say about it as though it were something?’