From the Beginning to Plato

146 PYTHAGOREANS AND ELEATICS
209a23–5). Elsewhere he gives the problem in the form: ‘if a place is something,
in what will it be?’ (Physics IV 3, 210b22–24). If this was originally one
argument, it constructed an infinite series out of the common assumption that
everything that is, is in a place, which is something other than itself: applying the
assumption to places themselves, we shall have places of places, places of places
of places, and so on. Such a series could have figured in one of the arguments
against plurality. In any case, it would be a good parry to any attack on
Parmenides’ monism which sought to show that his ‘One’ must occupy a place
other than itself.
Also from Aristotle (Physics VII 5, 250a19–22): Zeno argued that, if a heap of
grain makes a noise when it falls, then a single grain and any fractional part of it
must make a noise too. One may conjecture that Zeno’s dilemma was: either it
makes a proportionately small noise, or none at all. If the latter, a natural and
fundamental assumption of mathematizing physics is undermined: the
assumption that the magnitudes of effects are in direct proportion to the
magnitudes of their causes. But if the former, then why do we not hear the
proportionately small noise? If it fails to affect our senses, the assumption of
proportionality breaks down somewhere else. Such an argument would obviously
fit Zeno’s programme of attack on any possible mathematical physics.
Conclusion
Examination of the evidence for Zeno’s arguments leads to satisfyingly
consistent results, and bears out the testimony of Plato.
First, Zeno attacked principally certain commonly-held views involving the
reality of plurality and change, but did not confine himself to those targets. This
fits well with Parmenides, who saw the twin beliefs in the reality of essential
plurality and of change as the two marks of deluded ‘mortals’. 48
Second, Zeno’s argumentative assumptions are taken from his opponents.
They may be characterized as those of theoretical physics in its infancy, of
‘mathematicized common sense’.
PHILOLAUS AND ‘THE PEOPLE CALLED
PYTHAGOREANS’
In the mid to late fifth century, there were various people and groups claiming to
be ‘Pythagorean’; they were found principally in the west of the Greek world
(Sicily and southern Italy). Aristotle, our most reliable source, tells of certain
‘Italians’ or ‘people called Pythagoreans’ who had a programme of reducing
everything to mathematics (Metaphysics 1.5, 985b23–986b8 and 987a9–27). 49
The only individual one, about whom something of tangible philosophical
interest can be known, is Philolaus of Croton. 50
Five fragments which may be reasonably taken as genuine reveal a theory of
underlying structure in the universe which is heavily influenced by the