From the Beginning to Plato

150 PYTHAGOREANS AND ELEATICS
CONCLUSION
This chapter began with Pythagoras, as the presumed source of some persistently
influential thoughts. His influence on philosophy was diffuse and non-specific. His
questioning of ‘what we really are’, and his insistence that we are moral agents in
a morally polarized world, prepared for the creation of moral philosophy by
Socrates and Plato. 55
Above all, Pythagoras’ insistence on the relevance of mathematics and
importance of abstract structure links him to the Eleatics. For what seems to be
common to both Pythagoreans and Eleatics is that they take seriously the ideal of
mathematically exact knowledge, the constraining force of mathematically
rigorous argument, and the cardinal role of abstract structure in the nature of
things. (Pythagoras’ other main concerns—the nature and destiny of the self, and
the dualism of good and evil—surface in the Eleatics, if at all, only in
Parmenides’ cosmology.)
The Eleatic philosophers, likewise, had an influence which reached far beyond
their few actual followers, and is still active today. Higher standards of precision
in statement and rigour of argument are noticeable everywhere in the later fifth
century. Metaphysical argument in the Eleatic style appears: in Melissus, and as
an intellectual exercise or for sceptical purposes, as in the sophist Gorgias. More
significantly, Socrates’ step-by-step, mostly destructive argumentation is Eleatic
in spirit; it developed into the philosophical method of Plato and Aristotle, both
of whom pay tribute to ‘father Parmenides’.
In the philosophy of scientific theorizing, it was Zeno’s dazzling attacks on
incipient mathematizing physics that, for a long time, stole the show. Their effect
was not wholly negative: they stimulated further investigations into the
foundations of mathematics, and its relation to the physical world, which
culminated in the work of Aristotle. The more constructive thinking of
Parmenides and Philolaus about scientific theorizing has only very recently
begun to be understood and appreciated.
NOTES
1 The classic study of Walter Burkert (Burkert [2.25]) supersedes all previous
discussions of the evidence. It may go too far in the direction of scepticism about
Pythagoras as theoretician: see Kahn [4.2]. The (pre-Burkert) catalogue of sources
in Guthrie [2.13] Vol I: 157–71 is still serviceable.
2 Those of Aristoxenus, Dicaearchus and Heraclides Ponticus were the earliest and
most influential: see Burkert [2.25], 53–109.
3 Certain animal foods were taboo, but a comprehensive ban on the slaughter and
eating of animals is improbable and poorly attested for Pythagoras himself. Some
under Pythagorean or Orphic influence, such as Empedocles, did observe such a
ban. On the whole subject of the taboo-prescriptions and mystical maxims
(akousmata, sumbola) of the early Pythagoreans, see Burkert [2.25], 166–92.