according to which numbers are generated from an initial One as it 'breathes in' a portion of the adjacent
infinity; this portion becomes finite and at the same time divides the one into two. The evolution of the
cosmos from a primordial unity is simply an example of this process. Things are numbers, and their
relationships (justice, for instance) are mathematical relationships. Aristotle's allusions to the theory
hardly allow us to grasp its meaning, and he was doubtless justified in complaining that it left all sorts of
questions unanswered. But it is regrettable that we do not understand more about a doctrine which threw
the universe into such a novel perspective.
The thinkers so far discussed accepted that the material world is on the whole (allowing for certain
misinterpretations on our part) as our senses represent it to us. Meanwhile Parmenides, at the beginning
of the fifth century, had struck out along a path of logical reasoning about Being which threatened to
undermine that assumption. To put the argument in a nutshell: only Being can exist; there can be no
coming-to-be or passing-away, because they imply non-being; no gap or discontinuity in Being; no
movement, for lack of space ( = non-being); not even any qualitative change, for that would mean the
not-being of what had been. Ergo, reality consists simply of indivisible, changeless, featureless,
motionless, rock-solid Being. The whole phenomenal world with its colour, movement and
impermanence must be a sham. It is of course a sham with a pattern, and Parmenides feels obliged to
offer an account of it, while emphasizing that he is analysing an illusion or fable convenue. He reduces
its diversity to a basic duality of light and dark, each of which subsumes a range of other qualities. He
claims that this is the best analysis attainable by man, but, being unable to reconcile it with his account
of the nature of Being, he has to say that it is ultimately false.
Parmenides' reasoning, though brilliant, is at the same time so artificial that we may suspect his
conclusion of being preconceived, particularly as his vision of Being shows resemblances to a certain
type of mystical experience in which space and time seem to lose all significance and there is an acute
sense of the unbroken unity of all things with each other and with the self. He actually presents his
philosophy as derived from a private divine revelation. But nothing is more significant of the intellectual
climate in which he lives than the fact that he does not say 'the goddess showed me, and I saw', but 'the
goddess proved it with the following arguments'. He is concerned to rationalize his vision.
Parmenides had two followers. Zeno also came from Elea, Melissus from Samos; by convention the
three are collectively called the Eleatics. Zeno reinforced the case against plurality and motion with
arguments and paradoxes of a mathematical nature, including the famous paradox of Achilles and the
tortoise: Achilles can never overtake the tortoise because every time he reaches the point where it was, it
has moved on. Melissus went beyond Parmenides in arguing that Being is infinite in extent (Parmenides
had made it finite and spherical) and that it is incorporeal, because otherwise it would have parts,
implying plurality. The divorce between the philosopher's 'reality' and the world of experience could not
be made more complete.
Eleaticism was in one sense a dead end. But the concept of an unchanging reality beyond the material
world endured in, and because of, Plato; and a passage in which Melissus argues that if there were after
all a plurality of things, they would all have to be as unchanging as his One, points the way to the
greatest inspiration of ancient physical theory, the atomism of Leucippus of Miletus. Leucippus follows