e are no
degrees or kinds of sameness, likeness, difference, nor any adequate
conception of motion or change: (9) One, being, time, like space in
Zeno's puzzle of Achilles and the tortoise, are regarded sometimes as
continuous and sometimes as discrete: (10) In some parts of the argument
the abstraction is so rarefied as to become not only fallacious, but
almost unintelligible, e.g. in the contradiction which is elicited out
of the relative terms older and younger: (11) The relation between two
terms is regarded under contradictory aspects, as for example when
the existence of the one and the non-existence of the one are equally
assumed to involve the existence of the many: (12) Words are used
through long chains of argument, sometimes loosely, sometimes with the
precision of numbers or of geometrical figures.

The argument is a very curious piece of work, unique in literature.
It seems to be an exposition or rather a 'reductio ad absurdum' of the
Megarian philosophy, but we are too imperfectly acquainted with this
last to speak with confidence about it. It would be safer to say that it
is an indication of the sceptical, hyperlogical fancies which prevailed
among the contemporaries of Socrates. It throws an indistinct light upon
Aristotle, and makes us aware of the debt which the world owes to him or
his school. It also bears a resemblance to some modern speculations, in
which an attempt is made to narrow language in such a manner that number
and figure may be made a calculus of thought. It exaggerates one side
of logic and forgets the rest. It has the appearance of a mathematical
process; the inventor of it delights, as mathematicians do, in eliciting
or discovering an unexpected result. It also helps to guard us against
some fallacies by showing the consequences which flow from them.

In the Parmenides we seem to breathe the spirit of the Megarian
philosophy, though we cannot compare the two in detail. But Plato also
goes beyond his Megarian contemporaries; he has split their straws over
again, and admitted more than they would have desired. He is indulging
the analytical tendencies of his age, which can divide but not combine.
And he does not stop to inquire whether the distinctions which he makes
are shadowy and fallacious, but 'whither the argument blows' he follows.

III. The negative series of propositions contains the first conception
of the negation of a negation. Two minus signs in arithmetic or algebra
make