Parmenides

Plato · en
Other critics have regarded the final conclusion of the Parmenides
either as sceptical or as Heracleitean. In the first case, they assume
that Plato means to show the impossibility of any truth. But this is not
the spirit of Plato, and could not with propriety be put into the mouth
of Parmenides, who, in this very dialogue, is urging Socrates, not to
doubt everything, but to discipline his mind with a view to the more
precise attainment of truth. The same remark applies to the second of
the two theories. Plato everywhere ridicules (perhaps unfairly) his
Heracleitean contemporaries: and if he had intended to support an
Heracleitean thesis, would hardly have chosen Parmenides, the condemner
of the 'undiscerning tribe who say that things both are and are not,'
to be the speaker. Nor, thirdly, can we easily persuade ourselves with
Zeller that by the 'one' he means the Idea; and that he is seeking to
prove indirectly the unity of the Idea in the multiplicity of phenomena.

We may now endeavour to thread the mazes of the labyrinth which
Parmenides knew so well, and trembled at the thought of them.

The argument has two divisions: There is the hypothesis that

     1.  One is.
     2.  One is not.
     If one is, it is nothing.
     If one is not, it is everything.

     But is and is not may be taken in two senses:
     Either one is one,
     Or, one has being,

     from which opposite consequences are deduced,
     1.a.  If one is one, it is nothing.
     1.b.  If one has being, it is all things.

     To which are appended two subordinate consequences:
     1.aa.  If one has being, all other things are.
     1.bb.  If one is one, all other things are not.

     The same distinction is then applied to the negative hypothesis:
     2.a.  If one is not one, it is all things.
     2.b.  If one has not being, it is nothing.

     Involving two parallel consequences respecting the other or remainder:
     2.aa.  If one is not one, other things are all.
     2.bb.  If one has not being, other things are not.


.....

'I cannot refuse,' said Parmenides, 'since, as Zeno remarks, we are
alone, though I may say with Ibycus, who in his old age fell in love, I,
like the old racehorse, tremble at the prospect of the course which I am
to run, and which I know so well. But as I must attempt this laborious
game, what shall be the subject? Suppose I take my own hypothesis of
the one.' 'By all means,' said Zeno. 'And who will answer me? Shall I
propose the youngest? he will be the most likely to say what he thinks,
and his answers will give me time to breathe.' 'I am the youngest,' said
Aristoteles, 'and at your service; proceed with your questions.'--The
result may be summed up as follows:--