Plato: The Republic

4. BOOK IV (continued)

And suppose the objector to refine still further, and to draw the nice distinction that not only parts of tops, but whole tops, when they spin round with their pegs fixed on the spot, are at rest and in motion at the same time (and he may say the same of anything which revolves in the same spot), his objection would not be admitted by us, because in such cases things are not at rest and in motion in the same parts of themselves; we should rather say that they have both an axis and a circumference, and that the axis stands still, for there is no deviation from the perpendicular; and that the circumference goes round. But if, while revolving, the axis inclines either to the right or left, forwards or backwards, then in no point of view can they be at rest.

That is the correct mode of describing them, he replied.

Then none of these objections will confuse us, or incline us to believe that the same thing at the same time, in the same part or in relation to the same thing, can act or be acted upon in contrary ways.

Certainly not, according to my way of thinking.

Yet, I said, that we may not be compelled to examine all such objections, and prove at length that they are untrue, let us assume their absurdity, and go forward on the understanding that hereafter, if this assumption turn out to be untrue, all the consequences which follow shall be withdrawn.

Yes, he said, that will be the best way.

Well, I said, would you not allow that assent and dissent, desire and aversion, attraction and repulsion, are all of them opposites, whether they are regarded as active or passive (for that makes no difference in the fact of their opposition)?

Yes, he said, they are opposites.