In the latter half of The Republic, book 5, Socrates and Glaucon are discussing the difference between knowledge of things things that exist and ignorance about things that don't exist. They suppose that opinions, being different from both ignorance and knowledge, must pertain to things neither existing nor nonexistent. The following excerpt from the conversation ensues:
Socrates: Then what remains to be discovered is the object which partakes equally of the nature of being and not-being, and cannot rightly be termed either, pure and simple; this unknown term, when discovered, we may truly call the subject of opinion, and assign each to their proper faculty,—the extremes to the faculties of the extremes and the mean to the faculty of the mean.
This being premised, I would ask the gentleman who is of opinion that there is no absolute or unchangeable idea of beauty—in whose opinion the beautiful is the manifold—he, I say, your lover of beautiful sights, who cannot bear to be told that the beautiful is one, and the just is one, or that anything is one—to him I would appeal, saying, Will you be so very kind, sir, as to tell us whether, of all these beautiful things, there is one which will not be found ugly; or of the just, which will not be found unjust; or of the holy, which will not also be unholy?
No, he replied; the beautiful will in some point of view be found ugly; and the same is true of the rest.
And may not the many which are doubles be also halves?—doubles, that is, of one thing, and halves of another?
And things great and small, heavy and light, as they are termed, will not be denoted by these any more than by the opposite names?
True; both these and the opposite names will always attach to all of them.
And can any one of those many things which are called by particular names be said to be this rather than not to be this?
He replied: They are like the punning riddles which are asked at feasts or the children's puzzle about the eunuch aiming at the bat, with what he hit him, as they say in the puzzle, and upon what the bat was sitting. The individual objects of which I am speaking are also a riddle, and have a double sense: nor can you fix them in your mind, either as being or not-being, or both, or neither.
Could someone please explain the riddle at the end of that excerpt to me?