“Does it not happen, then, according to all this, that reminiscence arises partly from things like, and partly from things unlike?”

“It does.”

“But when one is reminded by things like, is it not necessary that one should be thus further affected, so as to perceive whether, as regards likeness, this falls short or not of the thing of which one has been reminded?”

“It is necessary,” he replied.

“Consider, then,” said Socrates, “if the case is thus.  Do we allow that there is such a thing as equality?  I do not mean of one log with another, nor one stone with another, nor any thing else of this kind, but something altogether different from all these—­abstract equality; do we allow that there is any such thing, or not?”

“By Jupiter! we most assuredly do allow it,” replied Simmias.

51.  “And do we know what it is itself?”

“Certainly,” he replied.

“Whence have we derived the knowledge of it?  Is it not from the things we have just now mentioned, and that from seeing logs, or stones, or other things of the kind, equal, we have from these formed an idea of that which is different from these—­for does it not appear to you to be different?  Consider the matter thus.  Do not stones that are equal, and logs sometimes that are the same, appear at one time equal, and at another not?”

“Certainly.”

“But what?  Does abstract equality ever appear to you unequal? or equality inequality?”

“Never, Socrates, at any time.”

“These equal things, then,” he said, “and abstract equality, are not the same?”

“By no means, Socrates, as it appears.”

“However, from these equal things,” he said, “which are different from that abstract equality, have you not formed your idea and derived your knowledge of it?”

“You speak most truly,” he replied.

“Is it not, therefore, from its being like or unlike them?”

“Certainly.”

“But it makes no difference,” he said.  “When, therefore, on seeing one thing, you form, from the sight of it, the notion of another, whether like or unlike, this,” he said, “must necessarily be reminiscence.”

“Certainly.”

52.  “What, then, as to this?” he continued.  “Are we affected in any such way with regard to logs and the equal things we have just now spoken of?  And do they appear to us to be equal in the same manner as abstract equality itself is, or do they fall short in some degree, or not at all, of being such as equality itself is?”

“They fall far short,” he replied.

“Do we admit, then, that when one, on beholding some particular thing, perceives that it aims, as that which I now see, at being like something else that exists, but falls short of it, and can not become such as that is, but is inferior to it—­do we admit that he who perceives this must necessarily have had a previous knowledge of that which he says it resembles, though imperfectly?”