Travis D. Breaux Carnegie Mellon University Travis D. Breaux
Assistant Professor of Computer Science
Institute for Software Research
School of Computer Science
5000 Forbes Avenue, Pittsburgh, PA 15213
5103 Wean Hall

Links: Home | Research | Teaching | Publications | Biography | Vitae

Socrates: Early Lectures on Abstraction

Below is an excerpt from The Republic, attributed to a dialogue between Socrates and his disciple Plato, the narrator, between 427 - 347 B.C. with translation by Benjamin Jowett, p. 476. I believe this passage is representative of an early formula for abstraction, including key concepts we use in object-oriented programming and ontology languages. The letters B, C, D in parenthesis demarcate paragraphs from the original text.

And inasmuch as they are two, each of them is one?

True again.

And of just and unjust, good and evil, and of every other class, the same remark holds: taken singly, each of them is one; but from the various combinations of them with actions and things and with one another, they are seen in all sorts of lights and appear many?

Very true.

And this is the distinction which I draw between the sight-loving, art-loving, practical class and those of (B) whom I am speaking, and who are alone worthy of the name philosophers.

How do you distinguish them? he said.

The lovers of sounds and sights, I replied, are, as I conceive, fond of fine tones and colours and forms and all the artificial products that are made out of them, but their mind is incapable of seeing or loving absolute beauty.

True, he replied.

Few are they who are able to attain to the sight of this.

Very true. (C)

And he who, having a sense of beautiful things has no sense of absolute beauty, or who, if another lead him to a knowledge of that beauty is unable to follow -- of such a one I ask, Is he awake or in a dream only? Reflect: is not the dreamer, sleeping or waking, one who likens dissimilar things, who puts the copy in the place of the real object?

I should certainly say that such an one was dreaming.

But take the case of the other, who recognizes the existence of absolute beauty and is able to distinguish (D) the idea from the objects which participate in the idea, neither putting the objects in the place of the idea nor the idea in place of the objects -- is he a dreamer, or is he awake?

He is wide awake.