56
Pro. I think you mean arithmetic and the other arts you mentioned with it just now.
56
Soc. Certainly. But, Protarchus, ought not these to be divided into two kinds? What do you say?
56
Pro. What kinds?
56
Soc. Are there not two kinds of arithmetic, that of the people and that of philosophers?
56
Pro. How can one kind of arithmetic be distinguished from the other?
56
Soc. The distinction is no small one, Protarchus. For some arithmeticians reckon unequal units, for instance, two armies and two oxen and two very small or incomparably large units; whereas others refuse to agree with them unless each of countless units is declared to differ not at all from each and every other unit.
56
Pro. You are certainly quite right in saying that there is a great difference between the devotees of arithmetic, so it is reasonable to assume that it is of two kinds.
57
Soc. And how about the arts of reckoning and measuring as they are used in building and in trade when compared with philosophical geometry and elaborate computations—shall we speak of each of these as one or as two?
57
Pro. On the analogy of the previous example, I should say that each of them was two.
57
Soc. Right. But do you understand why I introduced this subject?
57
Pro. Perhaps; but I wish you would give the answer to your question.
57
Soc. This discussion of ours is now, I think, no less than when we began it, seeking a counterpart of pleasure, and therefore it has introduced the present subject and is considering whether there is one kind of knowledge purer than another, as one pleasure is purer than another.
57
Pro. That is very clear; it was evidently introduced with that object.
57
Soc. Well, had not the discussion already found in what preceded that the various arts had various purposes and various degrees of exactness?
57
Pro. Certainly.
