12. Another preliminary point requiring some notice, is the consideration of those sciences which draw away the mind from the contemplation of sensible objects, and turn it to the study of universal truth. Among these are to be reckoned arithmetic and geometry; sciences which, according to Plato, are the best preparation by which the mind can be trained to the higher study of dialectic. Speaking of geometry, he says (the words are put into the mouth of Socrates): "You also know," says Socrates, "that the geometricians summon to their aid visible forms and discourse about them, though their thoughts are busy, not with these forms, but with their originals, and though they discourse not with a view to the particular square and diameter which they draw, but with a view to the absolute square and the absolute diameter, and so on. For while they employ by way of images those figures and diagrams aforesaid (which again have their shadows and images in water), they are really endeavouring to behold those things[1] which a person can only see with the eye of thought," that is to say, not this or that circle, or this or that square, but square and circle viewed universally, which they cannot be by sense or imagination, but only by the intellect (διάνοια). Again, speaking of geometry, the Platonic Socrates says: "It is indeed no easy matter to believe that, in the midst of these mathematical studies, an organ
- ↑ Not "abstractions," as wrongly rendered by the Cambridge translation.—Rep. vi. 610.
