[510d]
from these, and pursuing the
inquiry from this point on consistently, conclude with that for the
investigation of which they set out.”
“Certainly,” he said, “I know that.”
“And do you not also know that they further make use of the
visible forms and talk about them, though they are not thinking of them but
of those things of which they are a likeness, pursuing their inquiry for the
sake of the square as such and the diagonal as such, and not for the sake of
the image of it which they draw1?
1 Cf. 527 A-B. This explanation of mathematical reasoning does not differ at all from that of Aristotle and Berkely and the moderns who praise Aristotle, except that the metaphysical doctrine of ideas is in the background to be asserted if challenged.
Plato. Plato in Twelve Volumes, Vols. 5 & 6 translated by Paul Shorey. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1969.
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