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Rh of our soul is being purged from the blindness, and quickened from the deadness, occasioned by other pursuits—an organ whose preservation is of more importance than a thousand eyes, because only by it can truth be seen. Consequently, those who think with us will bestow unqualified approbation on these studies." These extracts may be sufficient to show the importance which Plato attached to mathematical science as a training of the mind for the study and reception of the purer and loftier truth revealed to it by dialectic. The words, however, which Plato is said to have inscribed over the gate of the academy where his discussions were held, "Let no one who is not a geometrician enter these walls"—, are erroneously attributed to the philosopher, although they are quite in accordance with the tone and spirit of his instructions.

13. The following passage from the 7th Book of the Republic, contains the celebrated similitude in which Plato allegorises the conversion of the mind from the world of sense to the world of ideas. I read it to you as preparatory to our discussion of his theory of ideas.

“Suppose," says Socrates, "a set of men in a subterraneous cavern, which opens to the day by a long straight wide passage, and that they have been kept in this cavern from childhood, fettered so that they