above the region of sense, although within that region they certainly rose into a stratum of atmosphere elevated above that of ordinary thinking.
5. Let us now pass to the Pythagorean philosophy. Whether the Pythagoreans emancipated themselves completely from the thraldom of the senses, or whether such an emancipation be either practicable or desirable, I shall not now attempt to determine; but this is certain, that their speculations shot up higher into the region of pure reason than did those of their Ionic predecessors. Number is more an object of reason, and less an object of sense, than either water or air; and therefore we say that, while the position of the Ionic school is more that of sense than that of reason, the position of the Pythagorean school is more that of reason than that of sense.
6. Number is a truer universal than either water or air, or any other sensible thing. It is possible that the conception of number may not be an adequate conception of the universal in all things; that it may not be identical or coincident with the conception of the ultimately and absolutely real; but it is certainly a nearer approximation to this than any conception which we find set forth in the systems of the Ionic philosophers. The test of which is this: Suppose you had to explain something about the universe to an intelligence different from man's, unless that intelligence had senses similar to man's, he could
