Note 3 — THE EVOLUTION OF THE SCIENTIFIC POINT OF VIEW[1]

A broad exception may perhaps be taken at this point, to the effect that this sketch of the growth of the scientific animus overlooks the science of the Ancients. The scientific achievements of classical antiquity are a less obscure topic to-day than ever before during modern times, and the more there is known of them the larger is the credit given them. But it is to be noted that, (a) the relatively large and free growth of scientific inquiry in classical antiquity is to be found in the relatively peaceable and industrial Greek communities (with an industrial culture of unknown pre-Hellenic antiquity), and (b) that the sciences best and chiefly cultivated were those which rest on a mathematical basis, if not mathematical sciences in the simpler sense of the term. Now, mathematics occupies a singular place among the sciences, in that it is, in its pure form, a logical discipline simply; its subject matter being the logic of quantity, and its researches being of the nature of an analysis of the intellect's modes of dealing with matters of quantity. Its generalisations are generalisations of logical procedure, which are tested and verified by immediate self-observation. Such a science is in a peculiar degree, but only in a peculiar degree, independent of the detail-discipline of daily life, whether technological or institutional; and, given the propensity—the intellectual enterprise, or "idle curiosity"—to go into speculation in such a field, the results can scarcely vary in a manner to make the variants inconsistent among themselves; nor need the state of institutions or the state of the industrial arts seriously color or distort such analytical work in such a field. Mathematics is peculiarly independent of cultural circumstances, since it deals analytically with mankind's native gifts of logic, not with the ephemeral traits acquired by habituation.