EPISTLE LXXXVIII.
aid us and yet are not parts of ourselves. Nay, if they were, they would not aid us. Food is an aid to the body, but is not a part of it. We get some help from the service which mathematics renders; and mathematics is as indispensable to philosophy as the carpenter is to the mathematician. But carpentering is not a part of mathematics, nor is mathematics a part of philosophy. 26. Moreover, each has its own limits; for the wise man investigates and learns the causes of natural phenomena, while the mathematician follows up and computes their numbers and their measurements.[1] The wise man knows the laws by which the heavenly bodies persist, what powers belong to them, and what attributes; the astronomer merely notes their comings and goings, the rules which govern their settings and their risings, and the occasional periods during which they seem to stand still, although as a matter of fact no heavenly body can stand still. 27. The wise man will know what causes the reflection in a mirror; but, the mathematician can merely tell you how far the body should be from the reflection, and what shape of mirror will produce a given reflection.[2] The philosopher will demonstrate that the sun is a large body, while the astronomer will compute just how large, progressing in knowledge by his method of trial and experiment; but in order to progress, he must summon to his aid certain principles. No art, however, is sufficient unto itself, if the foundation upon which it rests depends upon mere favour. 28. Now philosophy asks no favours from any other source; it builds everything on its own soil; but the science of numbers is, so to speak, a structure built on another man’s land—it builds on alien soil.[3] It accepts first principles, and by their
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