and deliberate matters date from the century of Galileo, when qualities which lend themselves to mathematical treatment were seized upon. "The most promising of these ideal systems at first were of course the richer ones, the sentimental ones. The baldest and least promising ones were the mathematical ones; but the history of the latter's application is a history of steadily advancing successes, while that of the sentimentally richer ones is one of relative sterility and failure."[9] There is no problem of why and how the plow fits, or applies to, the garden, or the watchspring to time-keeping. They were made for those respective purposes; the question is how well they do their work, and how they can be reshaped to do it better. Yet they were made out of physical material; men used ready limbs or roots of trees with which to plow before they used metal. We do not measure the worth or reality of the tool by its closeness to its natural prototype, but by its efficiency in doing its work--which connotes a great deal of intervening art. The theory proposed for mathematical distinctions and relations is precisely analogous. They are not the creations of mind except in the sense in which a telephone is a creation of mind. They fit nature because they are derived from natural conditions. Things naturally bulge, so to speak, and naturally alter. To seize upon these qualities, to develop them into keys for discovering the meanings of brute, isolated events, and to accomplish this effectively, to develop and order them till they become economical tools (and tools upon tools) for making an unknown and uncertain situation into a known and certain one, is the recorded triumph of human intelligence. The terms and propositions of mathematics are not fictions; they are not called into being by that particular act of mind in which they are used. No more is a self-binding reaper a figment, nor is it called momentarily into being by the man who wants to harvest his grain. But both alike are works of art, constructed for a purpose in doing the things which have to be done. We may say of terms what Santayana so happily said of expression: "Expression is a misleading term which suggests that something previously known is imitated or rendered; whereas the expression is itself an original fact, the values of which are then referred to the thing expressed, much as the honors of a Chinese mandarin are attributed retroactively to his parents." The natural history of imputation of virtue should prove to the philosopher a profitable theme. Even in its most superstitious forms (perhaps more _obviously_ in them than elsewhere) it testifies to the sense of a service to be performed and to a demand for application. The superstition lies in making the application to antecedents and to ancestors, where it is but a shroud, instead of to descendants, where it is a generating factor.