The Life of Reason by George Santayana — Read

Empirical alloy in dialectic.

When a polyglot person is speaking, foreign words sometimes occur to him, which he at once translates into the language he happens to be using. Somewhat in the same way, when dialectic develops an idea, suggestions for this development may come from the empirical field; yet these suggestions soon shed their externality and their place is taken by some genuine development of the original notion. In constructing, for instance, the essence of a circle, I may have started from a hoop. I may have observed that as the hoop meanders down the path the roundness of it disappears to the eye, being gradually flattened into a straight line, such as the hoop presents when it is rolling directly away from me. I may now frame the idea of a mathematical circle, in which all diameters are precisely equal, in express contrast to the series of ellipses, with very unequal diameters, which the floundering hoop has illustrated in its career. When once, however, the definition of the circle is attained, no watching of hoops is any longer requisite. The ellipse can be generated ideally out of the definition, and would have been generated, like asymptotes and hyperbolas, even if never illustrated in nature at all. Lemmas from a foreign tongue have only served to disclose a great fecundity in the native one, and the legitimate word that the context required has supplanted the casual stranger that may first have ushered it into the mind.