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 trains of abstracted thought and analyse and develop our imaginations ad infinitum. These speculations, however, were in the air or—what for these philosophers is much the same thing—in the mind; their applicability and their relevance to practical life and to objects given in perception remained quite problematical. A self-developing science, a synthetic science a priori, had a value entirely hypothetical and provisional; its practical truth depended on the verification of its results in some eventual sensible experience. Association was invoked to explain the adjustment of ideation to the order of external perception. Association, by which association by contiguity was generally understood, thus became the battle-cry of empiricism; if association by similarity had been equally in mind, the philosophy of pregnant reason could also have adopted the principle for its own. But logicians and mathematicians naturally neglect the psychology of their own processes and, accustomed as they are to an irresponsible and constructive use of the intellect, regard as a confused and uninspired intruder the critic who, by a retrospective and naturalistic method, tries to give them a little knowledge of themselves.

Rational ideas must arise somehow in the mind, and since they are not meant to be without application to the world of experience, it is interesting to discover the point of contact between the two and the nature of their interdependence.