The Quest for Certainty: A Study of the Relation of Knowledge and Action

By John Dewey | Go to book overview

CHAPTER VI
THE PLAY OF IDEAS

THE PROBLEM OF the nature, office and test of ideas is not exhausted in the matter of physical conceptions we have discussed in the preceding chapter. Mathematical ideas are indispensable instruments of physical research, and no account of the method of the latter is complete that does not take into account the applicability of mathematical conceptions to natural existence. Such ideas have always seemed to be the very type of pure conceptions, of thought in its own nature unadulterated with material derived from experience. To a constant succession of philosophers, the röle of mathematics in physical analysis and formulation has seemed to be a proof of the presence of an invariant rational element within physical existence, which is on that account something more than physical; this räle of conceptions has been the stumbling block of empiricists in trying to account for science on an empirical basis.

The significance of mathematics for philosophy is not confined to this seemingly superphysical phase of the physical world, and a superempirical factor in knowledge of it. Mathematical conceptions as expressions of pure thought have also seemed to provide the open gateway to a realm of essence that is independent of existence, physical or mental -- a self-subsisting realm of ideal and eternal objects which are the objects of the highest -- that is, the most assured -- knowledge. As was earlier noted, the Euclidean geometry was undoubtedly the pattern for the development of a formally rational logic; it was also a marked factor in leading Plato to his doctrine of a

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