Mathematical Philosophy, a Study of Fate And Freedom; Lectures for Educated Laymen

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— ^As to its scientific importance, the task of show- S84 MATHEMATICAL PHILOSOPHY ing it is very easy if we take " scientific " in its stricter and narrower sense. We may go at once to the heart of the matter by reflecting a little upon the most rigorously scientific of scientific subjects and procedures — ^the Dif- ferential and Integral Calculus — rand upon its ramifications and its applications. Some of you have had a beginner's course in the calculus; others of you, not; I am not going to o...ffer here an introduction to it but will merely state succinctly, by way of reminder or of information, a few such facts respecting it as will make indubitable the great scientific importance of the term in question. One of the facts is that the Calculus is primarily and mainly concerned with what mathematicians call continuous functions (or variables), and that both functional con- tinuity and functional discontinuity, with which latter the calculus is also concerned, are not only defined by means of limits, but are indeed not otherwise definable.

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