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“There is no inquiry which is not finally reducible to a question of number” wrote August Comte. However, the reader who has examined the first volume of this series and who leafs through the pages of this volume will find that, with some exceptions, the qualitative inquiry of modem mathematics itself is not always strictly reducible to a quantitative question of number. A greater effort is directed in modern mathematics toward structuring and characterizing systems than toward examining their quantitative implications. Either we must interpret Comte’s “question of number” as the logical ordering and description of the inquiry in a rigorous manner rather than its measurement, or we must conclude that perhaps in his day he could not comprehend what mathematics was to be about. Are the other sciences more susceptible to quantitative inquiry?
There is no more eloquent and symbolic monument than one constructed in the spirit of an age. We may hope that the lectures manifest this spirit and provide building stones for the monument of modern mathematics