J. M. Child on Gottfried Leibniz
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“Leibniz was certainly not alone among great men in presenting in his early work almost all the important mathematical ideas contained in his mature work.”
“The main ideas of his philosophy are to be attributed to his mathematical work, and not vice versa.”
“The manuscripts of Leibniz... show, perhaps more clearly than his published work, the great importance which Leibniz attached to suitable notation in mathematics and... in logic generally. He was perhaps the earliest to realize fully and correctly the important influence of a calculus [some mindless method of calculation] on discovery. ...There is a frivolous objection... to the effect that such economy of thought is an attempt to substitute unthinking mechanism for living thought. This contention fails... through the simple fact that this economy is only used in certain circumstances. In no science do we try to make subject to a mechanical calculus any trains of reasoning except such that have not been the object of careful thought many times previously. ...this reasoning has been universally recognized as valid, and we do not wish to waste energy of thought in repeating it when so much remains to be discovered by means of this energy. Since the time of Leibniz, this truth has been recognized, explicitly or implicitly, by all the greatest mathematical analysts.”