English translation of Moritz Pasch,“Der Begriff des Differentials,” Annalen der Philosophie und philosophischen Kritik4 (1924), pp. 161–187. Hans Vaihinger (co-founder of the Annalen der Philosophie) argued that various mathematical theories cannot be true because close inspection shows them to be absurd. Since Vaihinger recognized the utility of these theories, he confronted the problem of explaining how absurd theories can be useful. Pasch insists there is no need for such an explanation because the theories Vaihinger found absurd are, in fact, logically impeccable. To support this claim, Pasch offers a quick overview of the foundations of differential calculus and a more detailed analysis of Fermat’s rule for maxima and minima.
Instantaneous Velocity Function Difference Differential Calculus Function Differential Difference Quotient
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