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date: 18 December 2018

Abstract and Keywords

This article discusses generality in Gottfried Leibniz’s mathematics. In principle, Leibnizian mathematics has a philosophical-theological basis. From the beginning everything that exists is to be found in an orderly relation. The general and inviolable laws of the world are an ontological a priori. The universal harmony of the world consists in the largest possible variety being given the largest possible order so that the largest possible perfection is involved. After considering the relationship between the value of generality and the harmonies that are at the center of Leibniz’s concern, this article explores his view that generality implies beauty as well as conciseness and simplicity. It also examines how the interest in generality relates to notations, taking the examples of determinants and sums of powers, and to utility and fecundity. Finally, it demonstrates how generality is connected with laws of formation.

Keywords: generality, Gottfried Leibniz, mathematics, harmony, beauty, conciseness, simplicity, notation, utility, fecundity

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