
Contents
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3.1 Introduction: “Everything is ruled by reason” 3.1 Introduction: “Everything is ruled by reason”
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3.2 Generality and harmony 3.2 Generality and harmony
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3.3 Generality and beauty 3.3 Generality and beauty
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3.4 Generality and conciseness/simplicity 3.4 Generality and conciseness/simplicity
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3.5 Generality and notation 3.5 Generality and notation
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3.5.1 The notation for determinants 3.5.1 The notation for determinants
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3.5.2 The products of power sums 3.5.2 The products of power sums
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3.6 Generality and utility/fecundity 3.6 Generality and utility/fecundity
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3.7 Generality and the laws of formation 3.7 Generality and the laws of formation
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3.7.1 The general canon of division 3.7.1 The general canon of division
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3.7.2 The determinants 3.7.2 The determinants
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3.8 Epilogue: the order of the disciplines in view of their generality 3.8 Epilogue: the order of the disciplines in view of their generality
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References References
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3 Generality in Leibniz’s mathematics
Get accessEberhard Knobloch is Professor of History of Science and Technology at the Technische Universität Berlin (TUB)
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Published:06 July 2017
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Abstract
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.
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