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Algebraic generality versus arithmetic generality in the 1874 controversy between C. Jordan and L. Kronecker  

Frédéric Brechenmacher

Print publication date:
Jul 2016
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Jul 2017
This article revisits the 1874 controversy between Camille Jordan and Leopold Kronecker over two theorems, namely Jordan’s canonical forms and Karl Weierstrass’s elementary divisors ... More

Biological generality: general anatomy from Xavier Bichat to Louis Ranvier  

Jean- Gaël Barbara

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Jul 2016
Online publication date:
Jul 2017
This article examines generality in biology by focusing on two French schools of anatomy: the discipline of anatomie générale that was founded in France in 1800 by Xavier Bichat and the ... More

Elaboration of a statement on the degree of generality of a property: Poincaré’s work on the recurrence theorem  

Anne Robadey

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Jul 2016
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Jul 2017
This article examines the statement that a property is true for ‘almost all’ considered objects, in a precise mathematical sense, by referring to Henri Poincaré’s reflections on the ... More

Generality and structures in functional analysis: the influence of Stefan Banach  

Frédéric Jaëck

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Jul 2016
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Jul 2017
This article examines Stefan Banach’s contributions to the field of functional analysis based on the concept of structure and the multiply-flvored expression of generality that arises in ... More

Generality in Leibniz’s mathematics  

Eberhard Knobloch

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Jul 2016
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Jul 2017
This article discusses generality in Gottfried Leibniz’s mathematics. In principle, Leibnizian mathematics has a philosophical-theological basis. From the beginning everything that exists ... More

Generality, generalization, and induction in Poincaré’s philosophy  

Igor Ly

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Jul 2016
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Jul 2017
This article examines Henri Poincaré’s philosophical conceptions of generality in mathematics and physics, and more specifically his claim that induction in experimental physics does not ... More

Homology: an expression of generality in the life sciences  

Stéphane Schmitt

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Jul 2016
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Jul 2017
This article examines how the concept of homology is used as an expression of generality in the life sciences. Throughout its long history, homology expressed a quest for generality in the ... More

How general are genera? The genus in systematic zoology  

Yves Cambefort

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Jul 2016
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Jul 2017
This article examines how the genus category was perceived and conceived in zoology (with occasional references to botany), in reference to species on the one hand and to higher categories ... More

Leibnizian analysis, canonical objects, and generalization  

Emily Grosholz

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Jul 2016
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Jul 2017
This article examines Gottfried Leibniz’s notion of analysis by focusing on his investigation of transcendental curves. It argues that Leibnizian analysis can be understood as an art of ... More

Models, structure, and generality in Clerk Maxwell’s theory of electromagnetism  

Olivier Darrigol

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Jul 2016
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Jul 2017
This article examines the gradual development of James Clerk Maxwell’s electromagnetic theory, arguing that he aimed at general structures through his models, illustrations, formal ... More

Practices of generalization in mathematical physics, in biology, and in evolutionary strategies  

Evelyn Fox Keller

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Jul 2016
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Jul 2017
This article examines the different meanings as well as values associated with the mathematical and the biological sciences in relation to the kinds of generality favored by the ... More

The problem of a “general” theory in mathematics: Aristotle and Euclid  

David Rabouin

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Jul 2016
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Jul 2017
This article examines the so-called problem of generality in Euclid’s Elements. More specifically, it asks whether there is a ‘more general’ point of view from which magnitudes and numbers ... More

A process of generalization: Kummer’s creation of ideal numbers  

Jacqueline Boniface

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Jul 2016
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Jul 2017
This article examines Ernst Kummer’s creation of ideal factors, which provides an interesting example of generalization within the set of complex numbers. Kummer developed a theory of ... More

Prologue: generality as a component of an epistemological culture  

Karine Chemla, Renaud Chorlay, and David Rabouin

Print publication date:
Jul 2016
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Jul 2017
This book examines generality in mathematics and the sciences and how it has been shaped by actors, in part by introducing specific terminologies to distinguish between different levels or ... More

Questions of generality as probes into nineteenth-century mathematical analysis  

Renaud Chorlay

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Jul 2016
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Jul 2017
This article examines ways of expressing generality and epistemic configurations in which generality issues became intertwined with epistemological topics, such as rigor, or mathematical ... More

The role of genericity in the history of dynamical systems theory  

Tatiana Roque

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Jul 2016
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Jul 2017
This article examines the role of genericity in the development of dynamical systems theory. In his memoir ‘Sur les courbes définies par une équation différentielle’, published in four ... More

Universality versus generality: an interpretation of the dispute over tangents between Descartes and Fermat  

Evelyne Barbin

Print publication date:
Jul 2016
Online publication date:
Jul 2017
This article examines the ‘dispute over tangents’ between René Descartes and Pierre de Fermat, which began in 1638, by comparing their methods of constructing tangents. Descartes’s method ... More

The value of generality in Michel Chasles’s historiography of geometry  

Karine Chemla

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Jul 2016
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Jul 2017
This article discusses the value of generality in Michel Chasles’s historiography of geometry, articulated in his 1837 book Aperçu historique sur l’origine et le développement des méthodes ... More

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