The European Legacy 21 (5-6):535-555 (2016)

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The article explores the relationship between the philosopher and historian of mathematics Jacob Klein’s account of the transformation of the concept of number coincident with the invention of algebra, together with Husserl’s early investigations of the origin of the concept of number and his late account of the Galilean impulse to mathematize nature. Klein’s research is shown to present the historical context for Husserl’s twin failures in the Philosophy of Arithmetic: to provide a psychological foundation for the proper concept of number, and to show how this concept of number functions as the mathematical foundation of universal arithmetic. This context establishes that Husserl’s failures are ultimately rooted in the historical transformation of number documented in Klein’s research, from its premodern meaning as the unity of a multitude of determinate objects to its modern meaning as a symbolic representation with no immediate relation to a concrete multiplicity. The argum...
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DOI 10.1080/10848770.2016.1173480
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Phenomenology and the History of Science.Jacob Klein - 1940 - In Marvin Farber & Edmund Husserl (eds.), Philosophical Essays in Memory of Edmund Husserl. Cambridge: Mass., Published for the University of Buffalo by the Harvard University Press. pp. 143--163.
Alexandre KOYRÉ.[author unknown] - 1964 - Revue Philosophique de la France Et de l'Etranger 154:531-532.

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