Abstract
The well-known definition of the concept of number — as we may more briefly say in place of “whole number,” conforming to the common way of speaking — is: The number is a multiplicity of units. Since Euclid1 used it, this definition has returned again and again. Instead of “multiplicity,” the words “plurality,” “totality,” “aggregate,” “collection,” “group,” etc., are also used, all names of the same or almost the same signification, although not without appreciable nuances.2
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Notes
At the beginning of Book VII of the Elements.
Until explicitly indicated, we will refrain from excluding these nuances by using one of the names alone. The reasons why we prefer different names in different expositions (now “totality,” now “multiplicity” or “group”) will be explained later. see pp. 100, 146 and 155n.DW
De arte combinatoria (1666), Opera philosophica, Ed. J. E. Erdmann, Berlin 1840, p. 8.
An Essay Concerning Human Understanding, Book II, ch. XVI, sect. 1.
John Stuart Mill, A System of Logic, London 1970, Book III, ch. XXIV, §5. See also Book II, ch. IV, §7, where the character of number is deemed parallel to the physical characteristics of color, weight and extension. We frequently find analogous views also among mathematicians. Frege cites examples in his Grundlagen der Arithmetik, Breslau 1884, pp. 27ff.
Franz Brentano speaks here of “metaphysical” combination, and Carl Stumpf (Über den psychologischen Ursprung der Raumvorstellung, Leipzig 1873, p. 9) of the relationship of “psychological parts.”
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Husserl, E. (2003). The Origination of the Concept of Multiplicity Through that of the Collective Combination. In: Philosophy of Arithmetic. Edmund Husserl, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0060-4_2
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DOI: https://doi.org/10.1007/978-94-010-0060-4_2
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