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Collections as one-and-many—on the nature of numbers
Umeå University, Faculty of Arts, Department of historical, philosophical and religious studies.
2015 (English)In: Grazer Philosophische Studien, ISSN 0165-9227, E-ISSN 1875-6735, Vol. 91, no 1, p. 17-58Article in journal (Refereed) Published
Abstract [en]

Peter Simons has been rather alone in the modern philosophy of mathematics to argue that the natural numbers should be regarded as properties of multitudes or collections. This paper, however, sides with Simons, but it modifies his property view by adding the notion of imposed collection boundaries and accepting fictional collections. Although partly inspired by the Husserl of Philosophy of Arithmetic, Simons dismisses Husserl's talk of psychological acts of collective combination, but this paper saves them by dressing them in modern cognitive clothes. Hereby, a reasonable partially constructivist notion of the natural numbers emerges.

Place, publisher, year, edition, pages
BRILL ACADEMIC PUBLISHERS , 2015. Vol. 91, no 1, p. 17-58
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Philosophy
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URN: urn:nbn:se:umu:diva-138645ISI: 000211111800003OAI: oai:DiVA.org:umu-138645DiVA, id: diva2:1136074
Available from: 2017-08-25 Created: 2017-08-25 Last updated: 2018-06-09Bibliographically approved

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Johansson, Ingvar

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