Kant's Conception of Number

Bibliographic Data

ID10692679
AuthorsDaniel Sutherland (0000-0002-3529-6943, University of Illinois Chicago, corresponding author)
Year2017
Volume126
Issue2
Pages147-190
Publication date2017-04-01
Peer ReviewedYes
Open AccessNo
TypeARTICLE
VenueThe Philosophical Review (JOURNAL)
Journal identifiersISSN: 0031-8108 • E-ISSN: 1558-1470
PublisherDuke University Press (PUBLISHER • US)
DOI10.1215/00318108-3771988
OpenAlexW2606747463
LanguageEN
Citations received3
References cited21

Despite the importance of Kant's claims about mathematical cognition for his philosophy as a whole and for subsequent philosophy of mathematics, there is still no consensus on his philosophy of arithmetic, and in particular the role he assigns intuition in it. This inquiry sets aside the role of intuition for the nonce to investigate Kant's conception of natural number. Although Kant himself doesn't distinguish between a cardinal and an ordinal conception of number, some of the properties Kant attributes to number can be characterized as cardinal or ordinal. This essay argues that Kant's conception of number includes both cardinal and ordinal elements; it suggests that the cardinal elements provide the basis of a conception of number in general, while the ordinal elements contribute to specifying the exact size of particular collections. In considering these elements, roles for intuition begin to emerge, setting the stage for a reevaluation of the role of intuition in Kant's arithmetic

Analytic philosophy · Cardinal number (linguistics) · Contemporary philosophy · Epistemology · Intuition · Linguistics · Philosophy of Mathematics · Philosophy of science · Historical Philosophy and Science · Mathematics · Philosophical Ethics and Theory · Philosophy · Philosophy and Theoretical Science