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On a semantic interpretation of Kant's concept of number

Wing-Chun Wong

pp. 357-383

Abstract

What is central to the progression of a sequence is the idea of succession, which is fundamentally a temporal notion. In Kant's ontology numbers are not objects but rules (schemata) for representing the magnitude of a quantum. The magnitude of a discrete quantum 11...11 is determined by a counting procedure, an operation which can be understood as a mapping from the ordinals to the cardinals. All empirical models for numbers isomorphic to 11...11 must conform to the transcendental determination of time-order. Kant's transcendental model for number entails a procedural semantics in which the semantic value of the number-concept is defined in terms of temporal procedures. A number is constructible if and only if it can be schematized in a procedural form. This representability condition explains how an arbitrarily large number is representable and why Kant thinks that arithmetical statements are synthetic and not analytic.

Publication details

Published in:

(1999) Synthese 121 (3).

Pages: 357-383

DOI: 10.1023/A:1005106218147

Full citation:

Wong Wing-Chun (1999) „On a semantic interpretation of Kant's concept of number“. Synthese 121 (3), 357–383.