On a semantic interpretation of Kant's concept of number

Synthese 121 (3):357-383 (1999)
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.
Keywords Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
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DOI 10.1023/A:1005106218147
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