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.
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Wong, WC. On A Semantic Interpretation Of Kant's Concept Of Number. Synthese 121, 357–383 (1999). https://doi.org/10.1023/A:1005106218147
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DOI: https://doi.org/10.1023/A:1005106218147
Keywords
- Empirical Model
- Procedural Form
- Semantic Interpretation
- Representability Condition
- Counting Procedure