On A Semantic Interpretation Of Kant's Concept Of Number
- Wing-Chun WongAffiliated withDepartment of Philosophy, Towson University
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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.
- On A Semantic Interpretation Of Kant's Concept Of Number
Volume 121, Issue 3 , pp 357-383
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- Wing-Chun Wong (1)
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- 1. Department of Philosophy, Towson University, Baltimore, MD, 21252, U.S.A.