David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
George Bealer (1998). Analyticity. In Edward Craig (ed.), Routledge Encyclopedia of Philosophy. Routledge 234-9.
Kieran Setiya (2004). Transcendental Idealism in the 'Aesthetic'. Philosophy and Phenomenological Research 68 (1):63–88.
Beth Lord (2003). Kant's Productive Ontology: Knowledge, Nature and the Meaning of Being. Dissertation, University of Warwick
Verena Mayer (2003). Implicit Thoughts: Quine, Frege and Kant on Analytic Propositions. Grazer Philosophische Studien 66 (1):61-90.
Zvonimir Šikić (1996). What Are Numbers? International Studies in the Philosophy of Science 10 (2):159-171.
Zvonimir Šikić (1996). What Are Numbers? International Studies in the Philosophy of Science 10 (2):159 – 171.
Katherine Dunlop (2009). The Unity of Time's Measure: Kant's Reply to Locke. Philosophers' Imprint 9 (4):1-31.
Sacha Golob (2014). Kant on Intentionality, Magnitude, and the Unity of Perception. European Journal of Philosophy 22 (4):505-528.
William Blattner (1994). Is Heidegger a Kantian Idealist? Inquiry 37 (2):185 – 201.
Added to index2009-01-28
Total downloads23 ( #157,234 of 1,789,829 )
Recent downloads (6 months)2 ( #315,587 of 1,789,829 )
How can I increase my downloads?