Kant's theory of arithmetic: A constructive approach? [Book Review]
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal for General Philosophy of Science 39 (2):245 - 271 (2008)
Kant’s theory of arithmetic is not only a central element in his theoretical philosophy but also an important contribution to the philosophy of arithmetic as such. However, modern mathematics, especially non-Euclidean geometry, has placed much pressure on Kant’s theory of mathematics. But objections against his theory of geometry do not necessarily correspond to arguments against his theory of arithmetic and algebra. The goal of this article is to show that at least some important details in Kant’s theory of arithmetic can be picked up, improved by reconstruction and defended under a contemporary perspective: the theory of numbers as products of rule following construction presupposing successive synthesis in time and the theory of arithmetic equations, sentences or “formulas”—as Kant says—as synthetic a priori. In order to do so, two calculi in terms of modern mathematics are introduced which formalise Kant’s theory of addition as a form of synthetic operation.
|Keywords||Kant Arithmetic Construction Numbers Time|
|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
J. Michael Dunn (1980). Quantum Mathematics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
Shmuel Lifsches & Saharon Shelah (1997). Peano Arithmetic May Not Be Interpretable in the Monadic Theory of Linear Orders. Journal of Symbolic Logic 62 (3):848-872.
H. Jerome Keisler (2006). Nonstandard Arithmetic and Reverse Mathematics. Bulletin of Symbolic Logic 12 (1):100-125.
Paul Anthony Wilson, Constructing Numbers Through Moments in Time: Kant's Philosophy of Mathematics.
Pirmin Stekeler-Weithofer (1987). Sind Die Urteile der Arithmetik Synthetisch a Priori? Journal for General Philosophy of Science 18 (1-2):215-238.
Richard Pettigrew (2009). On Interpretations of Bounded Arithmetic and Bounded Set Theory. Notre Dame Journal of Formal Logic 50 (2):141-152.
Added to index2009-01-31
Total downloads41 ( #44,906 of 1,101,944 )
Recent downloads (6 months)5 ( #68,246 of 1,101,944 )
How can I increase my downloads?