Synthese 193 (3):937-969 (2016)
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Abstract |
The paper traces the development and the role of syntactic reduction in Edmund Husserl’s early writings on mathematics and logic, especially on arithmetic. The notion has its origin in Hermann Hankel’s principle of permanence that Husserl set out to clarify. In Husserl’s early texts the emphasis of the reductions was meant to guarantee the consistency of the extended algorithm. Around the turn of the century Husserl uses the same idea in his conception of definiteness of what he calls “mathematical manifolds.” The paper argues that the notion anticipates the notion of reduction in term rewrite theory in computer science. The role of the reduction for Husserl is, however, primarily epistemological: its purpose is to impart clarity to formal mathematics
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Keywords | Husserl Hermann Hankel Principle of permanence Equational computation Term rewriting Definite manifolds |
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DOI | 10.1007/s11229-015-0779-0 |
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References found in this work BETA
Formal and Transcendental Logic.A Study of Husserl's Formal and Transcendental Logic.Edmund Husserl - 1969 - The Hague: Martinus Nijhoff.
Logic and Philosophy of Mathematics in the Early Husserl.Stefania Centrone - 2009 - Dordrecht, Netherland: Springer.
Formalism.Michael Detlefsen - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press. pp. 236--317.
Logic and the Objectivity of Knowledge: A Study of Husserl's Early Philosophy.Robert S. Tragesser - 1984 - Philosophical Review 95 (4):611-614.
Towards Completeness: Husserl on Theories of Manifolds 1890–1901.Mirja Helena Hartimo - 2007 - Synthese 156 (2):281-310.
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Citations of this work BETA
Maddy On The Multiverse.Claudio Ternullo - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Berlin: Springer Verlag. pp. 43-78.
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