David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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International Studies in the Philosophy of Science 17 (2):117-125 (2003)
This article is a brief formulation of a radical thesis. We start with the formalist doctrine that mathematical objects have no meanings; we have marks and rules governing how these marks can be combined. That's all. Then I go further by arguing that the signs of a formal system of mathematics should be considered as physical objects, and the formal operations as physical processes. The rules of the formal operations are or can be expressed in terms of the laws of physics governing these processes. In accordance with the physicalist understanding of mind, this is true even if the operations in question are executed in the head. A truth obtained through (mathematical) reasoning is, therefore, an observed outcome of a neuro-physiological (or other physical) experiment. Consequently, deduction is nothing but a particular case of induction
|Keywords||physicalism philosophy of mathematics formalism|
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References found in this work BETA
Mark Steiner (1998). The Applicability of Mathematics as a Philosophical Problem. Harvard University Press.
A. J. Ayer (1952). Language, Truth and Logic. 2nd edition. Revue Philosophique de la France Et de l'Etranger 142:256-256.
Thomas Tymoczko (1979). The Four-Color Problem and its Philosophical Significance. Journal of Philosophy 76 (2):57-83.
Citations of this work BETA
Ferenc Csatari (2012). Some Remarks on the Physicalist Account of Mathematics. Open Journal of Philosophy 2 (2):165.
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László E. Szabó (2003). Formal Systems as Physical Objects: A Physicalist Account of Mathematical Truth. International Studies in the Philosophy of Science 17 (2):117 – 125.
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