Formal systems as physical objects: A physicalist account of mathematical truth

International Studies in the Philosophy of Science 17 (2):117-125 (2003)
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Abstract

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

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Citations of this work

Instability, Modus Ponens and Uncertainty of Deduction.Huajie Liu - 2006 - Frontiers of Philosophy in China 1 (4):658-674.
Intrinsic, Extrinsic, and the Constitutive A Priori.László E. Szabó - 2020 - Foundations of Physics 50 (6):555-567.
Some Remarks on the Physicalist Account of Mathematics.Ferenc Csatári - 2012 - Open Journal of Philosophy 2 (2):165.

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References found in this work

Language, Truth, and Logic.Alfred Jules Ayer - 1936 - London, England: Dover Publications.
Language, Truth and Logic. 2nd edition.A. J. Ayer - 1952 - Revue Philosophique de la France Et de l'Etranger 142:256-256.

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