Mathematical Demonstration and Experimental Activity: A Wittgensteinian Philosophy of Physics

Mathematical Demonstration and Experimental Activity: A Wittgensteinian Philosophy of Physics The purpose of this paper is to sketch a philosophy of physics in the spirit of Wittgenstein (though not a strictly Wittgensteinian philosophy of physics). A preliminary step is provided by some remarks on the relations between the Wittgensteinian conception of mathematics and the contemporary philosophy of physics.My first remark bears on the difference between mathematical propositions and factual propositions. At first glance, imposing a radical distinction between these two kinds of propositions is an inescapable feature of Wittgenstein's philosophy of mathematics. In his book Le pays des possibles, Jacques Bouveresse points out that if we do not keep this distinction between factual propositions and mathematical propositions in mind, we simply cannot understand Wittgenstein's insistence on the conceptual gulf between conjectures and demonstrations. In mathematics, it is demonstration, and demonstration alone, that gives meaning to the demonstrated proposition; by contrast, according to Wittgenstein, a conjecture is only “(…) a signpost for mathematical research, and an incentive for mathematical construction”. Since, in mathematics, a proposition has no meaning independent of the demonstration which leads to it, then in no case can one say that a conjecture and a demonstration point to the same pre‐existing “fact”; in no case can we http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Philosophical Investigations Wiley

Mathematical Demonstration and Experimental Activity: A Wittgensteinian Philosophy of Physics

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Publisher
Wiley
Copyright
Copyright © 2018 John Wiley & Sons Ltd
ISSN
0190-0536
eISSN
1467-9205
D.O.I.
10.1111/phin.12187
Publisher site
See Article on Publisher Site

Abstract

The purpose of this paper is to sketch a philosophy of physics in the spirit of Wittgenstein (though not a strictly Wittgensteinian philosophy of physics). A preliminary step is provided by some remarks on the relations between the Wittgensteinian conception of mathematics and the contemporary philosophy of physics.My first remark bears on the difference between mathematical propositions and factual propositions. At first glance, imposing a radical distinction between these two kinds of propositions is an inescapable feature of Wittgenstein's philosophy of mathematics. In his book Le pays des possibles, Jacques Bouveresse points out that if we do not keep this distinction between factual propositions and mathematical propositions in mind, we simply cannot understand Wittgenstein's insistence on the conceptual gulf between conjectures and demonstrations. In mathematics, it is demonstration, and demonstration alone, that gives meaning to the demonstrated proposition; by contrast, according to Wittgenstein, a conjecture is only “(…) a signpost for mathematical research, and an incentive for mathematical construction”. Since, in mathematics, a proposition has no meaning independent of the demonstration which leads to it, then in no case can one say that a conjecture and a demonstration point to the same pre‐existing “fact”; in no case can we

Journal

Philosophical InvestigationsWiley

Published: Jan 1, 2018

References

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