Mathematical Demonstration and Experimental Activity: A Wittgensteinian Philosophy of Physics

Abstract

AbstractThis article aims at reducing the gap between mathematics and physics from a Wittgensteinian point of view. This gap is usually characterized by two discriminating features. (1) The propositions of physics assert something which might be false; they have a hypothetical character. On the contrary, since mathematical propositions are rules that condition the form of assertions, they remain immune from falsification. (2) The propositions of physics refer to facts that may confirm or refute them. On the contrary, since mathematical propositions have no meaning independently of the demonstration procedures, it cannot be said that they refer to “facts” that pre‐exist demonstrations. If we take a closer look, however, these two differences fade away. On the one hand, the propositions of physics are more resistant to experimental tests than has been said in the wake of logical positivism. On the other hand, the “factual” empirical material is defined and co‐constituted by instruments whose arrangement is determined by the theory to be tested (just as mathematical propositions are defined and co‐constituted by demonstration procedures). I conclude by discussing the possibility of a Wittgensteinian philosophy of contemporary physics.