Mathematics studies abstract patterns, either instantiated in structured system of things given to perception or in imagination, or freely invented and characterized axiomatically. The method of modern physics, which defines it, consists in studying the reality man perceives by means of abstract patterns extracted from it and idealized as mathematical patterns, which, then, can be freely extended. In this way, modern physics invites mathematics in. By an elaborate interplay between symbolic mathematics and creative semantics of mathematical systems, or by purely formal analogies between the mathematical surrogate science substitutes for perceptual reality and no matter which mathematical domain, mathematics manages to play a fundamental role in scientific heuristics. The mystery of the applicability of mathematics in empirical science is a consequence of the belief that physical and mathematical realities are two completely isolated and self-sufficient domains which can only communicate by mysterious means. Here, I strive to show that this belief is false.
Professor of Mathematics, Department of Mathematics, University of the State of São Paulo at Rio Claro, SP, BRAZIL. Member of the Centre for Logic, Epistemology and the History of Science (CLE), University of Campinas, Campinas, BRAZIL. Member of the Institute of Philosophy of the University of Lisbon, Portugal. Researcher of the National Council for Scientific Development (CNPq), Ministry of Science and Technology, BRAZIL. Chief-editor of Cahiers of History and Philosophy of Science, published by CLE.
Download Essay PDF File