The Elusive Distinction Between Mathematics and Natural Science

Michael D. Resnik

in Mathematics as a Science of Patterns

Published in print December 1999 | ISBN: 9780198250142
Published online November 2003 | e-ISBN: 9780191598296 | DOI:
 The Elusive Distinction Between Mathematics and Natural Science

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It is commonly believed that the epistemology of mathematics must be different from the epistemology of science because their objects are different in kind, i.e. metaphysically different. In this chapter, I want to suggest that some careful work must be done before we can take the distinction between physical and mathematical objects for granted. This distinction has traditionally been drawn by making reference to location, causal powers, detectability in principle, and change in properties. By analysing the ontology of theoretical physics, I wish to show that some physical objects, like quantum particles as they are described by D. Bohm, are as much mathematical as physical, for they do not seem to be located in space and time, and they are as incomplete as mathematical objects. The upshot of this discussion is to address those who are realists about physical objects and anti‐realists about mathematical objects, and, more importantly, to suggest that mathematical realists should not assume that a realist epistemology should be radically different from ordinary scientific epistemology.

Keywords: Bohm; detectability; epistemology; location; mathematical object; mathematical realism; physical object; quantum particles; quantum physics; science

Chapter.  4175 words. 

Subjects: Philosophy of Mathematics and Logic

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