Tuesday, May 10, 2016

Mathematical pluralism

Scientific pluralism should apply to mathematics too. There is not one kind of geometry, there are many: Euclidean, non-Euclidean, projective, inversive, differential... There is not one set theory, there are many, each defined by different axioms.  There is not one formal logic, there are many: propositional logic, predicate logic, spatial logic, temporal logic, second order logic, ...  There is not one system of mathematics, there are many. (See Where Mathematics Comes From, Lakoff and Nunez, Basic Books, 2000 and Complementarity in Mathematics, Kuyk, Reidel Publishing, 1977)

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