THE EXPLANATORY INDISPENSAGBILITY ARGUMENT: A DEFENCE OF MATHEMATICAL PLATONISM
Vasiliy Dmitrievich Ershov
Ural Federal University named after the first President of Russia, Boris Yeltsin, Ekaterinburg, Russia
Keywords: the argument from the explanatory irreducibility of mathematics, new fictionalism, nominalist realism, mathematical platonism, mathematical fictionalism, mathematical structuralism
Abstract
The article examines one of the modern arguments in favor of mathematical platonism - the explanatory indispensability argument. The philosophical prerequisites for the formulation of this argument are considered, namely: the philosophical views of the late W.V.O. Quine and the mature H. Putnam, H. Field’s “Science without Numbers” and M. Balaguer’s “New Fictionalism”, with special attention paid to the analysis of the concept of “nominalist realism” of the latter. That “nominalist realism” not only does not correspond to the views of theoretical physicists and chemists, but also faces a number of philosophical problems, is shown by using examples from theoretical physics, chemistry, and biology.
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