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Mathematics and Reality$
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Mary Leng

Print publication date: 2010

Print ISBN-13: 9780199280797

Published to Oxford Scholarship Online: May 2010

DOI: 10.1093/acprof:oso/9780199280797.001.0001

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Explaining the Success of Mathematics

Explaining the Success of Mathematics

(p.217) 9 Explaining the Success of Mathematics
Mathematics and Reality

Mary Leng (Contributor Webpage)

Oxford University Press

This chapter considers how to choose between realism, mathematical fictionalism, and constructive empiricism as three different attitudes to our best scientific theories. It is argued that the choice should depend on consideration of which of these attitudes can best explain the predictive and explanatory successes of our scientific theories. While defenders of the ‘no miracles’ argument are correct in claiming that the predictive success of science as construed by constructive empiricism would be miraculous, they are mistaken in thinking that realism is the only alternative. Given their view of the nature of scientific theorizing, and the genesis of our scientific theories, mathematical fictionalists have at least as much reason as do realists for expecting those theories to be predictively successful. As for explanation, it is argued that mathematical posits do occur in scientific explanations, but that mathematical explanations can be explanatory without being true.

Keywords:   no miracles, explanation, prediction, success of science, realism, fictionalism, constructive empiricism

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