David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 187 (2):489-508 (2012)
The traditional formulation of the indispensability argument for the existence of mathematical entities (IA) has been criticised due to its reliance on confirmational holism. Recently a formulation of IA that works without appeal to confirmational holism has been defended. This recent formulation is meant to be superior to the traditional formulation in virtue of it not being subject to the kind of criticism that pertains to confirmational holism. I shall argue that a proponent of the version of IA that works without appeal to confirmational holism will struggle to answer a challenge readily answered by proponents of a version of IA that does appeal to confirmational holism. This challenge is to explain why mathematics applied in falsified scientific theories is not considered to be falsified along with the rest of the theory. In cases where mathematics seemingly ought to be falsified it is saved from falsification, by a so called 'Euclidean rescue'. I consider a range of possible answers to this challenge and conclude that each answer fails
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References found in this work BETA
Bas C. Van Fraassen (1980). The Scientific Image. Oxford University Press.
W. V. Quine (1992). Pursuit of Truth. Harvard University Press.
Willard V. O. Quine (1951). Two Dogmas of Empiricism. Philosophical Review 60 (1):20–43.
Michael D. Resnik (1997). Mathematics as a Science of Patterns. New York ;Oxford University Press.
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