David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Philosophia Mathematica 9 (1):21-36 (2001)
This paper contains a defense against anti-realism in mathematics in the light both of incompleteness and of the fact that mathematics is a ‘cultural artifact.’. Anti-realism (here) is the view that theorems, say, of aritltmetic cannot be taken at face value to express true propositions about the system of numbers but must be reconstrued to be about somctliiiig else or about nothing at all. A ‘bite-the-bullet’ aspect of the defease is that, adopting new axioms, liitherto independent, is not. a matter of recognizing trutlis wliich had previoasly been unrecognized, but of extending the domain of what is true.
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Karin Katz & Mikhail Katz (2012). A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography. Foundations of Science 17 (1):51-89.
Sharon Berry (2014). Malament–Hogarth Machines and Tait's Axiomatic Conception of Mathematics. Erkenntnis 79 (4):893-907.
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