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Mathematics and Scientific Representation$
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Christopher Pincock

Print publication date: 2012

Print ISBN-13: 9780199757107

Published to Oxford Scholarship Online: May 2012

DOI: 10.1093/acprof:oso/9780199757107.001.0001

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Constitutive Frameworks

Constitutive Frameworks

(p.121) 6 Constitutive Frameworks
Mathematics and Scientific Representation

Christopher Pincock

Oxford University Press

This chapter considers the proposals of Carnap, Kuhn and Michael Friedman to the effect that there is a special kind of constitutive representation against which more ordinary, derivative representations are successful. After criticizing Carnap’s and Kuhn’s positions, Pincock extracts a defensible claim from Friedman which links mathematics to a new sort of epistemic benefit. These arise when a belief in a set of representations is a necessary condition on confirming some associated set of derivative representations. This chapter concludes by considering the need for such representations and suggests that they are possible only if the relevant mathematics is largely justified prior to its use in science.

Keywords:   A priori, relative a priori, presupposition, linguistic frameworks, paradigms

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