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Mathematics as a Science of Patterns$
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Michael D. Resnik

Print publication date: 1999

Print ISBN-13: 9780198250142

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198250142.001.0001

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Holism: Evidence in Science and Mathematics

Holism: Evidence in Science and Mathematics

(p.112) 7 Holism: Evidence in Science and Mathematics
Mathematics as a Science of Patterns

Michael D. Resnik (Contributor Webpage)

Oxford University Press

I present a theory of justification for mathematical beliefs that is both non‐foundationalist, in that it claims that some mathematics must be justified indirectly in terms of its consequences, and holistic, in that it maintains that no claim of theoretical science can be confirmed or refuted in isolation but only as a part of a system of hypotheses. Our evidence for mathematics is ultimately empirical because the mathematics that is part of theoretical science, is, in principle, revisable in light of experience and confirmed by experience. Following Henry Kyburg, I develop this idea by claiming that in science we use combinations of mathematical and scientific principles to develop models (mini‐theories) that allow us to calculate values that we then compare with the data. ‘Separatists’ objections to holism revolve around the claim that holism fails to respect our intuitions about mathematics, e.g. that mathematics is clearly distinct from science and that mathematical evidence comes from proofs, rather than from experience. My response to these objections is that holism can accommodate these intuitions by appealing to pragmatic rationality that, on the one hand, underwrites the special role of mathematics and bids us to treat it as if it were a priori, and, on the other, justifies, on the grounds of simplicity and success, a local conception of evidence according to which data can confirm specific hypotheses.

Keywords:   confirmation, empirical, evidence, holism, indirect justification, Kyburg, mathematical realism, models, non‐foundationalism, pragmatism, separatists

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