Mathematics Dealing with 'Hypothetical States of Things'

Philosophia Mathematica 22 (2):209-230 (2014)
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This paper takes as a starting point certain notions from Peirce's writings and uses them to propose a picture of the part of mathematical practice that consists of hypothesis formation. In particular, three processes of hypothesis formation are considered: abstraction, generalisation, and an abductive-like inference. In addition Peirce's pragmatic conception of truth and existence in terms of higher-order concepts are used in order to obtain a kind of pragmatic realist picture of mathematics



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References found in this work

The nature of mathematical knowledge.Philip Kitcher - 1983 - Oxford: Oxford University Press.
Collected papers.Charles S. Peirce - 1931 - Cambridge,: Belknap Press of Harvard University Press.
Realism in mathematics.Penelope Maddy - 1990 - New York: Oxford University Prress.
Philosophy of mathematics: structure and ontology.Stewart Shapiro - 1997 - New York: Oxford University Press.
Naturalism in mathematics.Penelope Maddy - 1997 - New York: Oxford University Press.

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