Mathematics Dealing with 'Hypothetical States of Things'

Philosophia Mathematica 22 (2):209-230 (2014)
  Copy   BIBTEX

Abstract

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

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,271

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Peirce on the role of poietic creation in mathematical reasoning.Daniel G. Campos - 2007 - Transactions of the Charles S. Peirce Society 43 (3):470 - 489.
Realism in mathematics.Penelope Maddy - 1990 - New York: Oxford University Prress.
Peirce, fallibilism, and the science of mathematics.Elizabeth F. Cooke - 2003 - Philosophia Mathematica 11 (2):158-175.
The language of nature is mathematics—but which mathematics? And what nature?Lawrence Sklar - 1998 - Proceedings of the Aristotelian Society 98 (3):241–261.
Constructibility and mathematical existence.Charles S. Chihara - 1990 - New York: Oxford University Press.
Mathematical necessity and reality.James Franklin - 1989 - Australasian Journal of Philosophy 67 (3):286 – 294.
The principles of mathematics revisited.Jaakko Hintikka - 1996 - New York: Cambridge University Press.

Analytics

Added to PP
2014-02-02

Downloads
37 (#414,383)

6 months
4 (#754,937)

Historical graph of downloads
How can I increase my downloads?

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.

View all 27 references / Add more references