Independence and Ignorance: How agnotology informs set-theoretic pluralism

Journal of the Indian Council of Philosophical Research 34 (2):399-413 (2017)
  Copy   BIBTEX

Abstract

Much of the discussion of set-theoretic independence, and whether or not we could legitimately expand our foundational theory, concerns how we could possibly come to know the truth value of independent sentences. This paper pursues a slightly different tack, examining how we are ignorant of issues surrounding their truth. We argue that a study of how we are ignorant reveals a need for an understanding of set-theoretic explanation and motivates a pluralism concerning the adoption of foundational theory.

Categories

Keywords

Reprint years

DOI

10.1007/s40961-017-0102-1

Links

PhilArchive

External links

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

Through your library

My notes

Similar books and articles

Set-theoretic pluralism and the Benacerraf problem.Justin Clarke-Doane - 2020 - Philosophical Studies 177 (7):2013-2030.
Set Theory and Structures.Neil Barton & Sy-David Friedman - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 223-253.
Set Theory and Structures.Sy-David Friedman & Neil Barton - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 223-253.
Categories in context: Historical, foundational, and philosophical.Elaine Landry & Jean-Pierre Marquis - 2005 - Philosophia Mathematica 13 (1):1-43.
Categories in Context: Historical, Foundational, and Philosophical &dagger.Elaine Landry & Jean-Pierre Marquis - 2005 - Philosophia Mathematica 13 (1):1-43.
Interview With a Set Theorist.Deborah Kant & Mirna Džamonja - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 3-26.
Criminally Ignorant – an invitation for broader evaluation.Mark Dsouza - 2021 - Jurisprudence 12 (2):226-235.
From Geometry to Geology: An Invitation to Mathematical Pluralism Through the Phenomenon of Independence.Jonas Reitz - 2017 - Journal of the Indian Council of Philosophical Research 34 (2):289-308.
Interview With a Set Theorist.Deborah Kant & Mirna Džamonja - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 3-26.
Roads to Mathematical Pluralism: Some Pointers.Amita Chatterjee - 2017 - Journal of the Indian Council of Philosophical Research 34 (2):209-225.

Analytics

Added to PP
2018-05-15

Downloads
316 (#66,972)

6 months
78 (#73,014)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Neil Barton
University of Oslo

Citations of this work

Independence Proofs in Non-Classical Set Theories.Sourav Tarafder & Giorgio Venturi - 2023 - Review of Symbolic Logic 16 (4):979-1010.

Add more citations

References found in this work

Realism in mathematics.Penelope Maddy - 1990 - New York: Oxford University Prress.
Set Theory.T. Jech - 2005 - Bulletin of Symbolic Logic 11 (2):243-245.
On the question of absolute undecidability.Peter Koellner - 2010 - In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: essays for his centennial. Ithaca, NY: Association for Symbolic Logic. pp. 153-188.
Believing the axioms. II.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (3):736-764.
Is the Dream Solution of the Continuum Hypothesis Attainable?Joel David Hamkins - 2015 - Notre Dame Journal of Formal Logic 56 (1):135-145.

Add more references