Independence and Ignorance: How agnotology informs set-theoretic pluralism

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

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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.

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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.
Believing the axioms. II.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (3):736-764.
On the question of absolute undecidability.Peter Koellner - 2010 - In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Philosophia Mathematica. Association for Symbolic Logic. pp. 153-188.
Is the Dream Solution of the Continuum Hypothesis Attainable?Joel David Hamkins - 2015 - Notre Dame Journal of Formal Logic 56 (1):135-145.

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