Independence and Ignorance: How agnotology informs set-theoretic pluralism

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
Universität Konstanz

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What is Cantor's Continuum Problem?S. C. Kleene - 1948 - Journal of Symbolic Logic 13 (2):116-117.

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