V = L and intuitive plausibility in set theory. A case study

Bulletin of Symbolic Logic 17 (3):337-360 (2011)
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Abstract

What counts as an intuitively plausible set theoretic content (notion, axiom or theorem) has been a matter of much debate in contemporary philosophy of mathematics. In this paper I develop a critical appraisal of the issue. I analyze first R. B. Jensen's positions on the epistemic status of the axiom of constructibility. I then formulate and discuss a view of intuitiveness in set theory that assumes it to hinge basically on mathematical success. At the same time, I present accounts of set theoretic axioms and theorems formulated in non-strictly mathematical terms, e.g., by appealing to the iterative concept of set and/or to overall methodological principles, like unify and maximize, and investigate the relation of the latter to success in mathematics

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Citations of this work

Mathematics and Metaphilosophy.Justin Clarke-Doane - 2022 - Cambridge: Cambridge University Press.
Foundational Implications of the Inner Model Hypothesis.Tatiana Arrigoni & Sy-David Friedman - 2012 - Annals of Pure and Applied Logic 163 (10):1360-1366.

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References found in this work

The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
Philosophy of mathematics, selected readings.Paul Benacerraf & Hilary Putnam - 1966 - Revue Philosophique de la France Et de l'Etranger 156:501-502.
Iteration Again.George Boolos - 1989 - Philosophical Topics 17 (2):5-21.
Believing the Axioms. II.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (3):736-764.

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