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

Bulletin of Symbolic Logic 17 (3):337-360 (2011)
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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DOI 10.2178/bsl/1309952317
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References found in this work BETA
The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229-308.
The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
Reason and Intuition.Charles Parsons - 2000 - Synthese 125 (3):299-315.

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Citations of this work BETA
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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