Bulletin of Symbolic Logic

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

Tatiana Arrigoni

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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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Bull. Symbolic Logic Volume 17, Issue 3 (2011), 337-360.

First available in Project Euclid: 6 July 2011

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Arrigoni, Tatiana. V = L and intuitive plausibility in set theory. A case study. Bull. Symbolic Logic 17 (2011), no. 3, 337--360. doi:10.2178/bsl/1309952317. https://projecteuclid.org/euclid.bsl/1309952317

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