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V = L and Intuitive Plausibility in set Theory. A Case Study

Published online by Cambridge University Press:  15 January 2014

Tatiana Arrigoni
Tatiana Arrigoni*
Affiliation:
Fondazione Bruno Kessler, Povo- Via Sommarive 18, 1-38123 Trento, ItalyE-mail: [email protected]@istruzione.it
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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.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 17 , Issue 3 , September 2011 , pp. 337 - 360
Copyright
Copyright © Association for Symbolic Logic 2011

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