V = L and intuitive plausibility in set theory. A case study
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.
Permanent link to this document: http://projecteuclid.org/euclid.bsl/1309952317
Digital Object Identifier: doi:10.2178/bsl/1309952317
Zentralblatt MATH identifier: 05956502
Mathematical Reviews number (MathSciNet): MR2856077