V = Land Intuitive Plausibility in set Theory. A Case Study

Abstract

AbstractWhat 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 theaxiom of constructibility. I then formulate and discuss a view of intuitiveness in set theory that assumes it to hinge basically on mathematicalsuccess. At the same time, I present accounts of set theoretic axioms and theorems formulated in non-strictly mathematical terms, e.g., by appealing to theiterative conceptof set and/or to overall methodological principles, likeunifyandmaximize, and investigate the relation of the latter to success in mathematics.