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

Bulletin of Symbolic Logic 17 (3):337-360 (2011)
  Copy   BIBTEX

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

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Analytics

Added to PP
2011-07-07

Downloads
161 (#110,107)

6 months
3 (#445,838)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

Mathematics and Metaphilosophy.Justin Clarke-Doane - 2022 - Cambridge: Cambridge University Press.
Foundational implications of the inner model hypothesis.Tatiana Arrigoni & Sy-David Friedman - 2012 - Annals of Pure and Applied Logic 163 (10):1360-1366.

Add more citations

References found in this work

The iterative conception of set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
Philosophy of mathematics, selected readings.Paul Benacerraf & Hilary Putnam - 1966 - Revue Philosophique de la France Et de l'Etranger 156:501-502.
Iteration Again.George Boolos - 1989 - Philosophical Topics 17 (2):5-21.
Believing the axioms. II.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (3):736-764.

View all 16 references / Add more references