Lecture
LTP Colloquium "Bivalence, Fidelity, and Large-Cardinal Reflection: Variations on a Kreiselian Theme"
- Date
- Thursday 5 November 2026
- Time
- Location
-
P.J. Veth
Nonnensteeg 1-3
2311 VJ Leiden - Room
- 0.06
The Leiden University Centre Theoretical Philosophy is pleased to announce a lecture by Dr. Beau Madison Mount, associate professor and Sir Peter Strawson Fellow in Philosophy, University College Oxford.
Abstract
The continuum hypothesis (CH) is the claim that there exist no cardinalities strictly between that of the natural numbers and that of the real numbers. It is neither provable nor refutable from the axioms of standard Zermelo-Fraenkel set theory with choice (ZFC) (Gödel 1938; Cohen 1960). Even adding large cardinal axioms—principles about the size of the universe stronger than ZFC—can do nothing to resolve CH (Lévy and Solovay 1967).
In an influential essay, Georg Kreisel (1967) argued that CH nonetheless has a determinate truth value: either CH is true or CH is false, regardless of whether we have any means of knowing which. Part of the interest of Kreisel's argument is that it relies on distinctively mathematical considerations relating to second-order set theory, rather than the general theses about logic that ordinarily feature in global arguments for bivalence (e.g., Williamson 1994; Andjelković and Williamson 2000). As such, Kreisel's argument is potentially dialectically persuasive even for those who reject the global arguments.
In this talk, I reconstruct Kreisel's argument in detail, clarify its dialectical purchase, and explain the key role played by a fidelity-to-truth thesis—a thesis connecting truth-in-a-model for a privileged class of models with truth simpliciter. I then discuss ways to generalize the argument: I contend that the ideas behind reflection principles (the standard informal motivation for large cardinal axioms) motivate stronger fidelity-to-truth theses, yielding an argument that bivalence obtains for a swathe of important statements in set theory (although not for the entire language).
All are welcome!