Abstract
We provide infinitary proof theories for three common semantic theories of truth: strong Kleene, van Fraassen supervaluation and Cantinisupervaluation. The value of these systems is that they provide an easy method of proving simple facts about semantic theories. Moreover we shall show that they also give us a simpler understanding of the computational complexity of these definitions and provide a direct proof that the closure ordinal for Kripke’s definition is ωCK1. This work can be understood as an effort to provide a proof-theoretic counterpart to Welch’s game theoretic (Welch, 2009).
| Original language | English |
|---|---|
| Pages (from-to) | 207-235 |
| Number of pages | 29 |
| Journal | Review of Symbolic Logic |
| Volume | 8 |
| Issue number | 2 |
| Early online date | 8 Apr 2015 |
| DOIs | |
| Publication status | Published - Jun 2015 |
Bibliographical note
AcknowledgementsI would like to thank Philip Welch for his assistance and acknowledge the late Greg Hjorth for the time he spent in helping me learn how to use the tools used in the paper. I would also like to thank Hannes Leitgeb for giving me the
opportunity to present this material and for providing me with valuable feedback. And I would like to thank Benedict Eastaugh and Marcus Holland for helping make the final sections of this paper more accessible in the way it was intended.
Keywords
- Semantic Theories of Truth