Infinitary Tableau for Semantic Truth

Acknowledgements I 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.Peer reviewedPostprin

Unpicking Priest's Bootstraps

Date of Acceptance: 13/07/2015Peer reviewedPostprin

Computation in non-classical foundations?

The Church-Turing Thesis is widely regarded as true, because of evidence that there is only one genuine notion of computation. By contrast, there are nowadays many different formal logics, and different corresponding foundational frameworks. Which ones can deliver a theory of computability? This question sets up a difficult challenge: the meanings of basic mathematical terms (like "set", "function", and "number") are not stable across frameworks. While it is easy to compare what different frameworks say, it is not so easy to compare what they mean. We argue for some minimal conditions that must be met if two frameworks are to be compared; if frameworks are radical enough, comparison becomes hopeless. Our aim is to clarify the dialectical situation in this bourgeoning area of research, shedding light on the nature of non-classical logic and the notion of computation alike

Proceedings of Patient Reported Outcome Measure’s (PROMs) Conference Oxford 2017: Advances in Patient Reported Outcomes Research

A33-Effects of Out-of-Pocket (OOP) Payments and Financial Distress on Quality of Life (QoL) of People with Parkinson’s (PwP) and their Carer

Fixed Points for Consequence Relations

Peer reviewedPublisher PD

Naive Infinitism : The Case for an Inconsistency Approach to Infinite Collections

Peer reviewedPostprin

Truth, dependence and supervaluation: living with the ghost

In J Philos Logic 34:155-192, 2005, Leitgeb provides a theory of truth which is based on a theory of semantic dependence. We argue here that the conceptual thrust of this approach provides us with the best way of dealing with semantic paradoxes in a manner that is acceptable to a classical logician. However, in investigating a problem that was raised at the end of J Philos Logic 34:155-192, 2005, we discover that something is missing from Leitgeb's original definition. Moreover, we show that once the appropriate repairs have been made, the resultant definition is equivalent to a version of the supervaluation definition suggested in J Philos 72:690-716, 1975 and discussed in detail in J Symb Log 51(3):663-681, 1986. The upshot of this is a philosophical justification for the simple supervaluation approach and fresh insight into its workings