reasearch

My PhD, based in the Cambridge Philosophy Faculty, is funded through a Pigott Studentship and supervised by Prof Michael Potter and Dr Michael Gabbay.

The project, sitting mostly in philosophical logic and the philosophy of logic, focuses on the relationship between dialetheism (the view that there are true contradictions) and how (interpreted) logical systems handle contradictions.

One issue I am interested in concerns which logic a dialetheist may legitimately endorse. I’m particularly interested in the extent to which there can be a rapprocehment between dialetheism and classical consequence (which is normally thought to trivialise contradiction). The possibility of this is suggested by what I call ’extensionally classical inconsistency-tolerant’ (XCIT) logics, which, while they agree with classical logic about validity, do not trivialise contradiction. Two issues that arise in the context of this ‘classical dialetheism’ are:

• Normativity. How can a classical-strength logic adequately govern attitudes or commitments which are permitted to have inconsistent content? (For example, while explosion—from a contradiction anything follows—is valid, explosive reasoning is not in general permissible.)
• Transitivity. The XCIT logics I’m interested in place restrictions on the transitivity of consequence; in certain circumstances, A can entail B and B entail C without A entailing C. This is quite counterintuitive. How do we make sense of this, and how problematic, if at all, is it?

Another issue I’m thinking about is the relation between dialetheism and logic itself. In particular, as well as endorsing an inconsistency-tolerant logic, some dialetheists also endorse an inconsistency-tolerant metatheory (i.e. they characterise their preferred logic within an inconsistency-tolerant theory). Some questions here:

• How strong are the reasons for a dialetheist to endorse an inconsistency-tolerant metatheory?
• What does this tell us about satisfaction and validity? Can these notions coherently be given their intended meaning in such a context?
• Could logic itself be inconsistent?

I also have broader philosophical interest in philosophical logic, philosophy of language, philosophy of religion, and value theory.