My main research focus has been into the Liar Paradox and Formal Definitions of the Truth Predicate. The results of this research are a method by which a consistent Formal Truth definition can be provided for any reasonable formal logic. This research forms the basis of my PhD Thesis, which is available from the ANU Digital Theses Collection. I intend to post a detailed summary of the argument of my Thesis and my proposed Truth Definition in the near future. In the meantime, there is a limited two page summary available.

Another topic that has caught my attention came out of the Workshop on Truth Values in Dresden. I was intrigued by one of the recurring questions in the discussion: What actually is a Truth Value? Somewhat strangely there has not been much philosophical discussion of this point. I developed an answer to the question based on an analogy between Truth Values and the mathematical values returned by measurement. A draft of my paper on the topic can be found here. Any comments are welcome.

A common topic in the literature on the Liar Paradox is whether we should accept the Principle of Non-Contradiction. I have been working on a different argument in favour of rejecting the validity of true contradictions on the basis of the pragmatic consequences that arise. An early draft should be available here sometime soon.

I was supported by the Deutsche Akademischer Austausch Dienst to research the relationship between Semantic Presuppositions and Compositionality. My central result is that if we accept the existence of Semantic Presuppositions, then we must either reject a strictly compositional semantics, or accept that Meanings are not atomic but contain (in some cases) uneliminable internal structure. A draft of my argument will be posted when available.

### Tags

concept of truth connectives consistency formal languages formal semantics logic meaning natural languages reasoning Tarski truth