My website has been acting up a bit, so it's been redesigned somewhat. That's finally allowed me to post a few new papers. These are:
- Self-Reference: The Meta-Mathematics of the Liar Paradox (PDF)
Central to the liar paradox is the phenomenon of 'self-reference'. The paradox typically begins with a sentence like:
(L): (L) is not true
Historically, doubts about the intelligibility of self-reference have been quite common. In some sense, though, these doubts were answered by Kurt Gödel's famous 'diagonal lemma'. This paper surveys some of the methods by which self-reference can be achieved, focusing first on purely syntactic methods before turning attention to the 'arithmetized' methods introduced by Gödel. It's primary lesson is that we need to be more careful than we usually have been about self-reference.
- Sense as Mode of Representation (PDF)
There are two main models for explaining Frege's notion of sense, both of which have their roots in the work of Sir Michael Dummett. One, nowadays most familiar from the work of David Chalmers, is broadly internalist and descriptivist in character. The other, most familiar from the work of Gareth Evans, is externalist and anti-descriptivist. I first consider the former project, arguing that Dummett anticipated Chalmers's version of the view, and that no version of this view is going to be defensible. The arguments are somewhat different from those familiar from the literature. I then consider Evans's view and argue that, while it is not vulnerable to many of the objections that have been made to it, it does not really succeed as an account of sense, because it forces us to abandon Frege's view that sense is an aspect of representational content.
I've also updated the paper "Chalmers on Analyticity and A Priority", which will now appear in my book Modes of Representation, and "Speaker's Reference, Semantic Reference, and Intuition", which will appear in expanded form in the same book.
