Last weekend, I gave a talk at a philosophy of mathematics conference up in St Andrews: the Arche "Status Belli" conference. The conference marked the end of a major AHRC-funded project on the philosophy of mathematics at the Arche centre. I was a PhD student within that project for many years, and though I kept getting distracted into other areas (notably the other Arche projects, in Vagueness and Modality), it has a great big place in my heart. One thing I note with approval: Arche PhD students now seem to be doing loads of (linguistics-informed) philosophy of language. Since Herman Cappelan has just been appointed to a professorship there, no doubt this will continue. In my time, the centre was dominated by phil logic, epistemology and metaphysics: as my interests run centrally to phil language (as well as phil logic and metaphysics), I heartily approve of the current emphasis!
Working in the project was a really great experience, and seems to have been an objective success, to judge by all the philosophy that came out of it. It certainly gave me an appreciation of how much sheer work there is to be done in philosophy: the whole of philosophy exists in microcosm in a well-chosen problem. Over the years, the project got me working and thinking about the theory of truth and liar-like paradoxes, higher-order and plural logics, issues in the epistemology of basic knowledge and their relation to skepticism, Quinean and rival takes on ontological commitment, metaphysics of abstract objects, the applicability of mathematics, and (what I ended up writing my thesis on) the putative determinacy of reference and arguments for various forms of inscrutability.
Anyway, my paper at the conference was on the issue that I had intended to work on when I first arrived at St Andrews: the philosophy of the complex numbers, neofregean treatments of them and special issues of determinacy of reference that arise.
Following the conference, Agustin Rayo who was giving also giving a talk at the conference, travelled down to Leeds, presenting a paper drawn from his current project "On specifying content". The basic idea is that we should distinguish between the metalinguistic resources we need in order to give a (systematic, compositional) specification of the content of some belief (about the number of planets, or macroscopic objects, or higher-order quantification, or whatever) and the ontological/other commitments we build into the content as a prerequist for that content being true at a world. He gives a really detailed treatment of how this might work.
I think this stuff looks really exciting, with potential applications all over the place (for example, as I read him, Joseph Melia has been arguing for a while that something like the expressive resources/metaphysical demands distinction is crucial in a series of debates in modality, philosophy of mathematics, and elsewhere). I'm hoping to get to grips with it well enough to present and evaluate an application of it to defend mereological nihilism in the upcoming Structure in Metaphysics event here in Leeds.