I'm going to live up to the blogger stereotype and set a few posts on autofocus. The shameless project is to make the case that you might have good reason to read The Rules of Thought, the book that Benjamin Jarvis and I recently wrote. (OUP catalogue page) (my webpage)
I think that there are three possible hooks into our project. One of them -- the one that represented our own way into the project -- concerns the epistemology of the a priori in general, and the epistemology of philosophy in particular. Ben and I trace this interest pretty specifically to 2005, when, while PhD students at Brown, we took Joshua Schechter's seminar on the a priori, and also attended Timothy Williamson's Blackwell-Brown lectures, which eventually became The Philosophy of Philosophy. We were attracted by traditional idea that in many paradigmatic instances, philosophical investigation proceeded in some important sense independently from experience, but came to appreciate that (a) there were deep mysteries concerning the explanation for how this could be, and (b) there were strong challenges that suggested that the traditional idea couldn't be right. For example, the traditional idea has it that judgments about thought experiments constitute appreciate of facts that are both a priori and necessary; but Williamson gave what is now a somewhat famous argument that this can't be so: thought experiments don't include enough detail to entail the typical judgments. So the best they can support is something like a contingent, empirical counterfactual: if someone were in such-and-such circumstances, he would have JTB but no K, etc.
We wrote a defensive paper in response to Williamson's argument, explaining how one can understand the content of thought-experiment judgments in a way that renders them more plausibly necessary and a priori, invoking the notion of truth in fiction. ("Thought-Experiment Intuitions and Truth in Fiction" -- (draft) (published)) That paper did two useful things: it gave an objection to Wiliamson's treatment, and it defended a traditional aprioristic picture from Williamson's particular critique. But on the latter score, it was purely defensive; it did little to explain how a priori justification or knowledge was possible, or to articulate just what apriority could consist in. Another paper, "Rational Imagination and Modal Knowledge," (d) (p) gave a bit more epistemological background, and a focus on modal epistemology in particular. By the time of that paper, we were underway on the book.
What we needed, we realized, was a much fuller story about apriority, including detailed engagement with extant critiques of the notion. We give this in Part II of The Rules of Thought. Some of the critiques -- in particular, some of those from Williamson and Hawthorne, as well as some similar challenges from Yablo and Papineau -- show that a characterisation of apriority in terms of more psychological states like knowledge and justified belief is extremely difficult, perhaps impossible. (Here's a related blog post from last year.) Our general characterisation of the a priori is a negative one, given in terms of propositional justification. A subject has a priori propositional justification for p just in case she has justification for p, and this isn't due in constitutive part to any of the subject's experiences. We explain how this approach avoids the challenges to the a priori that are in the literature, and argue that there is strong reason to think that philosophical investigation is often a priori in our sense. The focus on propositional justification requires a fairly strong version of the traditional distinction between warranting and enabling roles for experience, which we attempt to explicate.
The negative characterisation is thin by design. We are explicitly open to a kind of pluralism about apriority, according to which various positive epistemic states can realise apriority. The state we focus on most is what we call 'rational necessity' -- certain contents are, we think, by their nature such that there is always conclusive reason to accept them. (Much more on this idea in another post on another motivation for the project.) But we allow that other states may realise apriority as well; we are open, for example, to the idea that it is a priori that perception is generally reliable, even though this isn't rationally necessary. Perhaps some kind of pragmatic explanation for these a priori propositions may be found.
In the context of our theory of the a priori, and our more detailed positive story about rational necessity, we rehearse the main ideas from our two previous papers on philosophical methodology: thought-experiment judgments, properly understood, often have contents that are rationally necessary, hence a priori; so likewise for many judgments in modal epistemology concerning what is metaphysically possible. This all happens in Part II of the book.
So that's the first hook for our book: understanding the a priori and the epistemology of philosophy. We tell a story that is able to vindicate a number of pretty traditional ideas about how philosophy works (but without problematic focus on words or concepts). The other two hooks will each get another post -- one concerning Fregean ideas about mental content, and one about the role of intuitions.