Tim Williamson has a paper on Conceptual Truth in the new Aristotelian Society Supplementary Volume. His target is the view that appealing to something like conceptual truth or analyticity can help us explain how a priori knowledge works.
But strangely, he focuses almost exclusively on one particular - and particularly weak - version of this type of view. Almost the entire discussion is concerned with the view that anyone who understands a conceptual truth knows it. I don’t know of any contemporary philosopher of the a priori who defends this claim, and indeed it is not attributed to anyone by Williamson. Although in footnote 5 Williamson claims that Boghossian holds ‘something like’ it, I doubt whether Boghossian would accept this reading of his work. Peacocke is also mentioned, but as I understand him Peacocke is not committed to anything in this vicinity either. The same footnote also says that ‘the focus of this paper is not on some few thinkers in particular; it aims to make explicit and criticize a conception on which many contemporary philosophers still rely, often tacitly, at various points in their work.’ But the paper would be more exciting if its took into account some of the potentially interesting versions of the conceptual approach currently being proposed by serious philosophers of the a priori. There is too much of the straw man about the view Williamson actually discusses. Even some examples of places where he thinks this view is being assumed by philosophers who are not specifically interested in the a priori would have helped to motivate the paper.
The only attempt to engage with slightly more sensible versions of the conceptual approach is fleeting: on pp. 26-7 he considers the view that understanding merely puts one in a position to know or justifies the relevant belief. He argues that some people who understand the relevant propositions aren’t even in a position to know them, because certain of their other commitments get in the way of their believing them. This may or may not be the best way of describing these cases, but even if it is, it isn’t particularly devastating: a nearby position which Williamson doesn’t consider is the view that whoever understands certain propositions and believes them on the basis of that understanding knows them. Not that I would defend anything like this view myself - my point is just that Williamson's arguments do nothing to touch it. (Moreover, the debate on, for instance, how Boghossian’s view fares with regard to the distinction between possessing knowledge and having a warrant available to one is already at a more advanced stage than Williamson’s discussion takes account of - see Philip Ebert’s 2005 paper on this point).
Also, the argument in this section relies heavily on assumptions I think are false, e.g. that ‘justification rather than knowledge is the central epistemological question only for internalist theories’ (p. 27). Justification, like knowledge, can be construed in an externalist or an internalist fashion, and an externalist about both notions could well take justification to be the, or at least a, central epistemological notion.
A good point is mentioned on p. 4, namely that conceptual approaches tend to assume the epistemological problem of a priori truth is somehow ‘automatically’ solved for conceptual truths, but they ‘do not say how it is solved’. This point, however, is anticipated (and developed in more sophisticated ways) in various places, including e.g. Field 2005 and BonJour 1998.
Williamson's discussion, which focuses on finding counterexamples to the view under consideration, does not take the most illuminating tack in attempting to show what's wrong with it. What's more illuminating is the fact that even if it were true that everyone who understood a certain proposition knew it, we still wouldn't have given any account of how they knew it.