Chapter two of Williamson presents a case study meant to show that not all philosophical problems are about language or thought. During the chapter he seems to be implicitly resisting two sorts of arguments:
A) any philosophical problem is equivalent to a conceptual/linguistic problem
B) B -> C
C) any philosophical problem is about concepts/language
1) if any sort of problem solved by examining concepts/language then it is a conceptual/linguistic problem
2) philosophical problems are solved by examining concepts/language
3) philosophical problems are conceptual/linguistic problems
Williamson seems to deny both (A) and (B), as well as (1). I'll concentrate on the response to the second argument.
The philosophical problem on the table is to decide the truth value (or lack thereof) of (M):
(M) Mars was always either dry or not dry
It's clear that (given mars dried gradually over time) no amount of empirical data will either confirm or deny (M). For simplicity, suppose all relevant data has already been collected. (M) is clearly about Mars and it's dryness or lack of dryness. To support this, Williamson notes that no metalinguistic or metaconceptual terminology appears in (M). However all proposed solutions to the problem involve analysis of the concepts or language involved(mostly analysis on the meta-logical level), what gives? To deny that this is a problem, Williamson takes an ordinary example from outside of philosophy and gives an argument.
4) When deciding a court verdict, consideration about thought/language are often brought into account. Irregardless, in a criminal case Guilt or Innocence of the defendant is the main issue, not language or concepts.
5) (4) -> (6)
A proponent of the linguistic/conceptual turn can simply assert that (2) -> (3) in response (and retain soundess of the previous argument). They can accept analysis in language and thought from other disciplines, but it's philosophy they're concerned with. Should they be sticklers about it, they can assert that the role of linguistic or conceptual analysis is clear in those other cases, but seems to be unusually dominant in the case of philosophy. Williamson's explanation as to what exactly we're up to when ascending to the metalinguistic/conceptual level can be seen as a response:
8) analysis of language & concepts help us decide what inferences are valid when discussing issues other than language & thought
9) (8) -> ~(3)
12) ~ ((2) -> (3))
A little motivation for (9) is needed. Basically, given (8) the role of linguistic/conceptual analysis in philosophy is explained in many cases (and that role is NOT to be subject matter). If this is so, then the motivation for accepting (3) is defeated, since we only accepted (3) in the first place because of the large unexplained role of linguistic/conceptual analysis in philosophy.
A possible response would be to deny (9). After all, (8) does not show that (3) is false. If some other motivation for accepting (3) were found, this argument would not cover it. Personally, this seems hand-wavey to me. As far as I can tell, Williamson has a pretty strong point in this chapter.