(1) Are bridge laws allowed in the scrutability base, and if so does this trivialize scrutability theses?Bridge laws are certainly not disallowed from the base in general (indeed, I'd have psychophysical bridge laws in my own base). When I said that bridge laws were not allowed in the base, I was discussing a specific scrutability thesis: microphysical scrutability (where the base must be microphysical truths alone). On the other hand, building in separate bridge laws for water, kangaroos, and everything else will lead to a non-compact scrutability base. So there's no trivialization of the central compact scrutability thesis here.
(2) Is Carnap's $\omega$-rule powerful enough to yield scrutability of mathematical truths?My discussion of the $\omega$ rule is intended to illustrate my response to the godelian objection to the scrutability of mathematical truths, rather than a general account of the knowability of mathematical truths. It's an example of an idealized infinitary process that can get around godelian limitations. The $\omega$-rule suffices to settle first-order arithmetical truths but of course other infinitary methods will be needed in other domains. It's just false that inference rules assume the knowability of their premises, so there's no trivialization here.
(3) Is there a circularity in nomic truths being scrutable from microphysical truths and vice versa?If one distinguishes ramsified and nonramsified versions of microphysical truths, any apparent circularity disappears. non-ramsified microphysical truths are scrutable from ramsified causal/nomic truths, which are scrutable from ramsified microphysical truths (including microphysical laws).
contemporary Newman problem" isn't a problem for my thesis, as my ramsification base isn't an observational base. As for Scheffler's problem: my first reaction (though this really is quick) is that Scheffler's example involves either ramsifying a trivial theory or giving an incomplete regimentation (and then ramsification) of a nontrivial theory. If those material conditionals really constitute the whole content of the theory (and the theory gives the whole content of the relevant theoretical term), then it's trivial in the way suggested. If the theory is formulated more completely e.g. with nomic or causal conditionals, the objection won't arise. Certainly the problem won't arise for the Ramsey sentences that my procedure yields.
(5) Why think special science truths are scrutable?The arguments for scrutability of special science truths are in Chapters 3 and 4 (supplemented by 6), which are not discussed in the critical notice. The excursus on the unity of science is not intended as a primary argument for scrutability of special science truths. Rather, it is connecting the scrutability thesis to the unity/reduction literature and making the case that the thesis is a weak sort of unity/reduction thesis that survives common objections to unity or reduction theses.
[i've de-e.e.-cummingsified dc's decapitalization - jk.]