Basic Expressions
Call an expression E scrutable with respect to a class of expressions C iff it is a priori that all true sentences involving both C and E are a priori deducible from all true sentences involving only C. Equivalently, E is scrutable with respect to C iff there are no worlds w1 and w2 of which exactly one is in the 1-intension of some C+E-sentence, whereas all 1-intensions of C-sentences contain either both worlds or neither.
Is every expression scrutable with respect to some class of expressions to which it does not belong? If the relevant language has synonyms for all expressions, that's trivial. We should better ask about families of expressions: what classes of expressions are scrutable only with respect to expressions containing other members of their class? Call such classes indispensible. Large classes of expressions like the class of all expressions are obviously indespensible, as is probably the class of indexicals and the class of quantifiers. Dave Chalmers would also add the class of phenomenal expressions. As a type-A materialist, I would rather not.
What about, say, mereological expressions? Suppose we're told that there are two electrons. Then we can infer that there is a fusion of the two electrons, that some part of one of the electrons is not part of the other, and so on. So at least some mereological truths are deducible from statements not containing mereological vocabulary. I'm inclined to believe that this holds for all mereological truths (and that this is a priori). If not, there would either be absolutely unknowable mereological truths or we would need to have some sense organ for irreducibly mereological facts. That sounds suspicious. So mereological terms can be defined in non-mereological terms, even though the definition might be horrendously complicated (at worst, an infinite disjunction of infinite conditionals).
The same holds for identity.
Now consider classes of expressions with respect to which all expressions are scrutable. Let's call such classes complete. Again, the class of all expressions is complete, as are lots of smaller classes. Complete and indispensible classes are related as follows: C is indispensible iff any complete class contains at least one member of C.
Let's call a class minimally complete if it is complete and none of its subclasses are. A minimally complete class of expressions is one that just suffices to characterize any counteractual situation as specific as it can be characterized in the entire language.
It need not characterize counteractual situations up to duplication. For instance, if two counteractual situations differ only quiddistically by which perfectly natural, intrinsic property plays the spin role, then no class of sentences (minimal or not) can distinguish between these situations. The problem is not that we lack names for perfectly natural, intrinsic properties. If that is the case, we could simply add names to our language, say "A" and "B". But how can we let these names track their referents across counteractual situations? We can stipulate that "A" denotes whatever actually occupies the spin role. That doesn't help: the 1-extension of "A" for the world where mass occupies the spin role will then be mass. We would need a kind of hyper-rigid designator for spin with a constant 1-intension. But we have none, and we can't introduce one. (In my view, we couldn't even introduce a hyper-rigid designator for intrinsic properties with which we are somehow directly acquainted, if there were properties of this kind. At least not into a public language.)
How similar are the minimally complete classes? I guess -- admittedly with no good reason -- that they are not very similar, since there are few interesting indispensible classes. All minimally complete classes will contain indexicals and quantifiers. But many other families of expressions can probably be traded against each other. Thus one can perhaps get rid of spatiotemporal expressions by including phenomenal expressions. Or consider microphysical terms like "spin" and "mass". As theoretical terms they are certainly not indispensible: we could eliminate them in favour of the "old" vocabulary occurring in the relevant physical theories, including various macrophysical terms. On the other hand, macrophysical terms are probably scrutable with respect to mircophysical and phenomenal terms (as argued by Chalmers and Jackson).
So I don't think there is a privileged class of fundamental expressions, or truths. Lewis probably held (though not as an a priori principle) that all truths are a priori deducible from truths about the spatiotemporal distribution of local intrinsic properties (stated in a language that has names for these properties, which our language may not). But this does not imply that truths about the spatiotemporal distribution of local intrinsic properties are not in turn deducible from other truths, not naming local intrinsic properties at all.
There are very different philosophical projects in which classes of fundamental expressions or truths can be employed. Lewis is interested in various kinds of metaphysical reductionism. By contrast, a descriptivist who believe that ordinary expressions get their meaning by associated descriptions might seek a complete class of expressions for which she can tell a different story, so as to avoid Global Descriptivism. Some class containing largely microphysical expressions will not be very helpful here. The descriptivist could instead try to get as far as possible with phenomenal terms, thereby employing a class of basic expressions for which I don't have much use at all. (I also doubt that phenomenal acquaintance helps against the problems of Global Descriptivism, but that's another matter.)
Hi Wo, this is the main topic of my paper on primitive concepts (which is itself related to my Konstanz talk on scrutability) -- Powerpoint at consc.net/papers/primitive.ppt. Your definition of scrutability seems odd, as it entails that e.g.'Wo' is scrutable with respect to 'Dave' (since there are no truth-evaluable sentences composed just of these terms). I'd put at least phenomenal, logical, nomic/causal, indexical, and categorical expressions in the base, and probably some mathematical expressions too.
I'm inclined to think that while trade-offs are certainly possible, they're not as easy or as ubiquitous as you think. For example, I think that microphysical expressions (such as 'charge', 'spin', etc) are implausible candidates for being in a scrutability base, as such theoretical terms are scrutable from causal and phenomenal terms that we will need for our scrutability base in any case. Even if the phenomenal were scrutable, one could still get away with just causal and/or spatiotemporal expressions in the base (plus indexicals etc) -- no need for microphysical expressions.
A type-A materialist who's also Humean about causation might be able to get away with just spatiotemporal expressions (plus categorical, indexical, etc). Or a nonHumean type-A materialist who holds the "Matrix as Metaphysics" view of spacetime might be able to get away with just causal/nomic expressions. But interestingly, it looks very hard to hold the Humean view of causation (on which it is scrutable in terms of regularities) and the "Matrix" view of spacetime (on which it is scrutable in terms of causation) simultaneously.