Bridge Laws versus Descriptivism
Suppose theory 1 says that entity x has certain properties, and theory 2 says that entity y has those properties. If we believe both theories, should we conclude that x=y?
It depends. Sometimes we not only should but must conclude that x=y, for example when theory 1 says that x is the planet Venus and theory 2 says that y is the planet Venus. In other cases, there is little reason to draw the conclusion, as when the theories merely say of x and y respectively that it is some planet or other. In yet other cases, the conclusion can be motivated by methodological considerations. For instance, whoever first realized that Hesperus is Phosphorus probably realized that the identity makes for a simpler overall theory.
Block and Stalnaker, in sections 5 and 6 of "Conceptual Analysis, Dualism, and the Explanatory Gap", argue that scientific reduction usually works in the third kind of way:
The view that heat and molecular kinetic energy are two rather than one is not contradictory or conceptually incoherent. It is false, and can be shown to be false by attention to certain methodological principles [...].
Others, notably Lewis in his early papers on theoretical terms, say that scientific reduction usually does not require methodologically motivated bridge laws but is analytically entailed by the theories themselves, as in the Venus example above.
Lewis' view is based on the Ramsey-Carnap-Lewis theory of theoretical terms, which says that if "x" is a theoretical term of theory 1, then analytically "x" denotes whatever satisfies the role theory 1 attributes to x. It follows that if, by theory 2, y satisfies this role, "x" must denote y. No further bridge principles are needed.
Block and Stalnaker point out that several different things can often share the relevant role. Then even if analytically, "x" denotes something that occupies the role, from the fact that y occupies the role we can't deduce that "x" denotes y. Thus, they say, one could consistently hold that even though molecular kinetic energy does what folk theory says heat does, heat might nevertheless be some other property that also does all that. Similarly, even though H2O plays the water role, it is not inconsistent to claim that water is something else that also plays that role.
Two things seem to be wrong here. First, it is often conceptually impossible that two things occupy the relevant role. If you know that Hesperus is a planet orbiting the sun on a certain path and that Phosphorus is also a planet orbiting the sun on that very path, Hesperus must be Phosphorus. It is impossible that they be dual occupiers of the same role: planets are not the kinds of thing of which more than one can be located at exactly the same spacetime positions. I suspect the same is true of heat and molecular energy and water and H2O; How could my glass be full of both water and H2O if these were two different watery stuffs?
Of course it could turn out that two different things occupy different parts of the water role, like two things occupy different parts of the Jade role. In this case it wouldn't be clear which of them, if any, we should call "water". But that is irrelevant. My point is that if H2O turns out to occupy the water role (more or less) entirely -- as seems very likely, and can in principle be conclusively settled -- then it is incoherent to assume that water might nevertheless be some other stuff that also occupies the water role entirely.
The other thing that's wrong with the Block-Stalnaker account is this. Suppose contrary to what I just said the water role can be entirely occupied by two different things, and even though H20 is one such thing there might be another one. The problem is: how does "water" in this case come to denote the other thing? On the Ramsey-Carnap-Lewis theory this is impossible: other than the theoretical role, there are no further facts in virtue of which "water" could get its denotation. If different things can completely occupy the role that defines a theoretical term then the definition is not entirely specific. And if in fact two things do satisfy it, the term is indeterminate between them. (Methodological considerations don't help much in such a situation. What is needed then is just a stipulation.) If on the other hand it turns out that only one thing satisfies the definition, the indeterminacy doesn't matter and the term determinately denotes that one thing. Thus as so far we have found only one thing, H2O, that occupies the water role, one could at best consistently deny that "water" determinately denotes H2O, by hypothesizing that further role-fillers will eventually turn up. Such a position would really be methodologically, not conceptually, deficient.
But note that this is much weaker than what Block and Stalnaker claim: they say one could consistently hold that even though H2O occupies the water role, water is not H2O. (The difference is between "not" and "not determinately".) Note also that at any rate, if we know enough facts about which things do and do not occupy the water role, it can be conclusively inferred whether H2O is water or not, without any further work for methodology.
The reason why Block and Stalnaker emphasize the role of methodology is, I guess, that they reject the Ramsey-Carnap-Lewis theory of theoretic terms. If "water" doesn't get its reference via its theoretical role but rather via some causal chain or some other kind of magic, then it could really happen that of two things both occupying the water role, "water" determinately denotes just one. This is why it is not clearly inconsistent even nowadays to say that Hesperus is not Phosophorus: The denotation of "Hesperus" and "Phosophorus" is not settled by their role in current astronomy.
Luckily, the Ramsey-Carnap-Lewis theory of theoretical terms also works for non-theoretical terms, even for causal and magical terms. We only have to replace the theoretical role by whatever else determines the reference. In some respects, the resulting picture is just like before: If "water" denotes whatever stands in the right causal/magical relation to our use of "water", then given that H2O in fact stands in that relation, we're logically forced to conclude that H2O is water, or at least -- in the unlikely event that several different things could stand in the relevant relation to our use of "water" and we haven't yet found out that H2O is the only one -- that H2O is not determinately not water.
There is one important difference though. If the role that determines reference is a causal/magical rather than a classical theoretical role, it is much harder to discover what actually occupies the role. (For magical roles it is presumably even impossible. Do Block and Stalnaker believe in reference by magic? I think so, as they approvingly cite Kripke's remarks that reference might be unanalysable.) But unless we make that discovery we can only guess what our terms denote. If we're unlucky, the causal/magical route leads from "heat" not to molecular energy but to C-fiber firing, or to Madagaskar. On the causal/magical account, we really need methodological principles in our current state of knowledge to rule out such possibilities and to support the view that "heat" denotes molecular energy.
Which of the two candidate kinds of roles are more credible as fixing the reference of our terms: the transparent, descriptively rich, theoretical roles, or the intransparent, deferential, causal or magical roles? It would be nice to say that it is different for different terms, and that most terms lie somewhere in the middle. But I'm afraid it is better to assign both kinds of meanings (as A-intensions) to utterances, a transparent one and a fairly intransparent one.
Example: I believe, and am willing to say, that elms are beautiful. I have some vague ideas what elms look like, but I claim no authority on recognizing elms. I could even be brought to accept that elms aren't really the kind of tree I thought they were, or that the elms I know are only untypical exemplars whereas the vast majority of elms are ugly bushes. Now I do believe that elms, real elms, are beautiful. This is what I express with "elms are beautiful". But I also believe that the trees I think of as elms are beautiful, no matter how experts call them and what other things they call "elms". And this belief I also express with "elms are beautiful". With the very same sentence. Even though the two beliefs have different truth-conditions: the first is false and the second true if elms turn out to be ugly bushes. Thus my utterance expresses two different truth-conditions, a transparent one and an intransparent one. (Isn't the intransparent meaning a C-intension? No. At any world w, the C-extension of "elm" is elms, but the intransparent A-extension is whatever the experts at w say are elms (or whatever stands in the right causal relation etc.) .)