Fodor's target in his article is the idea of the "unity of science" defended by the positivists and exemplified, for instance, in a major publishing project they called "The Encyclopedia of Unified Science." Their idea was that higher-level sciences could (and should!) be "reduced" to lower-level sciences, and ultimately to physics. The picture was that the "special sciences" (i.e. all the sciences that aren't physics!) formed a natural hierarchy, with higher-level sciences reducing to lower-level ones. Like this:
We need to discuss what they meant by "reduced" or "reduction." There are at least three things one might mean. Fodor does not necessarily disagree with the first, but he does with the other two.
Reduction of individual things
It seems plausible (for the most part, I think!) that the particular things that the higher-level sciences talk about are composed of things at lower levels. So: societies are composed of individual people; individual people are composed of cells; cells are composed of chemical compounds; and chemical compounds are composed of atoms. If this is right, then every particular thing (i.e. token thing) is identical with some particular physical thing (or collection of things). This is essentially the token-token identity theory, generalized from psychology to all the special sciences. [side note 1: there may be problems about this too: a cell isn't just a collection of chemical compounds; they have to be organized in a certain way. Moreover, the way they have to be organized may need to be described in something other than the language of physics. So it may be unclear exactly what "reduction" means or whether it's true even at this level.] [Side note 2: Of course, a substance dualist will reject even this relatively harmless sense of reduction!]
Reduction of types
It is a separate question whether the kinds of things higher-level sciences talk about can be "reduced to" lower-level kinds of things. To suppose that they can is basically to be committed to the type-type identity theory. For instance, in the case of genetics, it appears not just that particular (token) genes are identical with particular (token) strings of amino acids, but that in general for every type of gene there is a corresponding type of string of amino acids.
[Note to self: check up on this! Maybe it's not so straightforward. Genes seem to be functionally defined in terms of their causes and effects. Could a given type of gene be realized by different strings of amino acids in different species? Conversely, could a given string of amino acids realize different genes in different organisms? Maybe it's time to take a genetics class!]
Reduction of laws
Ultimately what the positivists wanted was some sort of reduction of higher-level laws to lower-level ones. Fodor says that two things are required for a high-level law to be "reduced" in the relevant sense. (1) The types that figure in the high-level law must be reduced to lower-level types (as in "reduction of types," above). (2) There must be a lower-level law connecting the lower-level types to which the higher-level types were reduced. If both (1) and (2) hold, we can say that the higher-level law has been reduced to a lower-level one.
Fodor suggests that multiple realizability (of the sort the functionalist defends for psychological states) poses problems for the idea that types or laws are reducible, for two related reasons. First, since the lower-level types to which the higher-level ones are reduced will be disjunctive, they don't qualify as "natural kinds."
Second, since the lower-level generalizations that ground the higher-level laws will be varied (basically, separate laws for each disjunct in the disjunctive types), there won't be a single lower-level law to which the higher-level law reduces.
Kim points to two elements of Fodor's position: (1) The laws of the special sciences are fine as they stand: there is no need to reduce them to laws of lower-level sciences. (2) Higher-level types will typically reduce only to disjunctive lower-level types, not to lower-level natural kinds. Kim suggests that there is a serious tension between these two claims, and we may need to give up one or the other of them (in various places, including his Philosophy of Mind).
Consider psychology. Suppose it's true that mental types reduce only to disjunctive physical types (not to unitary physical types). Then two cases may obtain. (1) Perhaps the disjunction is like that between jadeite and nephrite: the physical types are very different from one another, so that we wouldn't expect generalizations about the one to automatically apply to the other. Then Kim thinks we may need to give up Fodor's claim (1), the idea that the special science laws are fine as they stand. In the case of psychology, we might need to move to the idea that there is one psychology for humans, another for dolphins, and still another for extraterrestrials, should we find any.
(2) On the other hand, perhaps the disjunction is more like that between Asian nephrite, African nephrite, and American nephrite. In that case all that disjuncts are sufficiently similar that we might well expect laws that apply to the entire disjunction. But in that case, despite the disjunctive character of the reduced types, we should still say that the higher-level laws had successfully been reduced to lower-level ones.