Implicit Definitions, Part 2: Theoretical Terms
Scientific theories are often said to implicitly define their theoretical terms: phlogiston theory implicitly defines "phlogiston", quantum mechanics implicitly defines "spin". This is easily extended to non-scientific theories: ectoplasm theory implicitly defines "ectoplasm", folk psychology implicitly defines "pain".
The first problem from the mathematical case applies here too: Since all
these theories make substantial claims about reality, their truth is not a
matter of stipulation. For example, no stipulation can make phlogiston
theory true. That's why, according to the standard Ramsey-Carnap-Lewis
account, what defines a term (or several terms) t occurring in a theory
T(t) is not really the stipulation of T(t) itself, but rather the
stipulation of something like its 'Carnap sentence' 
x T(x) 
T(t). All substantial claims in T(t) are here cancelled out by the
antecedent.
What about the second problem from the mathematical case: Does the Carnap
sentence really succeed in giving a meaning to the theoretical terms? What
if nothing satisfies T(x)? And what if too many things do? Clearly, the
latter problem is not as grave here as it was in mathematics because
scientific theories usually contain old vocabulary, whose interpretation is
taken for granted. This is why not just anything could play the role of
pain in folk psychology. There are probably still several possible
candidates (quite a lot, I believe), but this remaining indeterminacy might
just be accepted. The problem of missing satisfaction however remains: If
x T(x) is false -- totally false, like phlogiston theory
--, how can the stipulation that x T(x) T(t) establish
a meaning for t?
One might argue that in this case, t does not have a meaning: Since there is no Phlogiston, "Phlogiston" is a meaningless expressions. Hence, on this view, only true theories implicitly define their theoretical terms, whereas false theories leave them undefined. To put this explicitly into the definition, Lewis proposes to add another clause to the Carnap sentence, stating that if nothing satisfies T(x), then t is denotionless.
Anyway, as Lewis observes, the result of all this is not really an implicit definition, but just an explicit definition in disguise: The proposed definition is logically equivalent to t = the x T(x).
I don't like the Ramsey-Carnap-Lewis account because it is only applicable to theoretical (singular) terms. I'd prefer an account for theoretical predicates, partly because definitions of singular terms always have this messy existence presupposition, partly because I think theoretical expressions usually really work more like predicates than like names in their respective theories. For example, I think that folk psychology is not committed to an abstract, universal entity pain, but only to individual pain-states in individual people. Note to self: When I'm done with implicit definitions I have to think about the necessary modifications of the Ramsey-Carnap-Lewis account.