Fixed and Variable Semantic Value
The orthodox view is that names are rigid designators and descriptions are (typically anyway) non-rigid designators: denotation varies from world to world in the latter case, but not in the former. What about connotation? The connotation of a description is fixed, even as it determines variable denotation from world to world. In the case of names, as Frege pointed out, connotation can vary from speaker to speaker and from time to time: speakers can have different individual concepts in mind, even though the same object is denoted. We use “London” to designate one thing, and the name is rigid across worlds, but what concepts are in our minds can differ, according to how we conceive of London (“the capital of England”, “the center of the music business”, “the place where parliament is”, etc). So the denotation is fixed (across worlds) while the connotation is variable (across minds): a name is a rigid designator but a non-rigid “expressor”. By contrast, a description has a fixed connotation, since the same individual concept is associated with the description from mind to mind: we all mean the same by “the tallest man”. The intension is fixed, while the extension varies–whereas for names the extension is fixed and the intension varies.
Thus names and descriptions semantically invert each other: what is fixed for one is variable for the other—yet each is fixed in one respect and variable in another. The name has a fixed reference and a variable sense, while the description has a fixed sense and a variable reference. This is the difference between names and descriptions. It is not merely that names are rigid and descriptions are not; names are also non-rigid (with respect to sense) and descriptions are rigid (with respect to sense). Each has a fixed semantic value and a variable semantic value, depending on whether we are considering denotation or connotation (extension and intension, reference and sense).
If we consider Frege’s view of indirect discourse the inversion is complete. A name in indirect discourse will designate its ordinary sense, but this can vary from speaker to speaker, or from time to time. On the other hand, a description in indirect discourse will designate, not its variable reference, but its fixed sense. So in indirect discourse a name is a non-rigid designator and a description is a rigid designator, following Frege’s theory. Now if we take the semantic functioning of expressions to be basically determined by their behavior in indirect discourse, it will turn out that names are basically non-rigid and descriptions are basically rigid—with respect to their sense, that is. It is only if we take ordinary objects to be basic designations that the orthodox way of describing things holds. We could describe things in the alternative Fregean way too, thus inverting the fixed-variable distinction. The fact is that both sorts of expression can rightly be said to be fixed with respect to one thing and variable with respect to another.
We can object to the description theory of names by arguing (as Kripke did) that descriptions are (typically) non-rigid while names are rigid; but we can also object that names are non-rigid with respect to sense while descriptions are rigid with respect to sense. We can argue, that is, that names could not be equivalent to descriptions, because names are non-rigid expressors, while descriptions are rigid expressors, which puts them in different semantic categories. The variability in the sense of a name is incompatible with the name being equivalent to a single description—just as the variability in the reference of a description is incompatible with it being equivalent to a name. The description theory of names fails both because of misplaced attributions of referential non-rigidity and because of misplaced attributions of expressive rigidity. Names and descriptions are rigid (fixed) and non-rigid (variable) in opposite ways, so they cannot be semantically equivalent.
In addition to the description theory of names, there is the name theory of descriptions, i.e. the idea that a description functions like a name (Frege, Meinong, early Russell). Thus it may be said that a description can always be replaced by a name without change of meaning, since it is a name. It is a name with both sense and reference, but still essentially a name. But such a theory can be refuted by pointing out that descriptions don’t have variable sense in the way names do—they are rigid expressors. They are also non-rigid designators, which makes them different from names in another respect. So the name theory of descriptions suffers from two sorts of difficulty: first, it gets the relation to sense wrong, by implying a variability of sense that just isn’t there; and second, it gets the relation to reference wrong, by implying a fixity of reference that just isn’t there.
The point about names being rigid designators and descriptions being non-rigid designators is thus part of a larger semantic picture, which undermines the alleged equivalence of names and descriptions from several angles. It is not wrong, just partial. The key point is that just as the denotation of a description can vary from world to world, so the connotation of a name can vary from mind to mind (or within the same mind over time). To put it simply, though somewhat inaccurately, names are inherently “ambiguous” while descriptions are not—that is, they have variable sense. The reason this is somewhat inaccurate is that the variability of sense or connotation is not incompatible with acknowledging a basic unity of meaning, since denotation is shared across differences of sense (and we don’t need to suppose that sense determines reference). What is important is that descriptive sense is uniquely fixed for descriptions, but not so for names. The underlying reason for this is that speakers need a way of conceiving their reference, and names themselves cannot supply such a way—so the speaker needs to come up with a way that suits her. The speaker’s information about the name’s bearer accordingly varies. But in the case of descriptions the information is right there in the description to begin with, needing no supplementation. For descriptions reference varies with world, while what is in the mind stays constant; for names sense varies with mind, while reference stays constant across worlds. Hence names and descriptions are fundamentally distinct semantic types.