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3. Semantic type: <e>

For expository reasons, textbooks of semantics commonly start with the assumption that proper names have the simplest possible semantic structure, i.e. proper names are assigned the semantic type individual <e>. This type assignment has intuitive appeal, for it suggests a direct equivalence between logical notation and ordinary language. In the realist framework of e.g. Heim/Kratzer (1998: 15), (6a) is thus translated as (6b):

(6)        

(a)         ||Ann|| = Ann

(b)        “the extension of the lexical item “Ann” is the individual Ann”

 (6b) implies a direct connection between a proper names and the objects referred to. This view thus stands in direct tradition of Mills claim that the functionality of names is exhausted in their reference relation. Kripke (1980) strengthens this claim by introducing the concept of ‘rigid designator’. Names as ‘rigid designators’ thus pick out their referent not on only in the actual world, but in all possible worlds, a view explicitly endorsed by Heim/Kratzer (1998: 304).

        Rosenberg (1994) challenges the internal logic of ‘rigid designation’:

“... when ‘stipulating’ a possible world, we need to hold fixed the references of any rigid designators we use in describing that world. Correlatively, then, our confidence in the conclusions we propose to draw from considerations of such a counterfactural stipulations extends no further than our ability to conform to this constraint, and so, inter alia, our ability to recognize which of the designators we have used in that stipulation are in fact rigid designators. But now it may well seem that we are traveling in a circle, for to identify these rigid designators, we will need to determine which of the expressions we have used in the stipulative specification of that possible word in fact designate the same object in every possible world. In other words, we have so far characterized rigid designators in terms of possible worlds, possible worlds in terms of admissible counterfactual descriptions, and the admissibility of a counterfactual description in terms of rigid designators....” (1994: 8)

        Even if it was possible to formulate a meaningful definition for ‘rigid designation’, the theory is challenged by the fact that

“there is a clear sense in which proper names in a natural language frequently simply are ambiguous... it as been customary to pretend that ambiguous proper names have been disambiguated (e.g. with notational indices), so that each (regimented) proper name has one and only one semantic referent. ...such expository conventions are at best infelicitous” (Rosenberg 144-145)

        It is certainly true that discourse participants utilize a pragmatic constraint like (7):

(7)        Do not use the same name for more than one discourse referent in the same discourse domain.

        But with common names like Mary or John, discourse situations with multiple potential referents per name are often unavoidable. Out of the blue, an utterance like (8A) is almost certain to elicit (8B) as response:

(8)        

A:         Did you see John

B:         Which one?

Notice that for (8B) to be felicitous, John may well be unambiguous in the domain of discourse accessible to A at the time of utterance of (8A). What (8B) shows is that the domain of discourse accessible to B contains more than one discourse referent that are identifiable by using John. The following situation is merely one out of many possible configurations in which the exchange in (8) is possible:

(9)

In situation (9), the John who is identifiable to A may be identical to one of the Johns accessible to B, or he may not be. Thus, the total number of relevant Johns is at least two, but may just as well be three (or more). The point of the discussion here is that the felicity of (8B) shows that discourse participants can treat names as denoting sets of individuals rather than individuals. And, to be fully self-referential again, in writing this paragraph, I set up sufficient context to be able to use     

(a)            a name as a nonspecific bare plural: Johns

(b)           a name that is part of a partitive expression: one of the Johns.

(c)            a name modified by a restrictive adverbial clause: the John who is identifiable to A

The fact that names can freely denote sets in spite of the pragmatic constraint in (4) is thus unquestionable (cf. Burge 1973) and should not come as a surprise to anyone.

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© Philipp Strazny 1998