Incomplete definite descriptions.
Scott Soames · Notre Dame Journal of Formal Logic · 1986
In [1], Barwise and Perry use set theoretical models called "abstract situations" to play the role of potential situations.For example, the potential situation in which Perry is tired and Barwise is not (at 4 pm, July 17, 1986, Stanford, California) is represented by the abstract situation (2).(2) (</, «tiredness, Perry), 1» 1 [</, «tiredness, Barwise), 0))J (where / is the spatio-temporal location: Stanford University-at-4pm-July-17-1986)An abstract situation-i.e., a set of a certain sort-is said to be factual iff it corresponds to some real situation. 1The meaning of a sentence is then seen as a relation between abstract situations representing potential contexts of utterance and sets of abstract situations that provide its truth-conditional interpretations in those contexts.In standard cases, an utterance of a sentence S in a context C is true iff some member of the interpretation of S in C is factual.The structure of this account is notably similar to that found in versions of possible worlds semantics that incorporate Kaplan's distinction between character and content (see [5] and[6]).The most striking difference between the two frameworks is between the completeness of possible worlds (which determine truth-values for all object language sentences) and the partiality of abstract situations (which do not).It is this difference that Barwise and Perry attempt to exploit in their theory of descriptions.In familiar, possible worlds treatments, a description, Γ the F π , is associated with a partial function, /, from possible circumstances of evaluation to unique F-ers in those circumstances.The intension of (an attributive understanding of) an example like (1) is then defined to be the set of circumstances C such that for some (possible) object o,f(C) = o and o "is G" in C. In general,/(C) may vary with C, and the sentence may be taken as "saying" that the F (whoever it may be) is G.If, in addition, a semantically referential interpretation is desired, it can be obtained by requiring/to be defined not on circumstances of evaluation, but rather on the circumstance given in the context (as is done by Kaplan's Γ dthat [ixFx] n ; see [4]-[6]).On this interpretation, the intension of (1), relative to a context C"\ is the set of circumstances C such that/(C*) = o and o "is G" in C (where C*' is the circumstance given in C*).The sentence is then seen as "saying" that a particular individual, o, is G. 2In a nutshell, the Barwise-Perry theory of descriptions is just like this, except that circumstances are identified with abstract situations rather than possible worlds.Γ TheF π is said to express a partial function,/, from abstract situations to unique F-ers in those situations; and examples like (1) are claimed to be semantically ambiguous, depending on which situations / is required to be defined on.The attributive understanding requires/to be defined on the abstract situations in the interpretation of the sentence (relative to the context).Thus, all these situations will contain unique F-ers, with (potentially) different objects playing this role in different situations.The referential interpretation requires /to be defined on a contextually supplied resource situation-typically, one that is given perceptually, or through preceding discourse. 3ormally, this means that contexts must be expanded to include resource