Page 404 - Encyclopedia of Philosophy of Language

Formal Semantics
the Russellian analysis, the liar sentence This prop- osition is not true' expresses the unique (non- wellfounded) proposition/satisfying/= [FALSE/].
According to the truth scheme introduced by Austin (1961), an assertively used declarative sentence S con- tributes two things: the descriptive conventions of language yield a certain type of situation 5 that is expressed by <£, whereas the demonstrative con- ventions refer to an actual, 'historic' situation s. So, an Austinian proposition can be written as a claim s: S (cf. Sect. 2 above). The rule of truth is simply that s:S is true if s is of type S. This holds in general, independently of the presence of indexical expressions in <f). On the Austinian analysis, there are many differ- ent propositions that can be expressed using the liar sentence.
Comparing the two accounts, Barwise and Etch- emendy show that while the Russelian view is crucially flawed in limiting cases, the Austinian view can be seen as a refinement which avoids the paradox while providing a straightforward understanding of the sem- antic intuitions that give rise to it.
On the basis of various examples involving inherently circular situations (aspects of perceptual knowledge, self-awareness, Gricean intentions of speakers and hearers, shared information),Barwise (1989: ch. 8) argues that reality, unlike the cumulative hierarchy of sets, is not wellfounded. Consistent with the assumption that situations are parts of reality (families of facts) that can be comprehended as com- pleted totalities, i.e., as sets, this article has been mod- eling situations as sets of infons, and infons as sequences<£/?",/,a,,...,an;i^ consistingofann-ary relation R", a location /, a sequence of n arguments a\,...,an (the constituents of the infon, which can be primitives, situations, or situation-types), and a polarity marker /. Now, if this sort of set theoretical model is to be used, then non-wellfounded sets are essential when circular situations are to be represented. Thus it should be possible that a situation scontainsinfon «/?",a,,...,an;/» asamember,while s itself also is (a constituent of a member of...) a member of«i or...oran.
In an interesting case study of non-wellfoun- dedness, Barwise (1989: ch. 9) addresses the phenom- enon of common knowledge, which is crucial for an understanding of communication. Common knowl- edge arises for instance when a card player (Jon, say), receives a card (e.g., the queen of clubs) that everyone (viz., Jon and John) can see. The orthodox 'iterate' account analyzes this in terms of an infinite hierarchy of iterated attitudes: (0) Jon has the queen of clubs; (1) Jo(h)n knows Jon has the queen of clubs: (2) Jo(h)n knows that Jo(h)n knows that Jon has the queen of clubs; and so on. Barwise contrasts this account with non-wellfounded approaches, and shows that it is inadequate. Moreover, it turns out that common knowledge is better analyzed in terms of shared infor- mation.
In spite of its pervasively indexical, 'efficient,' character (witness the speaker connections), the situ- ation semantics outlined in Sect. 3 is essentially Rus- sellian. More recent contributions, however, have incorporated the inherently indexical Austinian approach sketched in the present section. Gawron and Peters (1990), a book on quantification and anaphora, is a case in point.
Situation semantic accounts of anaphora and quantification make frequent use of so-called 'restric- ted parameters' or 'roles' (see S&A: 80-90; Gawron and Peters 1990; Devlin, et al. and Westerstahl in Cooper, et al. 1990). A restricted parameter is an indeterminate subscripted by a situation-type that contains the indeterminate. The idea is that the situ- ation-type restricts the domain of things onto which the indeterminate can be anchored. If r is a restricted indeterminate jcs, then an anchor/for r in situation 5 must be such that/anchors all parameters in S (among whichmayberestrictedones),S[f] c 5,and/(r)=/(x). Suppose S=^MAN,JC, 1»; then xs can only be an- chored to individualsa in s if a is a man in s. It is clear that restricted parameters introduce a form of restricted existential quantification. For instance, the proposition sk { ^ WALKS, x s ; 1»}, where S is as above, expresses that in s an individual a walks who is a man. Noticethatsitselfisnotrequiredtocontainthe information that a is a man, provided that some other situation s' does (Devlin, in Cooper, et al. 1990: 84). Instead of situation-types it is also possible to have propositions as restrictions on parameters (Gawron and Peters 1990). Such a proposition explicitly addresses a resource situation where the restriction is required to be satisfied. For example, if r is the par- ameter xsts, where S is as above, then sN«WALKS,
r; 1)) expresses that someone who is a man in s walks in 5. (Resource situations were already introduced in S&A. These situations are exploited by speakers and they figure as a kind of domains for reference and quantification.)
Gawron and Peters (1990; and in Cooper, et al. 1990) give a more or less uniform treatment of natural language noun phrases using restricted parameters. Proper names, pronouns, definite, and indefinite descriptions contribute restricted parameters to the interpretations of sentences. A use of the proper name 'John'introducesaparameterx^^^o^.,0^^ that restricts x to be anchored to an individual named 'John' in the resource situation. Definite descriptions like 'the dog' introduce a parameter that is restricted to be anchored to the unique dog in a resource situ- ation, if there is one. The content of the pronoun 'she' is captured with a parameter that is restricted to be anchored to females in a resource situation. Here the utterance situation (Gawron and Peters use the term 'circumstances') contains the information whether the pronoun is used deictically or anaphorically, and what the resource situation is. The first person pronoun /
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