Page 403 - Encyclopedia of Philosophy of Language

individuals a, and situations s such that {<see,/,a,s;!>}£/,itholdsthats^.sy.Everyfactual situation is a subset of an actual situation. So, if the interpretation of the embedded sentence is persistent, then the fact that it contains a factual situation entails that it also contains an actual situation. Hence, the sentence must be true.
'Less realistic' attitude reports like 'Jon believes that Jackie bites Molly' obey different semantic principles. Veridicality does not apply to believe thai-reports, since one can believe things that are not true. Neither does disjunction distribution: it is possible that 'Jon believes that Jackie or Molly has fleas' is true, whereas both 'Jon believes that Jackie has fleas' and 'John believes that Molly has fleas' are false. On the other hand, conjunction distribution is valid for believe that.
Situation semantics not only wants to account for these logical facts, but also for the way in which atti- tude reports are used in explanations of what people think and do. There is, for example, a big difference between John believingthat Jon is ill and Jon believing that Jon (i.e., he himself) is ill. Yet on an account which construes believing as a relation between indi- viduals and situations, John and Jon stand in exactly the same relation to the same situations if they both believe that Jon is ill, though Jon is the one to get up and go see the doctor. There is some intuitive sense in which John and Jon have different beliefs (i.e., are in different mental states) if they both believe that Jon is ill. Accordingly, situation semantics analyses believe that-reports in terms of represented belief.
The basic idea is to use situation-types to classify both what is believed and how it is believed. This does justice to the commonsense intuition that there are different ways of believing the same thing. Individuals a at locations / are in 'cognitive states': frames of mind which are related to the world by a setting. A frame of mind is given by a situation-type S, and a setting consists of an anchor/(assume that/is a total anchor for S). A belief, therefore, is a pair <5,/>, written as
<B«,/,a,S,f; 1>(brabbreviates'represented belief). Now, John's believing at / in s that Jon is ill at
/' can be rendered as: <BK, /, John, S,f; 1 >es, where S={<ILL,/,a;!>},/(/)=/', andf(l)=Jon. The fact that Jon is in a different mental state from John when he believes that Jon is ill is expressed by using the role i in his frame of mind, an indeterminate associated with the agent of a situation. (Roles will be discussed below.)
The semantics of believe that-reports is phrased in terms of situation-types and anchors. It is simply required that the agent has some belief <S,/> such that the anchoring of 5 by/classifies the interpretation of the embedded sentence. On this analysis, if a believes that <f>, and the statement that \j/ is a strong consequence of the statement that 0, then a believes that \l/. So, conjunction distribution is valid (whereas disjunction distribution and veridicality fail).
4. ExtensionsandDevelopments
Barwise and Etchemendy's The Liar (1987) is a tho- rough study of the liar paradox and related cases of circularity or self-reference. Assertions like 'I am now lying, 'What I am now saying is false,' This prop- osition is not true' are paradoxical, since if they were true, then what they claim would have to be the case, and so they would be not true. Conversely, if they are not true, then what they claim to be the case is in fact the case, so they must be true. Whereas the liar paradox has been known since antiquity, no sat- isfactory analysis of it has yet been given. In formal semantic practice, one usually follows Tarski's (1956) approach of avoiding the paradox by denying languages their own truth predicate. Saul Kripke, however, has shown that circular reference of the sort involved in the liar is not only a much more common phenomenon than had been supposed, but also that whether a given utterance is paradoxical may well depend on nonlinguistic, empirical facts. Ergo: 'there can be no syntactic or semantic "sieve" that will win- nowoutthe"bad" caseswhilepreservingthe"good" ones' (Kripke 1975). Barwise and Etchemendy's analysis of languages that admit circular reference and contain their own truth predicate supplements situation theory with the theory of non-wellfounded sets developed by Peter Aczel.
Aczel (1988: ii) introduces non-wellfounded ('extra- ordinary') sets with a quotation from Mirimanoff (1917): 'Let E be a set, E' one of its elements, E) any element of E', and so on. Call a descent the sequence of steps from E to E', E' to £>, etc I say that a set is ordinary when it only gives rise to finite descents; I say that it is extraordinary when among its descents there are some which are infinite.' The standard sys- tem of axiomatic set theory, ZFC,includes the foun- dation axiom FA. This axiom expresses that all sets are ordinary (i.e., wellfounded), thus giving rise to the familiar 'cumulative hierarchy of sets.' Instead, Aczel proposes an antifoundation axiom (AFA) which entails the existence of non-wellfounded sets such as Q: the unique set such that Q = {fl}. Using a version of Aczel's set theory with atoms, Barwise and Etch- emendy arrive at a notion of circular situations and circular propositions. On their view, truth is not a property of sentences, but of statements or prop- ositions. Sentences may well fail to express a prop- osition, and so fail to have a truth value. This does not hold for propositions, the kind of thing asserted by a successful statement: if a proposition is not true, then it is false. The Liar discusses two accounts of the relation between sentences and the propositions they express, the Russellian and the Austinian view.
According to the Russellian view, sentences are used to express propositions, claims about the world, and these claims are true just in case the world is as it is claimed to be. Relevant is that the truth of the proposition is arbitrated by the world as a whole. On
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