Semantic and pragmatic characterizability of linguistic usage

Abstract

In order to be able to discuss Stenius's very suggestive contribution to this symposium, we seem called upon to bring a little more order into the variety of key notions employed by him, e.g. those of sentence, sen tence-radical, mood, modal element, semantic characterization of (the meaning of) a modal element, language-game, modal (semantic) rule, and so forth. We shall try to do so by taking as our point of departure two fairly simple artificial languages L? and L2, the vocabulary of which is in relevant respects similar to the one figuring in what Stenius calls the report-game and the combined game, respectively. Thus, Lx and L2 both has as 'descriptive' signs two one-place predicate constants 'P9 and 'Q9 as well as some finite (but large enough) number of individual constants 'at9, 'a2 ,...,'a9. Any sequence of the form Fa, where F is a predicate constant and a an individual one, is a sentence in Ll9 and a sentence-radical in L2. L2, but not Ll9 also contains the follow ing modal signs, or syntactic modal elements: T (the indicative sign, read as 'It is the case that'), '0' (the imperative sign, read as 'Let it be the case that'), and '?' (the Yss-No-interrogative sign, read as 'Is it the case that'). A sentence in L2 is then any sequence mFa, where m is a modal sign in L2 and Fa a sentence-radical in L2. In an obvious way L2-sentences may then be divided into indicative, imperative, and interrogative ones. As far as the syntax of Lx and L2 goes, these explanations will have to do for the moment. Next, we want to interpret Lt and L2 along the main lines indicated by Stenius. First, suppose we are given some non-empty domain of individuals D as our 'universe of discourse'. A valuation is a binary function F which, given D, assigns an individual in D to each individual constant and a subset of D to each predicate-constant, with the following restriction: V('Q9, D)=D?V('P9, D). In his 'language-games', Stenius chooses a particular domain of individuals consisting of squares in a flower-bed, which are assigned as denotations to individual constants; moreover, he obviously takes 'P9 and 'Q9 to denote complementary classes, or proper