Recursive Semantics for Knowledge and Belief

1. This paper is an informal exposition of a model-theoretic semantics for knowledge and belief set out in full detail else where.1 Considerations of space and simplicity prevent any recapitulation of tracts of formal definitions. My aim is simply to inform the reader of the alleged existence of one "new direction" in semantics, and to direct him to the original source for its detailed development. I shall explain certain self-imposed limitations on the scope and adequacy conditions of this treatment. Then, in subsequent dis cussion of the semantical problems which I claim to have treated, I shall try to impart the flavour of the technical methods involved. For reasons which will be set out elsewhere in a longer exegetical and critical study of what may be called the Hintikka paradigm in the logic of knowledge and belief2, the adequate semantical treatment of propositional attitudes must consist of a truth definition along the lines of that of Tarski for classical first order languages. Not sharing Davidson's opposition to model theoretic versions of truth definitions3 my basic premiss is that a correct semantics for propositional attitudes should show how the truth or falsity of attitude reports is a matter arising from attitude schemes (or their formal representations) vis ? vis suitably chosen canonical sentences representing the logical forms of those reports on particular readings. Just as a formula of elementary number theory is true or false vis ? vis the particular relational structure in which it is interpreted, so in the system I propose a formula in volving operators corresponding to attitude verbs will be true or false vis ? vis the attitudinal model in which it is interpreted. So firstly, different readings (de re, de dicto) of, say, belief reports, must be captured by different canonical sentences from our logical grammar; and secondly, we must find some way of modelling people's belief schemes about the world and about others' belief schemes about the world. . . and so on.