A comparison of two intensional logics

entities which involve situations as parts. In our theory, unlike situation theory, there are maximal situations and some of them are possible worlds (see Zalta, 1988, forthcoming). The important thing is that we take all entities with relations, propositions, or situations as parts to be abstract. Concrete individuals are the only concrete things. Our propositions and situations do not have physical location (though their constituents may) and this is a major difference between situation theory and our theory. The second distinguishing, leading intuition which has governed the development of our theory is the idea that by utilizing special intensional entities to explain substitutivity failures (these entities will have some but not all of the features Fregean senses have), we can preserve much of the tradition in logic deriving from Frege, Russell, Tarski, and Montague. In contrast to Barwise and Perry, who believe that this tradition is inap propriate for representing natural language (1983, p. x), our main goals have been to show that the results of the paradigm system of the tradition can be preserved (possibly in a new guise), that the paradigm system itself falls out as a special case, and that the outstanding puzzles facing this system can be explained by the new theory. To achieve these goals, we have: (1) developed a theory of relations and propositions conceived as structured complexes, (2) developed a theory of intensional entities that allows them to be constituents of the structured complexes (these entities can represent other entities by encoding properties the other entities exemplify; but these intensional entities will not determine the denotations of the terms with which they are associated), and (3) cast these two theories in a Montague-style, type-theoretic framework. This new, very general framework will then reduce, as a special case, to the traditional framework when one ignores all of the intensional entities and the relations and propositions that have them as constituents. It is in the spirit of attempting to refine further the Fregean tradition that we offer the following comparison with what seems to be the paradigm system of this tradition, namely, Montague's intensional logic. This content downloaded from 157.55.39.243 on Thu, 06 Oct 2016 04:58:33 UTC All use subject to http://about.jstor.org/terms A COMPARISON OF TWO INTENSIONAL LOGICS 61 1. GENERAL FEATURES OF THE TWO LOGICS For certain heuristic purposes, it will prove useful to compare our system with Montague's as it is explained in the recent text, Introduction to Montague Semantics, by Dowty, Wall, and Peters (hereafter referred to as: [DWP 1981]). These authors outline very clear motivations for certain features of Montague's logic (see also Partee, 1975), and we plan to examine some of these motivations in light of the features of our intensional logic. In this section of the paper, however, the point is not to criticize his system, but rather to explain clearly the differences between the two systems and sometimes justify why it is we are doing things differently. Our comparison will be hampered somewhat by the fact that Montague uses the method of extension and intension in his semantics, whereas we use the method of denotation and satisfaction in ours. Montague's method is to place both terms and formulas into the more general category of "meaningful expression," and to assign every meaningful expression both an extension and an intension. Once an interpretation M is fixed, and an assignment to the variables g is fixed, Montague assigns to every meaningful expression an extension at each world-time pair. Where a is a meaningful expression, we write "[a]^,t'~" to indicate the extension of a at w and t with respect to model M and assignment g (this follows [DWP 1981]). He then recovers from this assignment an intension for each expression, namely, that function which takes each world-time pair to the extension of the expression at that world-time pair. What distinguishes formulas from other meaningful expressions is the fact that they are of a specific type, namely, the type of expression which is assigned truth values for its extension at various world-time pairs. This causes some difficulty for purposes of comparison, since our method of denotation and satisfaction doesn't quite correspond in a nice way to this method. The terms of our language receive only denotations; we do not assign them intensions. Moreover, we do not relativize the denotations of terms to world-time pairs. They are relativized only to interpretations of the language and assignments to the variables (this automatically makes every term a rigid designator). In addition, there is a whole class of formulas which are not terms (i.e. they do not have denotations), but which are nevertheless meaningful because they have well-defined satisfaction, and hence, truth conditions. Despite these differences, we are going to suppose that we can compare the denotation This content downloaded from 157.55.39.243 on Thu, 06 Oct 2016 04:58:33 UTC All use subject to http://about.jstor.org/terms