POSSIBILIA AND POSSIBLE WORLDS*

Ruth BARCAN MARCUS Yale University

Introduction The development of quantified modal logic' rekindled an interest in systematic accounts of modalities. Until that time modal propo­ sitional logic was widely perceived as, at best, a misleading way of representing metalogical and semantical notions such as validity, consistency, logical consequence and the like, through locutions like 'necessity', 'possibility' and 'entailment'. 2 With quantified modal logic (QML) the attack was sharper. For here it was claimed there emerged deep failures and confusions which went beyond the merely misleading representations of metalogical concepts. The criticisms fell into several categories often insufficient­ ly distinguished. I will discuss two among such continuing debates. The first and only briefly is the putative problem of failure of substitutivity of co-referential terms in modal contexts. The second is the apparent commitment of modal semantics to possible objects, possibilia. In conclusion I will discuss alternatives for a more adequate modal logic and its semantics, carrying on some themes of proposals from my earlier work. * This paper has been informed by study of the work, published or unpublished, of Joseph Almog, Keith Donnellan, David Kaplan, Saul Kripke, John Perry and Howard Wettstein.

1. See R. Barcan (Marcus), "A Functional Calculus of First Order Based on Strict Implication", Journal of Symbolic Logic 11 (1946): 1-16. "The Identity of Individuals in a Strict Functional Calculus", Journal of Symbolic Logic 12 (1947); 12-15. See also R. Carnap, Meaning and Necessity (Chicago: University of Cicago, 1947). 2. See W. V. Quine, From a Logical Point of View (Cambridge, Mass.: Harvard, 1953). Also, "Three Grades of Modal Involvement" in The Ways of Paradox (New York, 1966). 108 Substitutivity of identity: The dilemma about substitution was seen as the following predicament. Either QML leads to a failure of truth preserving substitutivity for co-referential names and hence the breakdown of the centrally valid principle of substitutivity for identity, or alternatively and equally odious if substitutivity was to be preserved, then the values of variables for modal logic were in­ dividual concepts or alternatively possible objects rather than or­ dinary objective referents. In this way substituting 'the evening star' for one occurrence of 'the morning star' in 'the morning star is the morning star' is not permitted, since those terms in modal contexts do not designate the same concept or the same possible object. But then it is claimed QML has a different subject matter than non-modal logic; a different domain over which its variables range. It is not a straightforward extension of standard predicate logic achieved by adding modal operators and syntactical rules for their use along with additional inference rules. The semantics will shift radically from ordinary object domains to domains of concepts. Something like Frege's thoughts would replace Russell's propositions. Russell's propositions are structures which have ontologically independent actual objects, not meanings, as constituents. It must be kept in mind throughout, that Russell's propositions are not constituted of lin­ guistic entities or meanings. Recall Frege's astonishment when told by Russell3 that Mont Blanc, the mountain, was "itself a component in the proposition 'Mont Blanc is 4,000 meters high'." How much confusion would have been avoided if the vocabulary of "states of affairs" had been deployed instead of "proposition" which for many suggests a linguistic or quasi-linguistic entity or a mental or quasi­ mental entity. It was for such reasons that of the first modal extensions of quantification theory, mine and Carnap's,4 although there were syntactical similarities, Carnap's was set aside since its semantics involved inter alia systematic ambiguity of reference relative to context in a Fregean way and ran counter to accepted views of objective reference, views which receive a realization in standard non­ modal model theoretic semantics.

3. G. Frege, Philosophical and Mathematical Correspondence, ed. Gabriel et al. (Chicago: University of Chicago, 1980) p. 163. 4. Op. cit.