Deriving and Validating Kripkean Claims Using the Theory of Abstract Objects∗

Saul Kripke has advanced interesting metaphysical and semantic claims that have strong appeal and engender conviction. In some cases, Kripke suggests that these claims constitute only a ‘picture’ rather than a theory, while in others, it is clear that the claims in question constitute a (formally) precise theory. In the former case, it is important to determine whether one can turn the picture into a precise theory and what the consequences are when this is done. In the latter case, it is important to determine whether Kripke’s claims are to be construed as proper (i.e., non-logical) axioms of metaphysics or whether they can be derived as theorems from a more general theory. Moreover, it would be of interest to learn that claims Kripke has put forward on a variety of different topics can be unified within the context of a single, precisely formulated theory. In what follows, I show that a variety of Kripke’s most important metaphysical and semantical claims can be derived or validated within the theory of abstract objects (Zalta [1983], [1988]). Hereafter, we refer ∗Published in Noûs, 40/4 (December 2006): 591–622. †I’d like to thank Jonathan Berg for inviting me to the Naming, Necessity, and More Conference held in honor of Saul Kripke at the University of Haifa, in June 1999. This essay was originally prepared for that conference. I am indebted to those who offered comments at that conference and at the other venues where the piece was subsequently presented: Australasian Association of Philosophy Conference (July 2000), Indiana University (November 2000), Pacific APA Symposium (March 2002), and University of Milan (June 2002). I’d like to thank Fred Kroon for reading the second draft of the manuscript and making interesting observations that led to improvements. I am especially indebted to Paul Oppenheimer, who read the final drafts very carefully and whose suggestions helped to refine the claims in the paper as well as remove infelicities of expression. Finally, thanks go to two anonymous referees at Noûs, who offered valuable suggestions for enhancing the paper, almost all of which were adopted. Edward N. Zalta 2