Deriving and Validating Kripkean Claims Using the Theory of Abstract Objects


Edward N. Zalta


Noûs, 40/4 (December 2006): 591-622.


Abstract: In this paper, the author shows how one can independently prove, within the theory of abstract objects, some of the most significant claims, hypotheses, and background assumptions found in Kripke's logical and philosophical work. Moreover, many of the semantic features of theory of abstract objects are consistent with Kripke's views — the successful representation, in the system, of the truth conditions and entailments of philosophically puzzling sentences of natural language validates certain Kripkean semantic claims about natural language.

In Kripke's work on modal language and logic, he assumes (in the semantic metalanguage) that there are possible worlds, that there is a distinguished actual world, that (in S5) the sentence "Necessarily, p" in the object language is true iff "p" is true in all possible worlds, and that (in S5) "Possibly, p" is true iff "p" is true in some possible world. These are shown to be theorems of formal object theory. In work on identity and necessity, Kripke endorses the claims that if x = y, then necessarily x = y, and that (in the case of natural kinds F and G) if F = G, then necessarily F = G. Both of these universal generalizations can be derived in our theory, and we show that rigid proper names and natural kind terms are system defaults.

In the final part of the paper we show that significant claims that Kripke has made in the philosophy of fiction can similarly be derived or validated. We consider not only his published work, in which he claims that fictional characters and species can't be identified with possible objects and possible species (respectively), but also some unpublished work, in which he suggests the following: (a) that an "empty" name used in a pretense subsequently becomes a referential part of natural language, (b) that natural language quantifies over a realm of abstract, fictional entities; (c) that fictional entities are contingent objects for which it is an empirical question as to whether there is such and such a fictional character; (d) that fictional characters exist in virtue of more concrete activities of telling stories; and (e) that there is a confusing double usage of predication and, in particular, there are two types of predication we can make about Hamlet (claims like "Hamlet has been discussed by many critics" constitute one type and claims like "Hamlet was melancholy" constitute a different type).

[Note: The final version has not yet been sent to the publisher. This version may change in minor ways.]
[Preprint available online in PDF]