Quantifiers and Frege's problem

Abstract

In On Sense and Reference, Frege (2009) tackles the following question (he-reafter, I refer to it simply as ‘Frege’s puzzle’): how can we often augment our knowledge by discovering the truth of identities of the form a=b? To this question, a subcase of the logical omniscience problem, Frege offers the following response in terms of a sense and reference dichotomy: an individu-al who ignores that a=b is true does not know that the senses of the proper names occurring in the sentence pick out the same reference. Although not uncontroversial, Frege’s solution is still very influential. Hence, it would be interesting to verify whether it can be generalized for other cases of the logi-cal omniscience problem. The present paper deals with this issue. I want to show that Frege’s puzzle as well as its solution in terms of a distinction between sense and reference can be applied to a broader set of cases of failu-re of logical omniscience related to our semantic competence in using quan-tifiers. Whereas Frege’s original puzzle considers cases of ignorance on the correferentiality of two proper names, the generalized version of the puzzle regards cases of ignorance on the co-extensionality of two or more quantifi-ers occurring in a formula. Drawing upon a 2-dimensionalist characterization of the concept of sense, I hold that quantifiers display an indexical feature and, consequently, are associated to character functions that, in some coun-terfactual linguistic contexts not ruled out by the imperfect epistemic situati-on of ordinary rational agents, ascribe non-extensional domains to different quantifiers occurring in the considered formula.