Robin Jeshion

Overview The debate over the semantics of proper names has, of late, heated up, focusing on the relative merits of referentialism and predicativism. Referentialists maintain that the semantic function of proper names is to designate individuals. They hold that a proper name, as it occurs in a sentence in a context of use, refers to a specific individual that is its referent and has just that individual as its semantic content, its contribution to the proposition expressed by the sentence. Furthermore, a proper name contributes its referent to the proposition expressed by virtue of mechanisms of direct reference to individuals, not by virtue of expressing properties. Predicativists embrace an opposing view according to which proper names are just a special kind of common noun. Their semantic function is to designate properties of individuals. A proper name, as it occurs in a sentence in a context of use, expresses a property, and that property is its contribution to the proposition expr ..

Controversy remains over exactly why Frege aimed to estabish logicism. In this essay, I argue that the most influential interpretations of Frege's motivations fall short because they misunderstand or neglect Frege's claims that axioms must be self-evident. I offer an interpretation of his appeals to self-evidence and attempt to show that they reveal a previously overlooked motivation for establishing logicism, one which has roots in the Euclidean rationalist tradition. More specifically, my view is that Frege had two notions of self-evidence. One notion is that of a truth being foundationally secure, yet not grounded on any other truth. The second notion is that of a truth that requires only clearly grasping its content for rational, a priori justified recognition of its truth. The overarching thesis I develop is that Frege required that axioms be self-evident in both senses, and he relied on judging propositions to be self-evident as part of his fallibilist method for identifying a foundation of arithmetic. Consequently, we must recognize both notions in order to understand how Frege construes ultimate foundational proofs, his methodology for discovering and identifying such proofs, and why he thought the propositions of arithmetic required proof.