Robin Jeshion

This paper offers a defense of Charles Parsons’ appeal to mathematical intuition as a fundamental factor in solving Benacerraf’s problem for a non-eliminative structuralist version of Platonism. The literature is replete with challenges to his well-known argument that mathematical intuition justifies our knowledge of the infinitude of the natural numbers, in particular his demonstration that any member of a Hilbertian stroke string ω-sequence has a successor. On Parsons’ Kantian approach, this amounts to demonstrating that for an “arbitrary” or “vaguely represented” string of strokes, we can always “add” one more stroke. Critics have contested the cogency of a notion of an arbitrary object, our capacity to vaguely represent a definite object, and the role of spatial and temporal representation in the demonstration that we can “add” one more. The bulk of this paper is devoted to demonstrating how to meet all extant criticisms of his key argument. Critics have also suggested that Parsons’ whole approach is misbegotten because the appeal to mathematical intuition inevitably falls short of providing a complete solution to Benacerraf’s problem. Since the natural numbers are essentially and exclusively characterized by their structural properties, they cannot be identified with any particular model of arithmetic, and thus a notion of intuition will fail to capture the universality of arithmetic, its applicability to all entities. This paper also explains why we should not reject appeal to mathematical intuition even though it is not itself sufficient to fully “close the gap” on Benacerraf’s challenge

Clarence Sloat, Ora Matushansky, and Delia Graff Fara advocate a Syntactic Rationale on behalf of predicativism, the view that names are predicates in all of their occurrences. Each argues that a set of surprising syntactic data compels us to recognize names as a special variety of count noun. This data set, they say, reveals that names’ interaction with the determiner system differs from that of common count nouns only with respect to the definite article ‘the’. They conclude that this special distribution of names is best explained by the-predicativism, the view that posits the existence of the null-determiner ‘the’ preceding bare singular names. This essay argues that they have incorrectly discerned the syntactic facts: their critical data point concerning the ungrammaticality of sentences like “The Katherine wants coffee” is mistaken. Such sentences’ grammaticality undermines the Syntactic Rationale and presents serious auxiliary problems for predicativism.

The epistemological argument against descriptivism about proper names is extremely simple. For a proper name ‘N’ and definite description ‘F’, the proposition expressed by “If N exists, then N is F” is not normally known a priori. But descriptivism about proper names entails otherwise. So descriptivism is false. The argument is widely regarded as sound. This paper aims to establish that the epistemological argument is highly unstable. The problem with the argument is that there seems to be no convincing rationale for the first premise that is independent of a view about the nature of the proposition expressed by the sentence “If N exists, then N is F”.

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 ..