Sofía Meléndez Gutiérrez

Possibilism is a realist theory of fictional entities which identifies these entities with concretist non-actual individuals. In his Princeton Lectures, Kripke presented an objection against possibilism which appeared fatal; but forty years later, Stone argued that the possibilist can bypass this objection on the grounds of a supervaluationist theory of fictive names. In this paper, I argue that Stone's theory is right now marred by a significant sort of incompleteness, and I attempt to take a firm step towards its completion.

Two entities are weakly discernible when they share every single one of their intrinsic and relational properties, but a symmetric and irreflexive relation holds between them. The theory of arbitrary reference, first proposed by Breckenridge and Magidor in 2012, states that some semantic facts are brute. And, in this paper, I argue that this theory is inconsistent with the thesis that weakly discernible entities are metaphysically possible. For the advocates of arbitrary reference, this result is problematic for two independent reasons. First: the thesis that weakly discernible entities are metaphysically possible is strikingly plausible and supported by a variety of compelling arguments. If it is true, though, then the theory of arbitrary reference is false. And second: some of the applications that the theory of arbitrary reference has been claimed to have depend on the assumption that weakly discernible entities are metaphysically possible. Those who have tried to take advantage of said applications (e.g., ante rem structuralists) will find, consequently, that their projects are doomed to fail.

Types are abstract, instantiatable and sui generis entities postulated by platonists to account for the truth of a particular species of intuitively true sentences. Nominalism is the view that, in fact, no types are needed to fulfil the purpose in question. Nominalism is ontologically parsimonious and, hence, commendable—but there is a compelling argument to the effect that, pace the nominalist, types are indispensable to vindicate the truth of the sentences at issue. In my paper, I contend that this argument fails. I also outline a novel, fictionalist account of the relevant sentences, and argue that this account holds a special promise over both nominalism and platonism. I close by defending my fictionalist theory from its most prominent potential objections.

There are compelling reasons to believe that musical works are abstract. However, this hypothesis conflicts with the platitude that musical works are appreciated by means of audition: the things that enter our ear canals and make our eardrums vibrate must be concrete, so how can musical works be listened to if they are abstract? This question constitutes the audibility problem. In this paper, I assess Julian Dodd’s elaborate attempt to solve it, and contend that Dodd’s attempt is unsuccessful. Then I discuss what I take to be the ideal response to the audibility problem, and show that it ultimately fails. I contend, consequently, that the project of construing musical works as audible is disheartening. Accordingly, in my last section, I will argue the audibility problem may be satisfactorily resolved without ascribing audibility to musical works.

This paper is a response to Haze’s brief argument for the falsity of the theory that instantial terms refer arbitrarily, proposed by Breckenridge and Magidor in 2012. In this paper, I characterise instantial terms and outline the theory of arbitrary reference; then I reconstruct Haze’s argument and contend that it fails in its purpose. Haze’s argument is supposed to be a _reductio ad absurdum:_ according to Haze, it proves that a contradiction follows from the most basic tenets of the theory of arbitrary reference. I will argue, however, that the contradiction in question follows not from these tenets, but from the surreptitious use that Haze makes of a self-referential expression. I conclude, consequently, that Haze’s argument is nothing more than an illustration of the well-known fact that self-referential expressions produce paradoxical results.

Ante rem structures were posited as the subject matter of mathematics in order to resolve a problem of referential indeterminacy within mathematical discourse. Nevertheless, ante rem structuralists are inevitably committed to the existence of indiscernible entities, and this commitment produces an exactly analogous problem. If it cannot be sorted out, then the postulation of ante rem structures is futile. In a recent paper, Stewart Shapiro argued that the problem may be solved by analysing some of the singular terms of mathematics not as genuinely referring expressions, but as instantial terms. In this paper, I discuss several competing accounts of the semantics of terms of this kind, and argue that they are all untenable for the ante rem structuralist. Shapiro, then, still owes us an account of the semantics of instantial terms that suits the ante rem structuralist project. Without it, the ante rem structuralist is still unable to determine the reference of the singular terms of mathematics.