We defend the view that defines the rigidity of general terms as sameness of designated universal across possible worlds from the objection that such a characterization is incapable of distinguishing rigid from non-rigid readings of general terms and, thus, that it trivializes the notion of rigidity. We also argue that previous attempts to offer a solution to the trivialization problem do no succeed.

Three-valued logics are standardly used to formalize gappy languages, i.e., interpreted languages in which sentences can be true, false or neither. A three-valued logic that assigns the same truth value to all gappy sentences is, in our view, insufficient to capture important semantic differences between them. In this paper we will argue that there are two different kinds of pathologies that should be treated separately and we defend the usefulness of a four-valued logic to represent adequately these two types of (...) gappy sentences. Our purpose is to begin the formal exploration of the four-valued logics that could be used to represent the phenomena in question and to show that these phenomena are present in natural language, at least according to some semantic theories of natural language. (shrink)

Here, I first prove that certain families of k-valued clones have the Gupta-Belnap fixed-point property. This essentially means that all propositional languages that are interpreted with operators belonging to those clones are such that any net of self-referential sentences in the language can be consistently evaluated. I then focus on two four-valued generalisations of the Kleene propositional operators that generalise the strong and weak Kleene operators: Belnap’s clone and Fitting’s clone, respectively. I apply the theorems from the initial part of (...) the paper to analyse the fixed-point property of Belnap’s and Fitting’s clones when some special operators that reflect the semantics are added. The conclusion of the paper is that Fitting’s clone is better suited than Belnap’s to provide self-referential languages with highly expressive resources. (shrink)

The Liar Paradox is a classic argument that creates a contradiction by reflection on a sentence that attributes falsity to itself: ‘this sentence is false’. In our paper we will discuss the ways in which the Liar sentence (and its paradoxical argument) can be represented in first-order logic. The key to the representation is to use first-order logic to model a self-referential language. We will also discuss several related sentences, like the Liar cycles, the empirical versions of the Liar and (...) the Truth teller sentences. (shrink)

Logical localism is a thesis within philosophy of logic according to which the correct logic is dependent on the topic, domain or subject matter of its application. There is a very straightforward problem for anyone defending a localist thesis, a problem that follows from the fact that we reason across domains. This challenge is known as the problem of mixed inferences. The problem is, very roughly, the following: suppose that there are at least two components, within the premises or conclusion (...) of an argument, belonging to domains governed by different logics. Then, which is the criterion of validity for the mixed argument? Our aim is to offer an answer to this question and, more concretely, a way out to the dilemma that Chase Wrenn has raised in his analysis of the problem of mixed inferences. We will use Joshua Schechter’s method of combining logics, juxtaposition, as the criterion of validity for mixed inferences. After exploring its virtues and possible shortcomings, we argue that juxtaposition is a first step towards a fully-fledged solution, but already a promising way out of the dilemma posed by Wrenn. (shrink)

we explore the view that defines rigidity of general terms as sameness of designation across possible worlds. On this view, a general term is rigid just in case it designates the same universal (species, substance or property) in every possible world. This view has been proposed most notably by Bernard Linsky, Nathan Salmon and more recently by Joseph LaPorte, and it has been criticised by several philosophers, including Stephen Schwartz and Scott Soames.