Grelling’s Paradox is the paradox which results from considering whether heterologicality, the word-property which a designator has when and only when the designator does not bear the word-property it designates, is had by ‘ ȁ8heterologicality’. Although there has been some philosophical debate over its solution, Grelling’s Paradox is nearly uniformly treated as a variant of either the Liar Paradox or Russell’s Paradox, a paradox which does not present any philosophical challenges not already presented by the two better known paradoxes. The (...) aims of this paper are, first, to offer a precise formulation of Grelling’s Paradox which is clearly distinguished from both the Liar Paradox and Russell’s Paradox; second, to offer a solution to Grelling’s Paradox which both resolves the paradoxical reasoning and accounts for unproblematic predications of heterologicality; and, third, to argue that there are two lessons to be drawn from Grelling’s Paradox which have not yet been drawn from the Liar or Russell’s Paradox. The first lesson is that it is possible for the semantic content of a predicate to be sensitive to the semantic context; i.e., it is possible for a predicate to be an indexical expression. The second lesson is that the semantic content of an indexical predicate, though unproblematic for many cases, can nevertheless be problematic in some cases. (shrink)

This brief note corrects an error in one of the reduction steps in my paper 'Normalisation for Bilateral Classical Logic with some Philosophical Remarks' published in the Journal of Applied Logics 8/2 (2021): 531-556.

To be a proposition is to possess propositional properties and to stand in inferential relations. This is the organic intuition, [OI], concerning propositional recognition. [OI] is not a circular characterization as long as those properties and relations that signal the presence of propositions are independently identified. My take on propositions does not depart from the standard approach widely accepted among philosophers of language. Propositions are truth-bearers, the arguments of truth-functions (‘not’, ‘or’, ‘and’, ‘if’), the arguments of propositional-attitude verbs (‘know’, ‘believe’, (...) ‘doubt’, ‘assume’, ‘reject’) and the kind of entity capable of standing in inferential relations (which are basically implication and incompatibility). The aim of this paper is to argue for [OI]. In doing so, I will show that even what is probably the most repeated argument against non-descriptivism, the so-called Frege-Geach Argument (FGA), presupposes something like [OI], a presupposition that Geach shares with his critics. Despite the huge success of FGA, a thorough analysis of the actual scope of this argument has yet to be given. I will provide such an analysis in section 3 below. In this paper, I argue that [OI] is a meta-theoretical principle which is neutral with respect to specific metaphysical debates about the nature of propositions, as well as specific proposals about the semantics of declarative sentences. (shrink)

Grelling's Paradox is the paradox which results from considering whether heterologicality, the word-property which a designator has when and only when the designator does not bear the word-property it designates, is had by 'heterologicality'. Although there has been some philosophical debate over its solution, Grelling's Paradox is nearly uniformly treated as a variant of either the Liar Paradox or Russell's Paradox, a paradox which does not present any philosophical challenges not already presented by the two better known paradoxes. The aims (...) of this paper are, first, to offer a precise formulation of Grelling's Paradox which is clearly distinguished from both the Liar Paradox and Russell's Paradox; second, to offer a solution to Grelling's Paradox which both resolves the paradoxical reasoning and accounts for unproblematic predications of heterologicality; and, third, to argue that there are two lessons to be drawn from Grelling's Paradox which have not yet been drawn from the Liar or Russell's Paradox. The first lesson is that it is possible for the semantic content of a predicate to be sensitive to the semantic context; i.e., it is possible for a predicate to be an indexical expression. The second lesson is that the semantic content of an indexical predicate, though unproblematic for many cases, can nevertheless be problematic in some cases. In Section 1, Grelling's Paradox is presented informally. After making some refinements, Grelling's Paradox is then presented formally. In Section 2, the formal version of Grelling's Paradox is evaluated, and several previously proposed solutions are discussed and argued to be inadequate. In Section 3, it is argued that the heterologicality predicate is an indexical expression. A semantics for the heterologicality predicate is given, and it is shown how this semantics accounts for the unproblematic predications of heterologicality, as well as the problematic cases, and therefore constitutes a satisfactory and complete solution to Grelling's Paradox. Objections to this solution are addressed in Section 4. The conclusions of this paper are summarized in Section 5. (shrink)