Pablo Rivas-Robledo

The papers contained in this collection were presented at the 24th Amsterdam Colloquium, organised by the Institute for Logic, Language and Computation (ILLC) at the University of Amsterdam, December 18–20, 2024. The Amsterdam Colloquia aim at bringing together linguists, philosophers, logicians, cognitive scientists, and computer scientists who share an interest in the formal study of the semantics and pragmatics of natural and formal languages. Besides the general programme, the 2024 edition featured two workshops. First, “Dynamic and Inquisitive: Themes from the Work of Jeroen Groenendijk”, dedicated to the memory of Jeroen Groenendijk. Second, “Identifying and Explaining Universals of Semantics”. The 2024 edition also included the Beth Lecture, jointly organised with the E.W. Beth Foundation. The programme included 7 invited talks, 34 contributed talks, and three poster sessions with 24 contributed posters.

In this article I present HYPER-REF, a model to determine the referent of any given expression in First-Order Logic (FOL). I also explain how this model can be used to determine the referent of a first-order theory such as First-Order Arithmetic (FOA). By reference or referent I mean the non-empty set of objects that the syntactical terms of a well-formed formula (wff) pick out given a particular interpretation of the language. To do so, I will first draw on previous work to make explicit the notion of reference and its hyperintensional features. Then I present HYPER-REF and offer a heuristic method for determining the reference of any formula. Then I discuss some of the benefits and most salient features of HYPER-REF, including some remarks on the nature of self-reference in formal languages.