Lecture Dr. Iris Loeb – Model Theory and Universalism in Carnap’s early Logic

Date: Friday 31 May, 15.30-17.00
Location: VU Amsterdam, Main Building, De Boelelaan 1105, room 0G11 (‘Filosofenhof’, access near the six elevator block on the 1st floor)

Abstract
To understand the history of modern logic and especially the emergence of metasystematic investigations in the first half of the 20th century, Van Heijenoort (1967) introduced the distinction between logic as a language and logic as a calculus. A prime feature of the logic as a language conception is universality of logic, which entails the ideas that there is only one language (the universal language) and that the interpretation of names of individuals of that language is fixed. Many times it has been argued that the universalistic stance of some logicians (e.g. Frege, Russell, and early Carnap) made metasystematic investigations — and thus also model theory — impossible for them. I will claim, however, that Carnap in his early work Untersuchungen zur Allgemeinen Axiomatik (1928/1929) both maintained a universalistic stance and developed a model theory worthy of that name. The key observations are that (1) he defined models only for fragments of his universal language, (2) models are meaningful expressions within this language, and (3) the connection between a fragment and a model is made by substitution.

Iris Loeb studied Mathematics at Radboud University Nijmegen and obtained her PhD in Computer Science from the same university. She is currently working as a postdoctoral Researcher in the Faculty of Philosophy at VU University.