Reconstructing Carnap Online Seminar Series

victorg, Thursday 23 May 2024 - 00:00:00 //

**We are pleased to announce Prof. Constantin C. Brîncuș's (Institute of Philosophy and Psychology, Romanian Academy /University of Bucharest) upcoming talk. The talk is part of the online Seminar Series**

*Reconstructing Carnap: The Aufbau Project a Century Later*, organized by the University of Naples Federico II. Join us via Zoom on Thursday, May 23, 2024, at 3 pm CET.

**The talk will be given in English. If you wish to participate, please put in contact with the organizers:**

**Caterina Del Sordo: caterina.delsordo@ehu.eus**

**Felice Masi: felice.masi@unina.it**

**Francesco Pisano: francesco.pisano2@unina.it**

**Here are title and abstract of the talk:**

By Constantin C. Brîncuș

*Carnap’s Categoricity Problem: Then and Now*By Constantin C. Brîncuș

**(Institute of Philosophy and Psychology, Romanian Academy /University of Bucharest)**

Carnap’s Gabelbarkeitssatz grew out of the Aufbau project, in his trying to obtain proper concepts defined by an axiom system, and asserts that a consistent axiom system is decidable if and only if it is categorical. However, due to Gdel’s incompleteness results, the system for whose decidability Carnap argued based on its categoricity is undecidable. One of the reasons that made Carnap’s argument to closely miss its target was the lack of a clear distinction at that time between the axiom system under investigation and the logical language in which the investigation is conducted. Still, Carnap did not abandon his investigations on decidability and categoricity. In my presentation, I shall discuss the relation between these two concepts with a focus on what is nowadays called Carnap’s Categoricity Problem for a system of logic, i.e. the question of whether the semantics of a logic can be uniquely determined by its proof theoretical systems. In particular, I shall examine two recent arguments for the idea that the natural deduction rules for the first-order universal quantifier are categorical, i.e., that they uniquely determine its semantic intended meaning. I argue that the success of both these arguments is relative to their semantic or infinitary assumptions, which could be easily discharged if the introduction rule for the universal quantifier is taken to be an infinitary rule. Consequently, I reconsider the use of the ω-rule and I show that its addition to the standard formalizations of first-order logic is categorical. Finally, I advance an argument for the categoricity of first-order Peano Arithmetic based on the inferential conservativity requirement. The presentation is mainly based on my two recent publications: "Categorical Quantification", Bulletin of Symbolic Logic, 2024, pp. 1-27; "Inferential Quantification and the ω-Rule". In Antonio Piccolomini d'Aragona (Ed.) Perspectives on Deduction, Synthese Library Series, Springer, 2024, pp. 345-372.