Fri Apr 4, 2008
60 Evans Hall, 4:10–6 PM
Paolo Mancosu (UC Berkeley)
Tarski on Categoricity and Completeness: An Unpublished Lecture from 1940
In the Tarski archive at Berkeley there is a lecture entitled “On the Completeness and Categoricity of Deductive Systems” that Tarski had intended to publish but never did. The lecture is an important historical document for the development of abstract notions of semantics, such as semantical completeness and categoricity. Versions of these notions had played an important role in the logical investigations of the twenties and thirties (most notably in Fraenkel, Carnap, and Gödel) but in this lecture Tarski has at his disposal the tools of semantics he had recently developed. In addition, the lecture provides welcome information on a topic of central interest to Tarski and to contemporary philosophy of logic, e.g. the Tarskian notion of logical consequence. Finally, some of the technical problems raised in the lecture, concerning semantical completeness and categoricity in higher order logic, are still open and have very recently been the object of renewed attention.
In my talk I will spell out the key elements in the lecture and provide extensive commentary with the aim of clarifying the conceptual background of the lecture and to point to the relevance of some of the issues discussed by Tarski to contemporary philosophical and logical discussions.