Gabriella Crocco

Gödel on Concepts

This article is an attempt to present Gödels discussion on concepts, from 1944 to the late 1970s, in particular relation to the thought of Frege and Russell. The discussion takes its point of departure from Gödels claim in notes on Bernays review of ‘Russells mathematical logic’. It then retraces the historical background of the notion of intension which both Russell and Gödel use, and offers some grounds for claiming that Gödel consistently considered logic as a free-type theory of concepts, called intensions, considered as the denotations of predicate names.

GÖDEL, CARNAP AND THE FREGEAN HERITAGE

Thorough a detailed analysis of version III of Gödels Is mathematics syntax of language?, we propose a new interpretation of Gödels criticism against the conventionalist point of view in mathematics. When one reads carefully Gödels text, it brings out that, contrary to the opinion of some commentators, Gödel did not overlook the novelty of Carnaps solution, and did not criticise him from an old-fashioned conception of science. The general aim of our analysis is to restate the Carnap/Gödel debate in the Fregean heritage. We stress the way both of them try to answer, from different Fregean perspectives, to the question of the nature of logic and mathematics in knowledge.

Gödel, Leibniz and “Russell’s Mathematical Logic”

Kurt Godel explicitly mentioned Leibniz in only one paper, “Russell’s mathematical logic”, which appeared in 1944 in the volume of the Library of Living Philosophers devoted to Bertrand Russell and edited by A. Schilpp.1 Nevertheless, the tribute paid by Godel to Leibniz in this text is so important that this alone suffices in attesting to the role that Leibniz’s work played in Godel’s thought.