Carnap's philosophy of mathematics

Bibliographic Data

ID4079928
AuthorsBenjamin Marschall (0000-0001-6265-0816, Trinity College, corresponding author)
Year2022
Volume17
Issue11
Publication date2022-11-01
Peer ReviewedYes
Open AccessYes
TypeARTICLE
VenuePhilosophy Compass (JOURNAL)
Journal identifiersISSN: 1747-9991 • E-ISSN: 1747-9991
PublisherWiley (PUBLISHER • GB)
DOI10.1111/phc3.12884
OpenAlexW4306793277
LanguageEN
References cited49

For several decades, Carnap's philosophy of mathematics used to be either dismissed or ignored. It was perceived as a form of linguistic conventionalism and thus taken to rely on the bankrupt notion of truth by convention. However, recent scholarship has revealed a more subtle picture. It has been forcefully argued that Carnap is not a linguistic conventionalist in any straightforward sense, and that supposedly decisive objections against his position target a straw man. This raises two questions. First, how exactly should we characterise Carnap's actual philosophy of mathematics? Secondly, is his position an attractive alternative to established views? I will tackle these issues by looking at Carnap's response to the incompleteness theorems. Drawing on arguments put forward by Gödel and Beth, I show that some crucial aspects of Carnap's positive account have remained underdeveloped. Suggestions on what a full evaluation of Carnap's position requires are made

Convention · Conventionalism · Epistemology · Philosophy of Mathematics · Political science · Scholarship · Social science · Sociology · Law · Philosophy · Philosophy and History of Science · Philosophy and Theoretical Science · Philosophy, Science, and History

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