Title
Carnap on the Formality of Logic and Mathematics
Author
Abstract
Throughout his intellectual career, Rudolf Carnap developed highly original views on the nature of mathematical knowledge, its relation to logic, and the application of mathematics in the natural sciences. A general line of continuity in his philosophical work on mathematics and logic is the conviction that these disciplines are formal or non-factual in nature. Let us call this Carnap’s formality thesis. The central role of this thesis in his philosophy of mathematics has been emphasized in recent scholarship. Compare, for instance, Friedman (2018, 142), who holds that “Carnap’s conception of analyticity was intended, above all, to make clear that both logic and mathematics are empty of factual content.” A similar verdict is reached in Koellner (2008, 1): “Throughout most of his philosophical career Carnap upheld and defended […] [t]he thesis that the truths of logic and mathematics are analytic and hence without content and purely formal.” As Friedman and Koellner point out, Carnap’s formality thesis can be identified in different formulations in his work, connecting his early contributions to the foundations of geometry and to general axiomatics from the 1920s with his later work on the general syntax of mathematical languages in the Logical Syntax of 1934.
Keywords
PhilosophyMathematicCarnapLogicAnalyticLogical Syntax
Object type
Language
English [eng]
Persistent identifier
Is contained in
Title
Interpreting Carnap
ISBN
9781009099080
Editor
Alan Richardson
Publisher
Cambridge University Press , 2024
From page
171
To page
191
Version type
Access rights
Rights
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