Carnap and Beth on the Limits of Tolerance

Canadian Journal of Philosophy 51 (4):282–300 (2021)
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Abstract

Rudolf Carnap’s principle of tolerance states that there is no need to justify the adoption of a logic by philosophical means. Carnap uses the freedom provided by this principle in his philosophy of mathematics: he wants to capture the idea that mathematical truth is a matter of linguistic rules by relying on a strong metalanguage with infinitary inference rules. In this paper, I give a new interpretation of an argument by E. W. Beth, which shows that the principle of tolerance does not suffice to remove all obstacles to the employment of infinitary rules.

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10.1017/can.2021.16

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Benjamin Marschall
Cambridge University

Citations of this work

Carnap's philosophy of mathematics.Benjamin Marschall - 2022 - Philosophy Compass 17 (11):e12884.
Carnap and the a priori.Benjamin Marschall - forthcoming - European Journal of Philosophy.

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References found in this work

Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.
Wittgenstein on rules and private language.Saul A. Kripke - 1982 - Revue Philosophique de la France Et de l'Etranger 173 (4):496-499.
Realism and reason.Hilary Putnam (ed.) - 1983 - New York: Cambridge University Press.
Testability and meaning.Rudolf Carnap - 1936 - Philosophy of Science 3 (4):419-471.

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