Carnap, formalism, and informal rigour

Philosophia Mathematica 16 (1):4-24 (2008)
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Carnap's position on mathematical truth in The Logical Syntax of Language has been attacked from two sides: Kreisel argues that it is formalistic but should not be, and Friedman argues that it is not formalistic but needs to be. In this paper I argue that the Carnap of Syntax does not eliminate our ordinary notion of mathematical truth in favour of a formal analogue; so Carnap's notion of mathematical truth is not formalistic. I further argue that there is no conflict between Carnap's use of informal notions and his principle of tolerance; so Carnap's definition of mathematical truth need not be formalistic. CiteULike    Connotea    What's this?



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Gregory Lavers
Concordia University

Citations of this work

Carnap’s Early Semantics.Georg Schiemer - 2013 - Erkenntnis 78 (3):487-522.
On the Quinean-analyticity of mathematical propositions.Gregory Lavers - 2012 - Philosophical Studies 159 (2):299-319.
The parallel structure of mathematical reasoning.Andrew Aberdein - 2012 - In Alison Pease & Brendan Larvor (eds.), Proceedings of the Symposium on Mathematical Practice and Cognition Ii: A Symposium at the Aisb/Iacap World Congress 2012. Society for the Study of Artificial Intelligence and the Simulation of Behaviour. pp. 7--14.
Benacerraf’s dilemma and informal mathematics.Gregory Lavers - 2009 - Review of Symbolic Logic 2 (4):769-785.

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