Abstract
The failed criterion of logical truth proposed by Carnap in the Logical Syntax of Language was based on the determinateness of all logical and mathematical statements. It is related to a conception which is independent of the specifics of the system of the Syntax, hints of which occur elsewhere in Carnap’s writings, and those of others. What is essential is the idea that the logical terms are invariant under reinterpretation of the empirical terms, and are therefore semantically determinate. A certain objection to Carnap’s version of the invariance conception has been repeated several times in the literature. It is based on Gödel incompleteness, which is puzzling, since Carnap’s Syntax is otherwise quite careful to take account of Gödel. We show here that, in fact, the objection is invalid and is based on a confusion about determinacy. Sorting this out is worthwhile not only for the purpose of better understanding Carnap’s thinking in the Syntax, though. The invariance conception is also related to recent work in the philosophy of logic regarding “logicality”—the characterization of logical concepts—following a proposal of Tarski’s. It is even connected to some very recent developments in the foundations of mathematics.
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Notes
This is the gist of an argument that has taken different forms and appeared in different contexts. The present discussion is not intended to single out any particular author, but to address a certain central motif common to many of these contexts; as given here, this motif is stripped down to a stylized minimum. Examples of its appearance in different contexts are Beth (1963), Goldfarb and Ricketts (1992), and Friedman (1999).
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Acknowledgments
Thanks to Hannes Leitgeb for inviting me to the Munich Center for Mathematical Philosophy where this work was done, to Georg Schiemer for organizing the workshop where it was presented, and to André Carus for much valuable input on the ideas contained herein and crucial assistance in actually writing the paper.
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Awodey, S. Carnap and the invariance of logical truth. Synthese 194, 67–78 (2017). https://doi.org/10.1007/s11229-015-0781-6
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DOI: https://doi.org/10.1007/s11229-015-0781-6