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Founding Mathematics on Semantic ConventionsA Convention for a Type-free Language

Founding Mathematics on Semantic Conventions: A Convention for a Type-free Language [This chapter and the two that follow it lay out an extensive semantic-conventionalist system, and are therefore technical in nature. Here, the author develops the specific gappy logic that he thinks is most useful for a mathematical system that is to include real numbers. Though it is strongly inspired by Saul Kripke’s gappy logic, it suggests that the latter is just a little too gappy. This problem is alleviated by adding a conditional with a special kind of supervaluational semantics that validates hypothetical proofs. The author proves that the result retains the virtues of consistency and “trustworthiness”.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Founding Mathematics on Semantic ConventionsA Convention for a Type-free Language

Part of the Synthese Library Book Series (volume 446)
Hansen, Casper Storm
Founding Mathematics on Semantic Conventions — Nov 5, 2021
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Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-88533-5
Pages
113 –143
DOI
10.1007/978-3-030-88534-2_7
Publisher site
See Chapter on Publisher Site

Abstract

[This chapter and the two that follow it lay out an extensive semantic-conventionalist system, and are therefore technical in nature. Here, the author develops the specific gappy logic that he thinks is most useful for a mathematical system that is to include real numbers. Though it is strongly inspired by Saul Kripke’s gappy logic, it suggests that the latter is just a little too gappy. This problem is alleviated by adding a conditional with a special kind of supervaluational semantics that validates hypothetical proofs. The author proves that the result retains the virtues of consistency and “trustworthiness”.]

Published: Nov 5, 2021

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