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Founding Mathematics on Semantic ConventionsBasic Mathematics

Founding Mathematics on Semantic Conventions: Basic Mathematics [Here, the framework provided in the previous chapter begins to be filled up with mathematical content, starting from arithmetic and other relatively basic areas of mathematics. The chapter demonstrates in detail how mathematics can be constituted by an open-ended language, where the classical mathematicians’ praxis of “building” mathematical objects out of sets is replaced with a praxis of stipulating syntactical forms of terms and sentences, together with truth conditions for those sentences. In addition, the author shows how to prove theorems in this mathematics and apply it to the empirical world.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Founding Mathematics on Semantic ConventionsBasic Mathematics

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
145 –167
DOI
10.1007/978-3-030-88534-2_8
Publisher site
See Chapter on Publisher Site

Abstract

[Here, the framework provided in the previous chapter begins to be filled up with mathematical content, starting from arithmetic and other relatively basic areas of mathematics. The chapter demonstrates in detail how mathematics can be constituted by an open-ended language, where the classical mathematicians’ praxis of “building” mathematical objects out of sets is replaced with a praxis of stipulating syntactical forms of terms and sentences, together with truth conditions for those sentences. In addition, the author shows how to prove theorems in this mathematics and apply it to the empirical world.]

Published: Nov 5, 2021

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