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Empiricism and Philosophy of PhysicsMathematical Knowledge and Mathematical Objects

Empiricism and Philosophy of Physics: Mathematical Knowledge and Mathematical Objects [This chapter is about the ontology and epistemology of mathematical objects. The core problem for an empiricist is that conceiving mathematical objects as existing independently of human thinking makes it impossible to understand how we can have mathematical knowledge, while the alternative, a constructivist conception, resolves the epistemological problem, but entails the identification of truth with provability. That entails that the law of excluded middle must be dismissed as a generally valid logical principle. The identificaiton of truth with provability is furthermore problematic when taking into account Gödel’s first incompleteness theorem. The chapter ends with suggesting a modified constructivism, which keeps the distinction between truth and provability, thus avoiding counter arguments based on Gödel’s theorem.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Empiricism and Philosophy of PhysicsMathematical Knowledge and Mathematical Objects

Part of the Synthese Library Book Series (volume 434)
Johansson, Lars-Göran
Empiricism and Philosophy of Physics — Jan 14, 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
978-3-030-64952-4
Pages
53 –71
DOI
10.1007/978-3-030-64953-1_4
Publisher site
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Abstract

[This chapter is about the ontology and epistemology of mathematical objects. The core problem for an empiricist is that conceiving mathematical objects as existing independently of human thinking makes it impossible to understand how we can have mathematical knowledge, while the alternative, a constructivist conception, resolves the epistemological problem, but entails the identification of truth with provability. That entails that the law of excluded middle must be dismissed as a generally valid logical principle. The identificaiton of truth with provability is furthermore problematic when taking into account Gödel’s first incompleteness theorem. The chapter ends with suggesting a modified constructivism, which keeps the distinction between truth and provability, thus avoiding counter arguments based on Gödel’s theorem.]

Published: Jan 14, 2021

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