Was Wittgenstein really a Constructivist about Mathematics?
Abstract
It will be argued that Wittgenstein did not outright reject the law of excluded middle for mathematics or the proof-techniques that constructivists reject in connection with the law of excluded middle. Wittgenstein can be seen to be critical of the dogmatic claims of Brouwer and Weyl concerning how proofs should be constructed. Rather than himself laying down a requirement concerning what is and is not a proof, Wittgenstein can be read as exploring the differences between constructive and non-constructive proofs. I will read Wittgenstein as arguing that Brouwer’s rejection of excluded middle is based upon an over-extension from examples that Wittgenstein reads as special cases. Wittgenstein is certainly interested in the difference between constructive and non-constructive proof but only for the purposes of exploring the easily-missed differences between the two, not in order to reject non-constructive approaches.
© 2016 by Walter de Gruyter Berlin/Boston
Artikel in diesem Heft
- Titelei
- Hinweis für Leser / Note for Readers
- Inhalt / Table of Contents
- Wittgenstein Today
- Ein Sack Rosinen
- Ethnologische Betrachtungsweisen: Wittgenstein, Frazer, Sraffa
- Survey and Surveyability
- Was Wittgenstein really a Constructivist about Mathematics?
- Wittgenstein on the Chain of Reasons
- Skepticism, Metaphors and Vertigo
- Identität und Tautologie bei Wittgenstein
- A Wittgensteinian Form of Moral Expressivism
- A von Wright Error and Wittgenstein’s Heracliteanism
- Arthur MacIver’s Diary: Cambridge (October 1929 – March 1930)
- „Das Buch ist voller Leben …“
- Die Autorinnen und Autoren des Bandes / Authors of this Volume
Artikel in diesem Heft
- Titelei
- Hinweis für Leser / Note for Readers
- Inhalt / Table of Contents
- Wittgenstein Today
- Ein Sack Rosinen
- Ethnologische Betrachtungsweisen: Wittgenstein, Frazer, Sraffa
- Survey and Surveyability
- Was Wittgenstein really a Constructivist about Mathematics?
- Wittgenstein on the Chain of Reasons
- Skepticism, Metaphors and Vertigo
- Identität und Tautologie bei Wittgenstein
- A Wittgensteinian Form of Moral Expressivism
- A von Wright Error and Wittgenstein’s Heracliteanism
- Arthur MacIver’s Diary: Cambridge (October 1929 – March 1930)
- „Das Buch ist voller Leben …“
- Die Autorinnen und Autoren des Bandes / Authors of this Volume
