Wittgenstein on Incompleteness Makes Paraconsistent Sense

Francesco Berto

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

I provide an interpretation of Wittgenstein’s much criticised remarks on Gödel’s First Incompleteness Theorem in a paraconsistent framework: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was consequent upon his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the model-theoretic features of paraconsistent arithmetics match with many intuitions underlying Wittgenstein’s philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any mathematical question.
Original languageEnglish
Title of host publicationParaconsistency
Subtitle of host publicationLogic and Applications
EditorsK. Tanaka, F. Berto, E. Mares, F. Paoli
PublisherSpringer
Pages257-276
Number of pages20
Volume26
ISBN (Electronic)978-94-007-4438-7
ISBN (Print)978-94-007-4437-0
DOIs
Publication statusPublished - 2012

Publication series

NameLogic, Epistemology, and the Unity of Science
PublisherSpringer
Volume26

Fingerprint

Incompleteness
Ludwig Wittgenstein
Finitism
Intuition
Rejection
Decidability
Metatheory
Philosophy of Mathematics

Cite this

Berto, F. (2012). Wittgenstein on Incompleteness Makes Paraconsistent Sense. In K. Tanaka, F. Berto, E. Mares, & F. Paoli (Eds.), Paraconsistency: Logic and Applications (Vol. 26, pp. 257-276). (Logic, Epistemology, and the Unity of Science; Vol. 26). Springer . https://doi.org/10.1007/978-94-007-4438-7_14

Wittgenstein on Incompleteness Makes Paraconsistent Sense. / Berto, Francesco.

Paraconsistency: Logic and Applications. ed. / K. Tanaka; F. Berto; E. Mares; F. Paoli. Vol. 26 Springer , 2012. p. 257-276 (Logic, Epistemology, and the Unity of Science; Vol. 26).

Research output: Chapter in Book/Report/Conference proceedingChapter

Berto, F 2012, Wittgenstein on Incompleteness Makes Paraconsistent Sense. in K Tanaka, F Berto, E Mares & F Paoli (eds), Paraconsistency: Logic and Applications. vol. 26, Logic, Epistemology, and the Unity of Science, vol. 26, Springer , pp. 257-276. https://doi.org/10.1007/978-94-007-4438-7_14
Berto F. Wittgenstein on Incompleteness Makes Paraconsistent Sense. In Tanaka K, Berto F, Mares E, Paoli F, editors, Paraconsistency: Logic and Applications. Vol. 26. Springer . 2012. p. 257-276. (Logic, Epistemology, and the Unity of Science). https://doi.org/10.1007/978-94-007-4438-7_14
Berto, Francesco. / Wittgenstein on Incompleteness Makes Paraconsistent Sense. Paraconsistency: Logic and Applications. editor / K. Tanaka ; F. Berto ; E. Mares ; F. Paoli. Vol. 26 Springer , 2012. pp. 257-276 (Logic, Epistemology, and the Unity of Science).
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