Philosophia Mathematica 17 (2):208-219 (2009)

Authors
Franz Berto
University of St. Andrews
Abstract
An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of 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. It is shown that the features of paraconsistent arithmetics match with some intuitions underlying Wittgenstein’s philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any mathematical question.
Keywords Gödel's Incompleteness Theorems  Wittgenstein's philosophy of mathematics  Paraconsistency
Categories (categorize this paper)
DOI 10.1093/philmat/nkp001
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

References found in this work BETA

Introduction to Mathematical Logic.Alonzo Church - 1956 - Princeton: Princeton University Press.
The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Philosophy of Mathematics.Paul Benacerraf - 1964 - Englewood Cliffs, N.J., Prentice-Hall.

View all 31 references / Add more references

Citations of this work BETA

Logic is a Moral Science.Hartley Slater - 2015 - Philosophy 90 (4):581-591.
A Note on Gödel, Priest and Naïve Proof.Massimiliano Carrara - forthcoming - Logic and Logical Philosophy:1.
Gödel's and Other Paradoxes.Hartley Slater - 2016 - Philosophical Investigations 39 (4):353-361.

Add more citations

Similar books and articles

Analytics

Added to PP index
2009-05-23

Total views
1,248 ( #3,261 of 2,427,440 )

Recent downloads (6 months)
64 ( #11,749 of 2,427,440 )

How can I increase my downloads?

Downloads

My notes