@inbook{a2b5e890a8de462e8c36602fec8a17b9,

title = "Wittgenstein on Incompleteness Makes Paraconsistent Sense",

abstract = "I provide an interpretation of Wittgenstein{\textquoteright}s much criticised remarks on G{\"o}del{\textquoteright}s First Incompleteness Theorem in a paraconsistent framework: in taking G{\"o}del{\textquoteright}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 G{\"o}del 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{\textquoteright}s philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any mathematical question.",

author = "Francesco Berto",

note = "Acknowledgements The non-technical parts of this work draw on a paper published in Philosophia Mathematica, 17: 208–219, with the title “The G{\"o}del Paradox and Wittgenstein{\textquoteright}s Reasons”. I am grateful to Oxford University Press and to the Editors of Philosophia Mathematica for permission to reuse that material. I am also grateful to an anonymous referee for helpful comments on this expanded version",

year = "2012",

doi = "10.1007/978-94-007-4438-7_14",

language = "English",

isbn = "978-94-007-4437-0",

volume = "26",

series = "Logic, Epistemology, and the Unity of Science",

publisher = "Springer ",

pages = "257--276",

editor = "Tanaka, {K. } and F. Berto and Mares, {E. } and Paoli, {F. }",

booktitle = "Paraconsistency",

}