A note of provability, truth and existence
type: Item
instance of: scholarly article
title: A note of provability, truth and existence
zbMATH Open document ID: 0748.03036
DOI: 10.1007/BF00249436
author: Arnon Avron
published in: Journal of Philosophical Logic
publication date: 1992-06-27T00:00:00Z
review text: The paper shows that if \(T\) is any consistent extension of Peano Arithmetic, there is a false \(\Sigma_ 1\) formula, \(A\), and a true \(\Pi_ 1\) formula, \(B\), such that \(T\cup \{ A\}\) is consistent, \(T\not\vdash B\), but \(T\cup \{ A\}\vdash B\). It also shows that \(B\) may be of the form Con(\(S\)) where \(S\) is a consistent theory. It cites these results as supporting the critique of Gödel's philosophy of mathematics by \textit{S. Feferman} [``Infinity in mathematics: Is Cantor necessary'', in: (\textit{G. Tolrado di Francia} (ed.)) Infinity in science, Inst. Enciclopedia Italiana, Rome (1987)].
Mathematics Subject Classification ID: 03F30
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 28339
zbMATH Keywords: consistency
zbMATH Keywords: Gödel's incompleteness theorem
zbMATH Keywords: extension of Peano Arithmetic
zbMATH Keywords: Gödel's philosophy of mathematics
reviewed by: Graham Priest
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00249436
OpenAlex ID: W1970297462
description: scientific article; zbMATH DE number 28339