Mathematical instrumentalism construes some parts of mathematics, typically the abstract ones, as an instrument for establishing statements in other parts of mathematics, typically the elementary ones. Gödel's second incompleteness theorem seems to show that one cannot prove the consistency of all of mathematics from within elementary mathematics. It is therefore generally thought to defeat instrumentalisms that insist on a proof of the consistency of abstract mathematics from within the elementary portion. This article argues that though some versions of mathematical instrumentalism are defeated by Gödel's theorem, not all are. By considering inductive reasons in mathematics, we show that some mathematical instrumentalisms survive the theorem.
...More
Book
Juliette Kennedy;
(2014)
Interpreting Godel: Critical Essays
(/isis/citation/CBB427455296/)
Article
Franks, Curtis;
(2009)
The Gödelian Inferences
(/isis/citation/CBB001211043/)
Article
Formica, Giambattista;
(2010)
Von Neumann's Methodology of Science: From Incompleteness Theorems to Later Foundational Reflections
(/isis/citation/CBB001034599/)
Book
Tieszen, Richard L.;
(2011)
After Gödel: Platonism and Rationalism in Mathematics and Logic
(/isis/citation/CBB001210605/)
Book
William Boos;
Florence S. Boos;
(2018)
Metamathematics and the Philosophical Tradition
(/isis/citation/CBB060593902/)
Book
Kurt Godel;
Solomon Feferman;
John W. Dawson;
Warren Goldfarb;
Charles Parsons;
Wilfried Sieg;
(2013)
Kurt Gödel: Collected Works: Volume IV
(/isis/citation/CBB660754544/)
Book
Goldstein, Rebecca;
(2005)
Incompleteness: The Proof and Paradox of Kurt Gödel
(/isis/citation/CBB000520034/)
Article
Manzano, Maria;
Alonso, Enrique;
(2014)
Completeness: From Gödel to Henkin
(/isis/citation/CBB001213927/)
Article
Weatherson, Brian;
(1999)
Begging the question and Bayesians
(/isis/citation/CBB000110819/)
Book
Emanuele Gambetta;
(2023)
Il Teorema di Dio
(/isis/citation/CBB058518438/)
Article
Karela, Catherine;
(2010)
Hilbert on Different Notions of Completeness: A Conceptual and Historical Analysis
(/isis/citation/CBB001220619/)
Book
Grattan-Guiness, I.;
(2000)
Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor Through Russell to Gödel
(/isis/citation/CBB000102346/)
Book
Gauthier, Yvon;
(2002)
Internal Logic: Foundations of Mathematics from Kronecker to Hilbert
(/isis/citation/CBB000301820/)
Book
Heijenoort, Jean van;
(2002)
From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931
(/isis/citation/CBB000201415/)
Book
Gödel, Kurt;
Feferman, Solomon;
Dawson, John W., Jr.;
Kleene, Stephen C.;
Moore, Gregory H.;
Solovay, Robert M.;
Heijenoort, Jean van;
(2001)
Collected Works, Volume 1: Publications, 1929--1936
(/isis/citation/CBB000630371/)
Article
Cassou-Noguès, Pierre;
(2005)
Gödel and “The objective existence” of Mathematical Objects
(/isis/citation/CBB000740617/)
Book
Emanuele Gambetta;
(2020)
Philosophy of the Infinite
(/isis/citation/CBB368392118/)
Thesis
Ogawa, Yoshinori;
(2002)
The Pursuit of Rigor: David Hilbert's Early Philosophy of Mathematics
(/isis/citation/CBB001562203/)
Book
Gabriele Lolli;
(2016)
Tavoli, sedie, boccali di birra: David Hilbert e la matematica del Novecento
(/isis/citation/CBB100106060/)
Article
McLarty, Colin;
(2007)
The Last Mathematician from Hilbert's Göttingen: Saunders Mac Lane as Philosopher of Mathematics
(/isis/citation/CBB000831434/)
Be the first to comment!