This paper is a discussion of Go del's arguments for a Platonistic conception of mathematical objects. I review the arguments that Go del offers in different papers, and compare them to unpublished material (from Go del's Nachlass). My claim is that Go del's later arguments simply intend to establish that mathematical knowledge cannot be accounted for by a reflexive analysis of our mental acts. In other words, there is at the basis of mathematics some data whose constitution cannot be explained by introspective analysis. This does not mean that mathematics is independent of the human mind, but only that it is independent of our `conscious acts and decisions', to use Godel's own words. Mathematical objects may then have been created by the human mind, but if so, the process of creation cannot be completely analysed and re-enacted. Such a thesis is weaker than some of the statements that Go del made about his conceptual realism. However, there is evidence that Godel seriously considered this weak thesis, or a position depending only on this weak thesis. He also criticized Husserl's Phenomenology from this point of view.
...More
Article
Manzano, Maria;
Alonso, Enrique;
(2014)
Completeness: From Gödel to Henkin
(/isis/citation/CBB001213927/)
Article
Formica, Giambattista;
(2010)
Von Neumann's Methodology of Science: From Incompleteness Theorems to Later Foundational Reflections
(/isis/citation/CBB001034599/)
Book
Juliette Kennedy;
(2014)
Interpreting Godel: Critical Essays
(/isis/citation/CBB427455296/)
Book
Kurt Godel;
Solomon Feferman;
John W. Dawson;
Warren Goldfarb;
Charles Parsons;
Wilfried Sieg;
(2013)
Kurt Gödel: Collected Works: Volume IV
(/isis/citation/CBB660754544/)
Article
Paseau, Alexander;
(2011)
Mathematical Instrumentalism, Gödel's Theorem, and Inductive Evidence
(/isis/citation/CBB001024149/)
Book
Tieszen, Richard L.;
(2011)
After Gödel: Platonism and Rationalism in Mathematics and Logic
(/isis/citation/CBB001210605/)
Article
Sayward, Charles;
(2005)
Steiner versus Wittgenstein: Remarks on Differing Views of Mathematical Truth
(/isis/citation/CBB000933620/)
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/)
Article
Oscar Orellana Estay;
Ronald Durán Allimant;
(2016)
Sobre el realismo matemático de Zubiri y su interpretación de los teoremas de Gödel y Cohen
(/isis/citation/CBB213803167/)
Article
Karela, Catherine;
(2010)
Hilbert on Different Notions of Completeness: A Conceptual and Historical Analysis
(/isis/citation/CBB001220619/)
Book
Heijenoort, Jean van;
(2002)
From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931
(/isis/citation/CBB000201415/)
Chapter
Awodey, S.;
(2003)
Carnap vs. Gödel on Syntax and Tolerance
(/isis/citation/CBB001213683/)
Article
Franks, Curtis;
(2009)
The Gödelian Inferences
(/isis/citation/CBB001211043/)
Book
Emanuele Gambetta;
(2023)
Il Teorema di Dio
(/isis/citation/CBB058518438/)
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/)
Book
William Boos;
Florence S. Boos;
(2018)
Metamathematics and the Philosophical Tradition
(/isis/citation/CBB060593902/)
Article
Atten, Mark van;
(2005)
On Gödel's Awareness of Skolem's Helsinki Lecture
(/isis/citation/CBB000740619/)
Book
B. Jack Copeland;
Carl J. Posy;
Oron Shagrir;
(2015)
Computability: Turing, Gödel, Church, and Beyond
(/isis/citation/CBB900019272/)
Article
Michael Friedman;
(2016)
Über drei Erscheinungen von Unterschied in der Mathematik
(/isis/citation/CBB583491506/)
Book
Stephen Budiansky;
(2021)
Journey to the Edge of Reason: The Life of Kurt Gödel
(/isis/citation/CBB142778671/)
Be the first to comment!