Godel's Disjunction: The Scope and Limits of Mathematical Knowledge

Oxford, England: Oxford University Press UK (2016)
  Copy   BIBTEX

Abstract

The logician Kurt Godel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is equivalent to a Turing machine (i.e., a computer), or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that intend to show that the mathematical mind is more powerful than any computer. These arguments, and counterarguments to them, have not convinced the logical and philosophical community. The reason for this is an insufficiency if rigour in the debate. The contributions in this volume move the debate forward by formulating rigorous frameworks and formally spelling out and evaluating arguments that bear on Godel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,088

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

The Scope of Gödel’s First Incompleteness Theorem.Bernd Buldt - 2014 - Logica Universalis 8 (3-4):499-552.
Kurt Godel and phenomenology.Richard Tieszen - 1992 - Philosophy of Science 59 (2):176-194.
Gödels disjunctie.L. Horsten - 1998 - Tijdschrift Voor Filosofie 60 (1):83 - 105.
Gödel and 'the objective existence' of mathematical objects.Pierre Cassou-Noguès - 2005 - History and Philosophy of Logic 26 (3):211-228.
To bridge Gödel’s gap.Eileen S. Nutting - 2016 - Philosophical Studies 173 (8):2133-2150.
The experiential foundations of mathematical knowledge.Nicolas D. Goodman - 1981 - History and Philosophy of Logic 2 (1-2):55-65.

Analytics

Added to PP
2016-03-29

Downloads
25 (#560,650)

6 months
7 (#213,770)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Leon Horsten
Universität Konstanz

References found in this work

No references found.

Add more references