Gödel's Disjunction

The scope and limits of mathematical knowledge

Nonfiction, Science & Nature, Mathematics, Logic, History
Cover of the book Gödel's Disjunction by , OUP Oxford
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: ISBN: 9780191077692
Publisher: OUP Oxford Publication: September 8, 2016
Imprint: OUP Oxford Language: English
Author:
ISBN: 9780191077692
Publisher: OUP Oxford
Publication: September 8, 2016
Imprint: OUP Oxford
Language: English

The logician Kurt Gödel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is not 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 Gödel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

The logician Kurt Gödel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is not 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 Gödel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.

More books from OUP Oxford

Cover of the book The Oxford Handbook of Local and Regional Democracy in Europe by
Cover of the book The Persistent Objector Rule in International Law by
Cover of the book Extraterritorial Application of Human Rights Treaties by
Cover of the book Once Upon a Time by
Cover of the book Categorial Grammar by
Cover of the book The IMLI Manual on International Maritime Law by
Cover of the book The Mayor of Casterbridge by
Cover of the book Planets: A Very Short Introduction by
Cover of the book The Oxford Handbook of Modern Irish Poetry by
Cover of the book Effi Briest by
Cover of the book Philosophical Foundations of Fiduciary Law by
Cover of the book Foundations of Modern Macroeconomics by
Cover of the book Scriptural Authority and Biblical Criticism in the Dutch Golden Age by
Cover of the book Amyotrophic Lateral Sclerosis and the Frontotemporal Dementias by
Cover of the book Strategic Reframing by
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy