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 Agriculture, Diversification, and Gender in Rural Africa by
Cover of the book Australia: A Very Short Introduction by
Cover of the book When Human Rights Clash at the European Court of Human Rights by
Cover of the book Heart of Darkness and Other Tales by
Cover of the book Molecular Electromagnetism: A Computational Chemistry Approach by
Cover of the book The Darwinian Tourist by
Cover of the book Before the Nation by
Cover of the book The Oxford Handbook of the Archaeology of Death and Burial by
Cover of the book Oliver Twist by
Cover of the book The Oxford English Literary History by
Cover of the book The Oxford Companion to Food by
Cover of the book Understanding Flowers and Flowering Second Edition by
Cover of the book Essays in the Metaphysics of Mind by
Cover of the book Run, Swim, Throw, Cheat:The science behind drugs in sport by
Cover of the book Resurrection of the Dead in Early Judaism, 200 BCE-CE 200 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