Godel's Disjunction: The Scope and Limits of Mathematical Knowledge
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The logician Kurt Godel 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 Godel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.
Format:Hardcover
Language:English
ISBN:0198759592
ISBN13:9780198759591
Release Date:October 2016
Publisher:Oxford University Press, USA
Length:288 Pages
Weight:1.30 lbs.
Dimensions:1.0" x 6.1" x 9.3"
Related Subjects
Math Mathematics Philosophy Science Science & Math Science & Scientists Science & TechnologyCustomer Reviews
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