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

Godel's Disjunction

The Scope and Limits of Mathematical Knowledge

By: Leon Horsten (Editor), Philip Welch (Editor)

Hardcover Published: 11th October 2016
ISBN: 9780198759591
Number Of Pages: 288

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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.

Industry Reviews

Recommended * CHOICE *
An introduction by the editors offers an accessible entry point to readers with a basic background in mathematical logic. Many of the papers are clearly aimed at experts, but their introductory sections are generally written for a broader audience. ... The editors do a particularly good job of establishing context and background, as well as summarizing the contributions of the individual papers. * Bill Satzer, MAA Reviews *

Algorithm, consistency and epistemic randomness 1: Dean: ALGORITHMS AND THE MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE 2: Visser: THE SECOND INCOMPLETENESS THEOREM REFLECTIONS AND RUMINATIONS 3: Moschovakis: ITERATED DEFINABILITY, LAWLESS SEQUENCES AND BROUWER'S CONTINUUM 4: Achourioti: A SEMANTICS FOR IN PRINCIPLE PROVABILITY Mind and Machines 5: Carlson: Collapsing Knowledge and Epistemic Church's Thesis 6: Koellner: G odel's Disjunction 7: Shapiro: Idealization, mechanism, and knowability Absolute Undecidability 8: Leach-Krouse: PROVABILITY, MECHANISM AND THE DIAGONAL PROBLEM 9: Williamson: Absolute Provability and Safe Knowledge of Axioms 10: Antonutti, Horsten: Epistemic Church's Thesis and Absolute Undecidability

ISBN: 9780198759591
ISBN-10: 0198759592
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 288
Published: 11th October 2016
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 23.5 x 16.51  x 1.91
Weight (kg): 0.6

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