Gödel's Disjunction: The scope and limits of mathematical knowledge

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Leon Horsten (Professor of Philosophy, Professor of Philosophy, University of Bristol) Philip Welch (Professor of Mathematical Logic, Professor of Mathematical Logic, University of Bristol)

Gödel's Disjunction

The scope and limits of mathematical knowledge

Leon Horsten (Professor of Philosophy, Professor of Philosophy, University of Bristol), Philip Welch (Professor of Mathematical Logic, Professor of Mathematical Logic, University of Bristol)

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English

Oxford University Press
23 June 2016

Philosophy of mathematics; Mathematical logic; History of mathematics

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.

Edited by: Leon Horsten (Professor of Philosophy Professor of Philosophy University of Bristol), Philip Welch (Professor of Mathematical Logic, Professor of Mathematical Logic, University of Bristol)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 239mm, Width: 174mm, Spine: 23mm
Weight: 1g
ISBN: 9780198759591
ISBN 10: 0198759592
Pages: 288
Publication Date: 23 June 2016
Audience: College/higher education , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Leon Horsten is a philosophical logician and philosopher of mathematics, working at the University of Bristol since 2007. His research is concentrated chiefly on bringing formal methods to bear on philosophical problems in the philosophy of science, the philosophy of mathematics, the philosophy of language, epistemology and metaphysics. Formal methods are meant to include not only logical methods, but also methods from other areas of mathematics and computer science (graph theory, probability theory, complexity theory, ...). Philip Welch is a set theorist and mathematical logician, working in Bristol since 1986. For the period 1997-2000 he was at Kobe University Graduate School setting up a research group in Set Theory. He is the author of some 75 papers in set theory, logic, theories of truth, and transfinite models of computation. He is a subject Co-editor for the Stanford Encyclopaedia of Philosophy for philosophy of mathematics, and is an Editor for set theory of the Journal of Symbolic Logic. His doctoral `grandfather' is Alan Turing, his supervisor at Oxford (1975-78) Robin Gandy, being Turing's only PhD student.

Reviews for Gödel's Disjunction: The scope and limits of mathematical knowledge

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