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

Leon Horsten and Philip Welch

Abstract

The logician Kurt Gödel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is 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 mathematicalmind ismore powerful than any computer. These arguments, and counte ... More

Keywords: Gödel’s disjunction, absolute provability, absolute undecidability, mathematical proof, incompleteness, Church’s Thesis

Bibliographic Information

Print publication date: 2016 Print ISBN-13: 9780198759591
Published to Oxford Scholarship Online: November 2016 DOI:10.1093/acprof:oso/9780198759591.001.0001

Authors

Affiliations are at time of print publication.

Leon Horsten, editor
Professor of Philosophy, University of Bristol

Philip Welch, editor
Professor of Mathematical Logic, University of Bristol

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Contents

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Front Matter

1 Introduction

Leon Horsten and Philip Welch

Part I Algorithm, Consistency, and Epistemic Randomness

Part II Mind and Machines

7 Gödel’s Disjunction

Peter Koellner

Part III Absolute Undecidability

11 Epistemic Church’s Thesis and Absolute Undecidability

Marianna Antonutti Marfori and Leon Horsten

End Matter