Computability: Computable Functions, Logic, and the Foundations of Mathematics

(2004)
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Abstract

This book is dedicated to a classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century, while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal logic to give a full development of Gödel's incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church's Thesis and readings on the foundations of mathematics. This new edition contains the timeline "Computability and Undecidability" as well as the essay "On mathematics".

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2008

ISBN(s)

049502886X   9780495028864   098155072X   0534103561   9780534103569

DOI

10.2307/2687742
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Citations of this work

On Gödel Sentences and What They Say.Peter Milne - 2007 - Philosophia Mathematica 15 (2):193-226.
How Not To Use the Church-Turing Thesis Against Platonism.R. Urbaniak - 2011 - Philosophia Mathematica 19 (1):74-89.
The intrinsic difficulty of recursive functions.F. W. Kroon - 1996 - Studia Logica 56 (3):427 - 454.
Computable Diagonalizations and Turing’s Cardinality Paradox.Dale Jacquette - 2014 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 45 (2):239-262.

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