Set Theory and its Philosophy
Set Theory and its Philosophy

Author: Michael Potter

Publisher: Clarendon Press

Published: 2004-01-15

Total Pages: 362

ISBN-13: 0191556432

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Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

Philosophical and Mathematical Logic
Philosophical and Mathematical Logic

Author: Harrie de Swart

Publisher: Springer

Published: 2018-11-28

Total Pages: 539

ISBN-13: 3030032558

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This book was written to serve as an introduction to logic, with in each chapter – if applicable – special emphasis on the interplay between logic and philosophy, mathematics, language and (theoretical) computer science. The reader will not only be provided with an introduction to classical logic, but to philosophical (modal, epistemic, deontic, temporal) and intuitionistic logic as well. The first chapter is an easy to read non-technical Introduction to the topics in the book. The next chapters are consecutively about Propositional Logic, Sets (finite and infinite), Predicate Logic, Arithmetic and Gödel’s Incompleteness Theorems, Modal Logic, Philosophy of Language, Intuitionism and Intuitionistic Logic, Applications (Prolog; Relational Databases and SQL; Social Choice Theory, in particular Majority Judgment) and finally, Fallacies and Unfair Discussion Methods. Throughout the text, the author provides some impressions of the historical development of logic: Stoic and Aristotelian logic, logic in the Middle Ages and Frege's Begriffsschrift, together with the works of George Boole (1815-1864) and August De Morgan (1806-1871), the origin of modern logic. Since "if ..., then ..." can be considered to be the heart of logic, throughout this book much attention is paid to conditionals: material, strict and relevant implication, entailment, counterfactuals and conversational implicature are treated and many references for further reading are given. Each chapter is concluded with answers to the exercises. Philosophical and Mathematical Logic is a very recent book (2018), but with every aspect of a classic. What a wonderful book! Work written with all the necessary rigor, with immense depth, but without giving up clarity and good taste. Philosophy and mathematics go hand in hand with the most diverse themes of logic. An introductory text, but not only that. It goes much further. It's worth diving into the pages of this book, dear reader! Paulo Sérgio Argolo

The Philosophy of Set Theory
The Philosophy of Set Theory

Author: Mary Tiles

Publisher: Courier Corporation

Published: 2012-03-08

Total Pages: 258

ISBN-13: 0486138550

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DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div

Logic, Set-theory, and Philosophy of Mathematics
Logic, Set-theory, and Philosophy of Mathematics

Author: John-Michael Kuczynski

Publisher: John-Michael Kuczynski

Published:

Total Pages: 276

ISBN-13:

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This collection of papers contains original work in mathematical logic and in the philosophy of mathematics. It also contains unusually clear and precise discussions, both mathematical and philosophical, of the central concepts of arithmetic and analysis. The first chapter is a list of logical and set-theoretic laws, making it useful for students and instructors.

Set Theory, Logic and Their Limitations
Set Theory, Logic and Their Limitations

Author: Moshe Machover

Publisher: Cambridge University Press

Published: 1996-05-23

Total Pages: 304

ISBN-13: 9780521479981

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This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.

Lectures on the Philosophy of Mathematics
Lectures on the Philosophy of Mathematics

Author: Joel David Hamkins

Publisher: MIT Press

Published: 2021-03-09

Total Pages: 350

ISBN-13: 0262542234

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An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Philosophical Introduction to Set Theory
Philosophical Introduction to Set Theory

Author: Stephen Pollard

Publisher: Courier Dover Publications

Published: 2015-07-15

Total Pages: 196

ISBN-13: 0486797147

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This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.

Logic, Set-Theory, and Philosophy of Mathematics
Logic, Set-Theory, and Philosophy of Mathematics

Author: John-michael Kuczynski

Publisher: Createspace Independent Publishing Platform

Published: 2016-04-28

Total Pages: 276

ISBN-13: 9781532994135

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This collection of papers contains original work in mathematical logic and in the philosophy of mathematics. It also contains unusually clear and precise discussions, both mathematical and philosophical, of the central concepts of arithmetic and analysis. The first chapter is a list of logical and set-theoretic laws, making it useful for students and instructors.