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Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Book Synopsis Conceptions of Set and the Foundations of Mathematics by : Luca Incurvati
Download or read book Conceptions of Set and the Foundations of Mathematics written by Luca Incurvati and published by Cambridge University Press. This book was released on 2020-01-23 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics.
Book Synopsis Conceptions of Set and the Foundations of Mathematics by : Luca Incurvati
Download or read book Conceptions of Set and the Foundations of Mathematics written by Luca Incurvati and published by Cambridge University Press. This book was released on 2021-07-15 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics.
Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics.
Book Synopsis Conceptions of Set and the Foundations of Mathematics by : Luca Incurvati
Download or read book Conceptions of Set and the Foundations of Mathematics written by Luca Incurvati and published by Cambridge University Press. This book was released on 2020-01-23 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics.
Book Synopsis Abstract Set Theory by : Abraham Adolf Fraenkel
Download or read book Abstract Set Theory written by Abraham Adolf Fraenkel and published by . This book was released on 1968 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. The axioms of set theory have long played this role, so the question of how they are properly judged is of central importance. Maddy discusses the appropriate methods for such evaluations and the philosophical backdrop that makes them appropriate.
Book Synopsis Defending the Axioms by : Penelope Maddy
Download or read book Defending the Axioms written by Penelope Maddy and published by Oxford University Press. This book was released on 2011-01-27 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. The axioms of set theory have long played this role, so the question of how they are properly judged is of central importance. Maddy discusses the appropriate methods for such evaluations and the philosophical backdrop that makes them appropriate.
"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)
Book Synopsis Labyrinth of Thought by : Jose Ferreiros
Download or read book Labyrinth of Thought written by Jose Ferreiros and published by Springer Science & Business Media. This book was released on 2001-11-01 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: "José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)
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.
Book Synopsis Lectures on the Philosophy of Mathematics by : Joel David Hamkins
Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
Book Synopsis The Foundations of Mathematics in the Theory of Sets by : John P. Mayberry
Download or read book The Foundations of Mathematics in the Theory of Sets written by John P. Mayberry and published by Cambridge University Press. This book was released on 2000 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
Alain Badiou's Being and Event continues to impact philosophical investigations into the question of Being. By exploring the central role set theory plays in this influential work, Burhanuddin Baki presents the first extended study of Badiou's use of mathematics in Being and Event. Adopting a clear, straightforward approach, Baki gathers together and explains the technical details of the relevant high-level mathematics in Being and Event. He examines Badiou's philosophical framework in close detail, showing exactly how it is 'conditioned' by the technical mathematics. Clarifying the relevant details of Badiou's mathematics, Baki looks at the four core topics Badiou employs from set theory: the formal axiomatic system of ZFC; cardinal and ordinal numbers; Kurt Gödel's concept of constructability; and Cohen's technique of forcing. Baki then rebuilds Badiou's philosophical meditations in relation to their conditioning by the mathematics, paying particular attention to Cohen's forcing, which informs Badiou's analysis of the event. Providing valuable insights into Badiou's philosophy of mathematics, Badiou's Being and Event and the Mathematics of Set Theory offers an excellent commentary and a new reading of Badiou's most complex and important work.
Book Synopsis Badiou's Being and Event and the Mathematics of Set Theory by : Burhanuddin Baki
Download or read book Badiou's Being and Event and the Mathematics of Set Theory written by Burhanuddin Baki and published by Bloomsbury Publishing. This book was released on 2014-11-20 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alain Badiou's Being and Event continues to impact philosophical investigations into the question of Being. By exploring the central role set theory plays in this influential work, Burhanuddin Baki presents the first extended study of Badiou's use of mathematics in Being and Event. Adopting a clear, straightforward approach, Baki gathers together and explains the technical details of the relevant high-level mathematics in Being and Event. He examines Badiou's philosophical framework in close detail, showing exactly how it is 'conditioned' by the technical mathematics. Clarifying the relevant details of Badiou's mathematics, Baki looks at the four core topics Badiou employs from set theory: the formal axiomatic system of ZFC; cardinal and ordinal numbers; Kurt Gödel's concept of constructability; and Cohen's technique of forcing. Baki then rebuilds Badiou's philosophical meditations in relation to their conditioning by the mathematics, paying particular attention to Cohen's forcing, which informs Badiou's analysis of the event. Providing valuable insights into Badiou's philosophy of mathematics, Badiou's Being and Event and the Mathematics of Set Theory offers an excellent commentary and a new reading of Badiou's most complex and important work.
Book Synopsis Principles of Mathematics by : Bertrand Russell
Download or read book Principles of Mathematics written by Bertrand Russell and published by . This book was released on 2009-08 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics.
