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Cover: 9781108994880 | A Logical Foundation for Potentialist Set Theory | Sharon Berry | Buch
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A Logical Foundation for Potentialist Set Theory
Taschenbuch von Sharon Berry
Sprache: Englisch

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Beschreibung
In many ways set theory lies at the heart of modern mathematics, and it does powerful work both philosophical and mathematical - as a foundation for the subject. However, certain philosophical problems raise serious doubts about our acceptance of the axioms of set theory. In a detailed and original reassessment of these axioms, Sharon Berry uses a potentialist (as opposed to actualist) approach to develop a unified determinate conception of set-theoretic truth that vindicates many of our intuitive expectations regarding set theory. Berry further defends her approach against a number of possible objections, and she shows how a notion of logical possibility that is useful in formulating Potentialist set theory connects in important ways with philosophy of language, metametaphysics and philosophy of science. Her book will appeal to readers with interests in the philosophy of set theory, modal logic, and the role of mathematics in the sciences.
In many ways set theory lies at the heart of modern mathematics, and it does powerful work both philosophical and mathematical - as a foundation for the subject. However, certain philosophical problems raise serious doubts about our acceptance of the axioms of set theory. In a detailed and original reassessment of these axioms, Sharon Berry uses a potentialist (as opposed to actualist) approach to develop a unified determinate conception of set-theoretic truth that vindicates many of our intuitive expectations regarding set theory. Berry further defends her approach against a number of possible objections, and she shows how a notion of logical possibility that is useful in formulating Potentialist set theory connects in important ways with philosophy of language, metametaphysics and philosophy of science. Her book will appeal to readers with interests in the philosophy of set theory, modal logic, and the role of mathematics in the sciences.
Über den Autor
Sharon Berry is Associate Professor of Philosophy at Ashoka University. She has published articles in journals including Philosophical Studies, the British Journal of Philosophy of Science and Analysis.
Inhaltsverzeichnis
1. Introduction; Part I: 2. Actualist set theory; 3. Putnamian potentialism: Putnam and Hellman; 4. Overview of my proposal; 5. Parsonian potentialism; Part II: 6. Purified potentialist set theory: An informal sketch; 7. Content restriction; 8. Inference rules; 9. Defense of ZFC; Part III: 10. Platonism or nominalism?; 11. Indispensability; 12. Modal If-thenist paraphrase strategy; 13. Explanatory indispensability; 14. Physical magnitude statements and sparsity; 15. Weak quantifier variance and mathematical objects; 16. Weak quantifier variance, knowledge by stipulative definition and access worries; 17. Logicism and structuralism; 18. Anti-objectivism about set theory; 19. Conclusion; Bibliography; Index.
Details
Erscheinungsjahr: 2024
Fachbereich: Allgemeines
Genre: Philosophie
Jahrhundert: Antike
Rubrik: Geisteswissenschaften
Thema: Lexika
Medium: Taschenbuch
ISBN-13: 9781108994880
ISBN-10: 1108994881
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Berry, Sharon
Hersteller: Cambridge University Press
Maße: 244 x 170 x 14 mm
Von/Mit: Sharon Berry
Erscheinungsdatum: 04.04.2024
Gewicht: 0,438 kg
Artikel-ID: 128828701
Über den Autor
Sharon Berry is Associate Professor of Philosophy at Ashoka University. She has published articles in journals including Philosophical Studies, the British Journal of Philosophy of Science and Analysis.
Inhaltsverzeichnis
1. Introduction; Part I: 2. Actualist set theory; 3. Putnamian potentialism: Putnam and Hellman; 4. Overview of my proposal; 5. Parsonian potentialism; Part II: 6. Purified potentialist set theory: An informal sketch; 7. Content restriction; 8. Inference rules; 9. Defense of ZFC; Part III: 10. Platonism or nominalism?; 11. Indispensability; 12. Modal If-thenist paraphrase strategy; 13. Explanatory indispensability; 14. Physical magnitude statements and sparsity; 15. Weak quantifier variance and mathematical objects; 16. Weak quantifier variance, knowledge by stipulative definition and access worries; 17. Logicism and structuralism; 18. Anti-objectivism about set theory; 19. Conclusion; Bibliography; Index.
Details
Erscheinungsjahr: 2024
Fachbereich: Allgemeines
Genre: Philosophie
Jahrhundert: Antike
Rubrik: Geisteswissenschaften
Thema: Lexika
Medium: Taschenbuch
ISBN-13: 9781108994880
ISBN-10: 1108994881
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Berry, Sharon
Hersteller: Cambridge University Press
Maße: 244 x 170 x 14 mm
Von/Mit: Sharon Berry
Erscheinungsdatum: 04.04.2024
Gewicht: 0,438 kg
Artikel-ID: 128828701
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