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Full Description
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.
Contents
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.
