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Summary

This chapter suggests classic indispensability worries about nominalizing scientific theories can be answered by adding some cheap tricks to the modal if-thenist paraphrase strategy of Chapter 12.

Summary

This chapter contrasts some different Indispensability arguments (Quinean, Explanatory, Reference and Grounding) against mathematical nominalism and tries to clarify what it takes to answer them.

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.

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14 - Physical Magnitude Statements and Sparsity

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11 - Indispensability

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A Logical Foundation for Potentialist Set Theory

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3 results

14 - Physical Magnitude Statements and Sparsity

Summary

11 - Indispensability

Summary

A Logical Foundation for Potentialist Set Theory