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From the Foundations of Mathematics to Mathematical Pluralism

In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 363-380 (2019)

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Mathematical Pluralism.Edward N. Zalta - 2024 - Noûs 58 (2):306-332.details Mathematical pluralism can take one of three forms: (1) every consistent mathematical theory consists of truths about its own domain of individuals and relations; (2) every mathematical theory, consistent or inconsistent, consists of truths about its own (possibly uninteresting) domain of individuals and relations; and (3) the principal philosophies of mathematics are each based upon an insight or truth about the nature of mathematics that can be validated. (1) includes the multiverse approach to set theory. (2) helps us to understand (...) Download Export citation Bookmark 1 citation
(1 other version)Mathematical Pluralism and Indispensability.Silvia Jonas - 2023 - Erkenntnis 1:1-25.details Pluralist mathematical realism, the view that there exists more than one mathematical universe, has become an influential position in the philosophy of mathematics. I argue that, if mathematical pluralism is true (and we have good reason to believe that it is), then mathematical realism cannot (easily) be justified by arguments from the indispensability of mathematics to science. This is because any justificatory chain of inferences from mathematical applications in science to the total body of mathematical theorems can cover at most (...) Download Export citation Bookmark 1 citation
How Do You Apply Mathematics?Graham Priest - 2022 - Axiomathes 32 (3):1169-1184.details As far as disputes in the philosophy of pure mathematics goes, these are usually between classical mathematics, intuitionist mathematics, paraconsistent mathematics, and so on. My own view is that of a mathematical pluralist: all these different kinds of mathematics are equally legitimate. Applied mathematics is a different matter. In this, a piece of pure mathematics is applied in an empirical area, such as physics, biology, or economics. There can then certainly be a disputes about what the correct pure mathematics to (...) Download Export citation Bookmark
A note on mathematical pluralism and logical pluralism.Graham Priest - 2019 - Synthese 198 (Suppl 20):4937-4946.details Mathematical pluralism notes that there are many different kinds of pure mathematical structures—notably those based on different logics—and that, qua pieces of pure mathematics, they are all equally good. Logical pluralism is the view that there are different logics, which are, in an appropriate sense, equally good. Some, such as Shapiro, have argued that mathematical pluralism entails logical pluralism. In this brief note I argue that this does not follow. There is a crucial distinction to be drawn between the preservation (...) Download Export citation Bookmark 5 citations
Stefania Centrone, Deborah Kant, Deniz Serikaya, Reflections on the Foundations of Mathematics. Univalent Foundations, Set Theory and General Thoughts, vol. 407 of Synthese Library, Springer, 2019, pp. 494+xxviii; ISBN: 978-3-030-15654-1 (Hardcover) 149.79€, ISBN: 978-3-030-15655-8 (eBook). [REVIEW]Matteo de Ceglie - forthcoming - Studia Logica:1-7.details Download Export citation Bookmark

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