Title: Abstraction and Critical Plural Logic
By Øystein Linnebo (University of Oslo, Philosophy) (joint work with Salvatore Florio)
Date: Monday, October 20, 2025
Time: 1730-1900
Room: H-232
Abstract: Frege’s attempt to found arithmetic on a theory of set abstraction foundered because of Russell’s paradox. Neo-Fregean have proposed to build instead on consistent forms of abstraction, such as Hume’s Principle for cardinality abstraction. However, this proposal faces “the bad company problem”, namely, that there are bad forms of abstraction mixed in among the good forms. Dummett wished to solve the bad company problem by requiring that abstraction be predicative in some sense. The dominant way to pursue this idea has been to impose predicativity restrictions on the second-order logic. I review why this strategy has not been a success. I propose an alternative development of Dummett’s idea, loosely speaking, that we successively abstract on “available” objects. This alternative is developed by (i) abstracting on pluralities of objects rather than Fregean concepts, and (ii) using the Critical Plural Logic recently developed by Salvatore Florio and myself rather than traditional plural logic. In this way, we obtain a large and natural class of permissible abstractions.
About the speaker: Øystein Linnebo is Professor of Philosophy at the University of Oslo. His work focuses on issues in metaphysics, the philosophy of logic, and the philosophy of mathematics. His work has appeared in such journals as The Journal of Philosophy, Mind, Noûs, The Journal of Philosophical Logic, and the Proceedings of the Aristotelian Society. He has also authored three books: Philosophy of Mathematics: An Introduction (2017, Princeton University Press); Thin Objects: An Abstractionist Account (2018, Oxford University Press); and, with Salvatore Florio, The Many and the One: A Philosophical Study of Plural Logic (2021, Oxford University Press).
Organized by the Department of Philosophy
