Tag Archives: Talk

Talk: Contingentist sets as potentialist properties

Philosophy of Mathematics Seminar, Oxford, 2024

Philosophers who take being to be contingent face a problem involving sets of possibilia. Semantic reflection gives contingentists a powerful motivation to posit sets with non-actual members or even sets with incompossible members. On the other hand, good metaphysics assures us that there are no such sets. This talk outlines an interpretation of set theory based on a potentialist theory of properties that permits ‘sets’ with non-actual or incompossible members. This provides a way, I argue, for contingentists to meet the needs of semantics without resorting to bad metaphysics.

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Talk: Type-theoretic potentialism

Actualism and Potentialism: Konstanz 28th September 2023

There has been recent interest in intensional type theory, both as a framework to tackle metaphysical questions about modality, propositions, properties, and so on (e.g. Bacon and Dorr, ‘Classicism’) and as an alternative to set theory as a foundation of mathematics (e.g. Goodsell and Yli-Vakkuri, Logical Foundations). These type theorists typically adopt an ‘actualist’ attitude towards the type-theoretic hierarchy: quantifiers in each type are assumed to range over absolutely every entity of the appropriate type (e.g. type e quantifiers range over absolutely every individual). This talk considers a ‘potentialist’ alternative, which permits entities of arbitrary type to be nominalized as new individuals.  

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Generality, Extensibility, and Paradox

Proceedings of the Aristotelian Society (2017) 117 (1): 81–101 https://doi.org/10.1093/arisoc/aox003

Delivered to the Aristotelian Society, 28th November 2016

Slides [new tab, .pdf]

Abstract: Absolutism is the view that quantifiers like ‘everything’ sometimes range over an absolutely comprehensive domain. The debate between absolutists and the relativists opposing them comes down, in significant part, to a trade off between generality and collectability. But to reach this conclusion we must dispense with some long-standing concerns over the coherence of the argument from the paradoxes in favour of relativism and a heterodox absolutist response that seeks to reconcile the indefinite extensibility of set with the availability of an absolutely comprehensive domain.