DPhil Thesis: The Higher-order Conception of Property

This thesis presents a case for the higher-order conception of property. The idea that properties are what we predicate of things is central to our ordinary, pre-theoretic conception of property. But as it is usually regimented, in the form of the naïve comprehension principle for properties, it leads to contradiction. This thesis suggests instead a natural and consistent refinement of this idea, on which properties, roughly speaking, lie in the range of quantifiers that occupy predicate as opposed to singular term position. Quantification into predicate position is understood as a sui generis form of quantification, not reducible to either objectual or substitutional quantification. The thesis then applies this idea to a range of issues in the metaphysics of properties, including the problem of universals and Bradley’s regress of relations. Thus it argues that higher-order formal languages, which allow quantification into predicate as well as singular term position, can be used to do the work that has traditionally been expected of first-order property theory in metaphysics.

Recent talks

'A Higher-order Perspective on the Transcendence-Immanence Debate'
DPhil Seminar, Faculty of Philosophy, University of Oxford, November 2023

'The Intended Interpretation of Higher-order Languages'
Metaphysics and Epistemology Group, University of Oxford, October 2023

'The Higher-order Conception of Property'
Oriel Philosophy Group, Oriel College, University of Oxford, June 2023