Higher-order metaphysics and the tropes versus universals dispute

Abstract

Higher-order realists about properties express their view that there are properties with the help of higher-order rather than first-order quantifiers. They claim two types of advantages for this way of formulating property realism. First, certain gridlocked debates about the nature of properties, such as the immanentism versus transcendentalism dispute, are taken to be dissolved (roughly: avoided). Second, a further such debate, the tropes versus universals dispute, is taken to be resolved (roughly: decided). In this paper I first argue that higher-order realism does not in fact resolve the tropes versus universals dispute. In a constructive spirit, I then develop higher-order realism in a way that leads to a dissolution, rather than a resolution, of this dispute too.

Higher‐order metaphysics

“…Accordingly, they (i) will regard predicates such as ‘… is wise’ to be the linguistic vehicles of choice when it comes to property talk, (ii) will take simple predications such as ‘Plato is wise’ to be the most perspicuous form of ascribing properties to objects and (iii) will consider higher‐order quantifications such as ‘∃ X ( X (Plato))’ as faithful expressions of their property realism. A higher‐order conception of properties along these lines is advocated for example by Williamson (2013), Jones (2018), Bacon (2020), Skiba (2020), Trueman (2021). We can discern three major types of advantages cited in favour of it by its proponents 3…”

“…So, from the perspective of higher‐orderists, the question cannot even be intelligibly formulated, which absolves them of any obligation to even engage with it (see Jones, 2018). Further questions to be eschewed in this way include the question of whether higher‐order entities are sets (Jones, 2019, p. 172), once more the question whether properties are tropes or universals (which Skiba, 2020 marks out for dissolution, rather than resolution), and the question whether properties need to be connected to objects by an instantiation relation, a question which famously serves as the starting point for Bradley's Regress (Trueman, 2021, Ch. 10, §2).…”

“…For discussions of various free higher‐order logics, including positive free higher‐order logic, see Bacon et al. 2016; Besson 2009; Skiba 2020.…”

Quantification and Ontological Commitment

“…Let me close with an objection to this argument for Higher-Order Commitment, drawing on (Skiba 2021). I'll focus on second-order quantification as representative of higher-order quantification more generally.…”