Higher-order metaphysics and the tropes versus universals dispute
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Higher-order metaphysics and the tropes versus universals dispute Lukas Skiba1
Accepted: 23 October 2020 The Author(s) 2020
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. Keywords Higher-order metaphysics Properties Tropes Universals Higherorder logic Higher-order quantification
1 Higher-order metaphysics and property theories A foundational question in metaphysics is what (formal) language metaphysical theorizing should be conducted in. An increasingly popular response is provided by higher-orderism. Higher-orderists insist that metaphysical theories should be formulated in a language that allows not only for first-order quantification, i.e. quantification into the position of singular terms, but also for sui generis higherorder quantification, i.e. quantification into other syntactic positions which is not reducible to or explicable in first-order terms. & Lukas Skiba [email protected] 1
¨ berseering 35, Postfach #4, 22297 Hamburg, Philosophisches Seminar, Universita¨t Hamburg, U Germany
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L. Skiba
In this spirit, higher-order resources have recently been brought to bear on a diverse list of topics, including unrestricted quantification (Williamson 2003), essence (Correia 2006), the internalism versus externalism debate (Besson 2009), the contingentism versus necessitism debate (Stalnaker 2012; Williamson 2013; Fritz and Goodman 2017), generalized identity (Rayo 2013; Dorr 2016), propositions (Trueman 2018, 2020; Jones 2019) and grounding (Correia and Skiles 2019). A further and particularly natural focal point for higher-orderism is the metaphysics of properties. After all, properties are intimately connected to predicates and quantification into predicate position constitutes the paradigm case of higher-order quantification. Exploiting this connection, Jones (2018) and Trueman (forthcoming) argue that property realism finds its natural habitat in a higher-order, rather than a first-order, setting. To bring out what is at issue here, we can follow Jones (809–811) in taking proponents of first-order realism about properties (FOR) to endorse a range of substitution instances of the following schema: (Exist1)
h8xðUx ! 9yðIxy ^ h8zðIzy ! UzÞÞÞ
Here ‘Ixy’ is to be read as ‘x instantiates y’ so that replacing the schematic letter ‘U’ with, say, the predicate
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