Modal Dispositionalism and the (T) Axiom
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Modal Dispositionalism and the (T) Axiom Matthew James Collier 1 Received: 5 May 2020 / Revised: 28 August 2020 / Accepted: 7 September 2020 # The Author(s) 2020
Abstract Yates has recently argued that modal dispositionalism invalidates the (T) axiom. Both Yates and Allen have advanced responses to the objection: Yates’s response proposes installing truth into the possibility biconditional, and Allen’s response requires that all properties be construed as being essentially dispositional. I argue that supporters of Borghini and Williams’s modal dispositionalist theory cannot accept these responses, given critical tenets of their theory. But, since these responses to the objection are the most plausible in the literature, I conclude that the threat that Borghini and Williams’s modal dispositionalist theory invalidates the (T) axiom still looms large. Keywords Modal Dispositionalism . Modal logic . Dispositions . Categorical and
dispositional properties
1 Introduction Modal dispositionalism (MD) semantically reduces, and ontologically explicates, possibility and necessity in terms of dispositionality. For MD, the dispositions of actual objects are taken as the truth-makers of modal claims.1 So, (roughly) some object’s having the disposition to bring it about that p makes-true the modal claim . Borghini and Williams’s (2008) version of MD (‘MD’ shall refer exclusively to their
1
For the most dominant possible worlds accounts, see Lewis (1986), Plantinga (1974) and Adams (1974).
* Matthew James Collier [email protected]
1
Oriel College Oriel Square, Oxford OX1 4EW, UK
Philosophia
theory) is the chief dispositionalist theory of concern here – however some of the points I raise generalize to other modal dispositionalist theories.2 The roadmap for this paper is the following: Section 2 sets up MD’s ontology by explaining what dispositions and dispositional properties are, and provides an exposition of MD; and, section 3 examines an instance of MD’s formal deficiency – specifically, I examine Yates’s (2015) objection that, in the case of certain actualized necessities, modal dispositionalism’s biconditionals for possibility and necessity invalidate the (T)-axiom, and I apply this objection to MD. To Yates’s objection, I assess the two most plausible responses – one of which is owed to Yates (which is also provided in his (2015)), and the other to Allen (2017). I argue that both responses fail to save MD: crucially, they ignore critical aspects of MD.3 Indeed, Yates’s response requires one to ignore MD’s universal dispositionalist aim insofar as his response threatens to render dispositions redundant in MD’s explication of modality, and Allen’s response requires one either to ignore MD’s naturalism or to accept that MD is – at best – ontologically bizarre or – at worst – absurd. I conclude that neither of the two most plausible responses to Yates’s objection are successful. Thus, MD should be rejected – whilst some modal logical axioms may be negotiable, some are not; certainly (T) is not.
2 Disposit
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