In this article, we discuss a simple argument that modal metaphysics is misconceived, and responses to it. Unlike Quine's, this argument begins with the observation that there are different candidate interpretations of the predicate ‘could have been the case’. This is analogous to the observation that there are different candidate interpretations of the predicate ‘is a member of’. The argument then infers that the search for metaphysical necessities is misguided in much the way the ‘set-theoretic pluralist’ claims that the search (...) for the true axioms of set theory is. We show that the obvious responses to this argument fail. However, a new response has emerged that purports to prove, from higher-order logical principles, that metaphysical possibility is the broadest kind of possibility applying to propositions, and is to that extent special. We distill two lines of reasoning from the literature, and argue that their import depends on premises that any ‘modal pluralist’ should deny. Both presuppose that there is a unique typed hierarchy, which is what the modal pluralist, in the context of higher-order logic, should disavow. In other words, both presupposes that there is a unique candidate for what higher-order claims could mean. We consider the worry that, in a higher-order setting, modal pluralism faces an insuperable problem of articulation, collapses into modal monism, is vulnerable to the Russell-Myhill paradox, or even contravenes the truism that there is a unique actual world, and argue that these worries are misplaced. We also sketch the bearing of the resulting ‘Higher-Order Pluralism’ on the theory of content. One theme of the discussion is that, if Higher-Order Pluralism is correct, then there is no fixed metatheory from which to characterize higher-order reality. (shrink)

An increasing amount of contemporary philosophy of mathematics posits, and theorizes in terms of special kinds of mathematical modality. The goal of this paper is to bring recent work on higher-order metaphysics to bear on the investigation of these modalities. The main focus of the paper will be views that posit mathematical contingency or indeterminacy about statements that concern the ‘width’ of the set theoretic universe, such as Cantor’s continuum hypothesis. Within a higher-order framework I show that contingency about the (...) width of the set-theoretic universe refutes two orthodoxies concerning the structure of modal reality: the view that the broadest necessity has a logic of S5, and the ‘Leibniz biconditionals’ stating that what is possible, in the broadest sense of _possible_, is what is true in some possible world. Nonetheless, I suggest that the underlying picture of modal set-theory is coherent and has attractions. (shrink)

The modality of normality distinguishes states of affairs which are normal from those which are abnormal. Existing work on the modality of normality assumes that it is a restriction of metaphysical modality. In this paper, we argue that this assumption is inappropriate and explore the consequences of abandoning it. -/- After preliminary discussion (§1), we introduce the dominant framework for reasoning about normality (§2) and argue that it ascribes implausibly strong structural properties to the modality. In its place, we propose (...) a new framework, which avoids this commitment (§§3-5). This account has a number of interesting features, which we explore in both an informal and formal setting. If correct, it implies that the modality of normality occupies a distinctive place in the space of modalities. Before concluding, we consider some of the wider implications of our account (§6), focusing on the role normality has played in epistemic theorizing. (shrink)

In the metaphysics of modality, one finds a distinction between two families of modalities: the so-called ‘objective’, ‘real’ or ‘circumstantial’ modalities and the ‘non-objective’, ‘non-real’ or ‘non-circumstantial’ modalities. The guiding thought is that in some intuitive sense the former modalities pertain to contingency in worldly circumstance—how things could have genuinely otherwise been—whereas the latter do not. Moreover the distinction has acquired importance through attempts to elucidate the modality of metaphysical necessity by assigning it a distinctive role within the objective modalities. (...) In this paper I use the resources of higher-order modal logic to explore how one might systematize these ideas. I present a formal tension which shows that one natural way of systematizing them is unstable. And whilst I show that there are ways of stabilizing the guiding picture, even the best of them involves deeply non-trivial departures from how that picture is ordinarily understood. I conclude by revisiting the motivation for the underlying picture of modalities. (shrink)

In the metaphysics of modality, one finds a distinction between two families of modalities: the so-called ‘objective’, ‘real’ or ‘circumstantial’ modalities and the ‘non-objective’, ‘non-real’ or ‘non-circumstantial’ modalities. The guiding thought is that in some intuitive sense the former modalities pertain to contingency in worldly circumstance—how things could have genuinely otherwise been—whereas the latter do not. Moreover the distinction has acquired importance through attempts to elucidate the modality of metaphysical necessity by assigning it a distinctive role within the objective modalities. (...) In this paper I use the resources of higher-order modal logic to explore how one might systematize these ideas. I present a formal tension which shows that one natural way of systematizing them is unstable. And whilst I show that there are ways of stabilizing the guiding picture, even the best of them involves deeply non-trivial departures from how that picture is ordinarily understood. I conclude by revisiting the motivation for the underlying picture of modalities. (shrink)