John Divers

Colin McGinn proposes that acceptance of the supervenience of the modal on the actual is the natural form of expression of a non-objectual realism about modality. Here, some of the difficulties that arise in applying theses of supervenience to the modal-actual case are discussed. It is then argued: 1)that the truth of many such theses is determined on uncontroversial modal logical and conceptual grounds, and 2) that this and other independent considerations render it highly implausible that the affirmation of modal-actual supervenience amounts to a modal realism.

Lewis’ analysis of modality faces a problem in that it appears to confer unintended truth values to certain modal claims about the pluriverse: e.g. ‘It is possible that there are many worlds’ is false when we expect truth. This is the problem of advanced modalizing. Divers presents a principled solution to this problem by treating modal modifiers as semantically redundant in some such cases. However, this semantic move does not deal adequately with advanced de re modal claims. Here, we motivate and detail a comprehensive semantics for advanced modalizing de dicto and de re. The generalized semantic feature of the initial solution is not redundancy but absence from counterpart-theoretic translations of world-constrictions.

According to the Genuine Modal Realist, there is a plurality of possible worlds, each world nothing more than a maximally inter-related spatiotemporal sum. One advantage claimed for this position is that it offers us the resources to analyse, in a noncircular manner, the modal operators. In this paper, we argue that the prospects for such an analysis are poor. For the analysis of necessity as truth in all worlds to succeed it is not enough that no modal concepts be used in the realist's account of a possible world (a fact we grant); rather, such an analysis will succeed only if the set of worlds that is postulated is complete. By appealing to plausible truths about the number of possible alien natural properties, we show that there are serious difficulties in guaranteeing that such a set exists without taking some modal concept as primitive. Accordingly, at least in its current form, Genuine Modal Realism must curtail its analytic ambitions.

We outline a theory of the cognitive role of belief in absolute necessity that is normative and intended to be metaphysically neutral. We take this theory to be unique in scope since it addresses simultaneously the questions of how such belief is (properly) acquired and of how it is (properly) manifest. The acquisition and manifestation conditions for belief in absolute necessity are given univocally, in terms of complex higher-order attitudes involving two distinct kinds of supposition (A-supposing and C-supposing). It is subsequently argued that the proposed acquisition and manifestation conditions are rationally interdependent, and that such harmony affords explanations of connections between different facets of belief in necessity that otherwise remain mysterious.

The modal primitivist who takes a sentential possibility operator as her only modal resource can provide adequate representations of the familiar concepts of weak, strong and global supervenience. The primitivist representations of these concepts can be applied to provide adequate interpretations of speciflc supervenience theses which will be considered. Moreover the modal primitivist is no better and no worse placed than the genuine modal realist to present supervenience as a simple and unifled notion. Therefore, Lewis is unjustified in claiming that a genuine modal realist approach to the analysis of the concept of supervenience is superior to a modal primitivist approach.

Kant states that necessity and strict universality are criteria of a priori knowledge. Interpreting this dictum standardly and straightforwardly in respect of necessity, it is inconsistent with there being necessary a posteriori truths or contingent a priori truths (cf Kripke). This straightforward interpretation may convict Kant of understandable error (at worst) in the case of necessity, but it is so uncharitable in the case of strict universality that we ought to seek an alternative. I offer a charitable interpretation of the doctrine that necessity and strict universality are sufficient conditions of a priority, commenting briefly on comparable necessary conditions.

In this reply, we defend our argument for the incompleteness of Genuine Modal Realism against Paseau's criticisms. Paseau claims that isomorphic set of worlds represent the same possibilities, but not only is this implausible, it is inimical to the target of our paper: Lewis's theory of possible worlds. We argue that neither Paseau's model-theoretic results nor his comparison to arithmetic carry over to GMR. We end by distinguishing two notions of incompleteness and urge that, for all that Paseau has said, GMR remains incomplete in the relevant sense.