John Divers

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.

In section 1 I motivate and execute the presentation of a well-defined Lewisian conception of analysis and of what it would be to analyse modality successfully. That conception is then put to two applications. In section 2 various inadequacies are exposed in a (recently popular) separatist approach to the understanding and/or evaluation of Lewis's analysis of modality. Section 3 provides a defence against a resilient argument for the claim that Lewis's analysis of modality cannot be fully reductive while also dealing adequately with alien possibility.

The modal antirealist, as presented here, aims to secure at least some of the benefits associated with talking in genuine modal realist terms while avoiding commitment to a plurality of Lewisian (or ersatz) worlds. The antirealist stance of agnosticism about other worlds combines acceptance of Lewis's account of what world-talk means with refusal to assert, or believe in, the existence of other worlds. Agnosticism about other worlds does not entail a comprehensive agnosticism about modality, but where such agnosticism about modality is enforced, the aim of the agnostic programme is to show that it is not detrimental to our modal practices. The agnostic programme consists in an attempt to demonstrate the rational dispensability of that disputed class of modal beliefs which the agnostic eschews, but which are held by the realist and the folk. Here I attempt to motivate, describe, and illustrate such an agnostic antirealist programme in modal philosophy.

The principle of modal ubiquity - that every truth is necessary or contingent - and the validity of possibility introduction, are principles that any modal theory suffers for failing to accommodate. Advanced modal claims are modal claims about entities other than spatiotemporally unified individuals (perhaps, then, spatiotemporally disunified individuals, sets, numbers, properties, propositions and events). I show that genuine modal realism, as it has thus far been explicitly developed, and in so far as it deals with advanced modal claims, cannot accommodate the principles in question. On behalf of the genuine modal realist I motivate and propose a redundancy interpretation of advanced possibility claims and extend that interpretation to the cognate cases of necessity, impossibility and contingency. I then show that the problematic principles as they apply to advanced modal claims can be derived from these interpretations. I show further how the proposed interpretation enables the genuine modal realist to deal with a number of objections that centre on the alleged inadequacy of the genuine modal realist's expressive resources. I conclude that genuine modal realism emerges the stronger for having been shown capable of dealing with advanced modal claims on the basis of no conceptual and ontological resources beyond those it requires to deal with ordinary modal claims.