Phillip Bricker

In this chapter, I evaluate various conceptions of distance. Of the two most prominent, one takes distance relations to be intrinsic, the other extrinsic. I recommend pluralism: different conceptions can peacefully coexist as long as each holds sway over a distinct region of logical space. But when one asks which conception holds sway at the actual world, one conception stands out. It is the conception of distance embodied in differential geometry, what I call the Gaussian conception. On this conception, all fundamental facts about distance are “local” facts.” But there is a problem: the Gaussian conception, notwithstanding its mathematical and physical credentials, appears metaphysically suspicious on Humean grounds. In the final section, I suggest that the Gaussian conception can be given a sound metaphysical footing in terms of non-standard analysis.

The most commonly heard proposals for reducing possible worlds to language succumb to a simple cardinality argument: it can be shown that there are more possible worlds than there are linguistic entities provided by the proposal. In this paper, I show how the standard proposals can be generalized in a natural way so as to make better use of the resources available to them, and thereby circumvent the cardinality argument. Once it is seen just what the limitations are on these more general proposals, it can be clearly seen where the real difficulty lies with any attempt to reduce possible worlds to language. Roughly, the difficulty is this: no actual language could have the descriptive resources needed to represent all the ways things might have been. I conclude by arguing that this same difficulty spells doom for any nominalist or conceptualist proposal for reducing possible worlds.

It follows from Humean principles of plenitude, I argue, that island universes are possible: physical reality might have 'absolutely isolated' parts. This makes trouble for Lewis's modal realism; but the realist has a way out. First, accept absolute actuality, which is defensible, I argue, on independent grounds. Second, revise the standard analysis of modality: modal operators are 'plural', not 'individual', quantifiers over possible worlds. This solves the problem of island universes and confers three additional benefits: an 'unqualified' principle of compossibility can be accepted; the possibility of nothing can be accommodated; and the identity of indiscernible worlds can be decisively refuted.

According to the Truthmaker Principle: every truth has a truthmaker. Attempts to come to grips with the Truthmaker Principle played a prominent role in Lewis’s metaphysical writings over the last fifteen years of his career. Although Lewis agreed that the truth of propositions must somehow be ontologically grounded, the Truthmaker Principle was too strong: it conflicted with two of Lewis’s most fundamental metaphysical assumptions, the uniqueness of composition and the Humean denial of necessary connections. Lewis endorsed instead a weaker principle: Truth Supervenes on Being. But towards the end of his career, he changed course, noting that his critique of the Truthmaker Principle rested on essentialist assumptions that he, as a counterpart theorist, does not accept. Once freed from those assumptions, a counterpart theorist can accept the Truthmaker Principle after all without buying into unmereological composition and mysterious necessary connections.

In this discussion of Colin McGinn's book, 'Logical Properties', I comment first on the chapter "Existence", then on the chapter "Modality." With respect to existence, I argue that McGinn's view that existence is a property that some objects have and other objects lack requires the property of existence to be fundamentally unlike ordinary qualitative properties. Moreover, it opens up a challenging skeptical problem: how do I know that I exist? With respect to modality, I argue that McGinn's argument that quantificational analyses of modality in terms of possible worlds are inevitably circular does not apply to modal theorists who hold that the notion of an impossible world is incoherent.