Phillip Bricker

According to David Lewis, a realist about possible worlds must hold that actuality is relative: the worlds are ontologically all on a par; the actual and the merely possible differ, not absolutely, but in how they relate to us. Call this 'Lewisian realism'. The alternative, 'Leibnizian realism', holds that actuality is an absolute property that marks a distinction in ontological status. Lewis presents two arguments against Leibnizian realism. First, he argues that the Leibnizian realist cannot account for the contingency of actuality. Second, he argues that the Leibnizian realist cannot explain why skepticism about one's own actuality is absurd. In this paper, I mount a defense of Leibnizian realism.

Some argue, following Bertrand Russell, that because general truths are not entailed by particular truths, general facts must be posited to exist in addition to particular facts. I argue on the contrary that because general truths (globally) supervene on particular truths, general facts are not needed in addition to particular facts; indeed, if one accepts the Humean denial of necessary connections between distinct existents, one can further conclude that there are no general facts. When entailment and supervenience do not coincide it is only failure of supervenience, not failure of entailment, that carries ontological import.

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.

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.