A Coarse-Grained World-View

Abstract

AbstractThe theory motivated in the previous chapters is summed up. What emerges is a familiar modal view of metaphysics, on which a proposition is necessary just in case it is true in all possible worlds, and propositions are identical just in case they are true in the same possible worlds. A number of questions are noted to be left open by the view, including questions of a mathematical character such as higher-order versions of the axiom of choice and the continuum hypothesis. Two general objections to such modal views of metaphysics are considered: The first concerns the central role possible worlds play, which leads to a problem identified by Kaplan. The problem is noted to be much more general, due to a theorem by Prior. The second concerns the challenge of making sense of type-neutral quantification. In response, an extension of standard type theory is sketched which allows relation terms of infinite arity.