How Many Angels Can Dance on the Point of a Needle? Transcendental Theology Meets Modal Metaphysics

We argue that certain modal questions raise serious problems for a modal metaphysics on which we are permitted to quantify unrestrictedly over all possibilia. In particular, we argue that, on reasonable assumptions, both David Lewis's modal realism and Timothy Williamson's necessitism are saddled with the remarkable conclusion that there is some cardinal number of the form aleph(alpha) such that there could not be more than aleph(alpha)-many angels in existence. In the last section, we make use of similar ideas to draw a moral for a recent debate in meta-ontology.