Reality as Tall and Fine, Not Flat and Coarse
Øystein Linnebo · 2024
Abstract The dominant view in today's higher-order metaphysics favors strong higher-order comprehension axioms. This enables us to prove some strong generalizations of Cantor's theorem, which place strict limits on how finely individuated higher-order entities can be. This article discusses some arguments for and against the strong comprehension axioms. Existing arguments are found wanting. Based on a hierarchical conception of reality, an improved case is developed for restricting comprehension, in a way that makes the world safe for fine-grained higher-order entities. Thus, for all we know, reality may be tall and fine, not flat and coarse.