Truth without truths: Grim's Cantorian paradox and the ontology of the objects of omniscience

Abstract

I argue that Grim's diagonalization argument against the possibility of omniscience is not sound by arguing that the properties of being a proposition or a truth are not legitimate sortal properties. Thus, the fact that there can be no set corresponding to the extension of these properties does not imply that there is no completed totality of the things possessing it. First, I demonstrate that a correspondence theory of truth implies that propositions are non-linguistic representations of a type that resist determinate and uniform individuation into units and allow for arbitrary division into parts that are also propositions. The property is, therefore, an abstract mass property with no determinate cardinality of individuals that possess it. I then sketch a new theory of omniscience with this as its basis.