The Shape of a Total Theory's Base: Categorial Foreclosures and What They Force

Abstract

What must a theory's fundamental categories be like if it is to account for everything, its own theorists included? A recent paper derives the domains such a theory must address (Wozniak 2026). This paper asks what base could address them all, and answers by elimination. It first sharpens what accounting for a domain requires: the phenomenon must follow from primitives the base already needs elsewhere, and an axiom asserting the link does not count, however it is labeled. Against that standard three familiar arguments turn eliminative. Newman's theorem and Putnam's permutation argument rule out bases of pure structure, whose content collapses into a claim about cardinality. The explanatory gap rules out bases of third-person facts. The gap run in reverse rules out bases of experience alone, though weakly, since experience already carries rich structure. Each result closes a route without refuting a view; denial and category change stay open. A narrow specification survives: a base whose general primitives carry an intrinsic aspect alongside a relational one, whose reference is fixed from inside, whose dynamics apply to the theorist who states them, and which has a well-defined formal object beneath it. The specification converges on Russellian monism from an unfamiliar direction, the demands of totality rather than the mind–body problem, and hands that position burdens rather than support, chief among them the individuation of whatever carries the intrinsic aspect. Whitehead and Spinoza sit in the surviving region; neither built the formal object. The paper certifies no candidate and proposes none.