Heapness, Homogeneity, and an Asymptotic Reconstruction of the Sorites Paradox

Rather than offering another general semantics for vagueness, this paper argues thatthe Sorites paradox of the heap is partly misframed when treated solely as a searchfor a sharp finite cutoff. It develops a structural and asymptotic account of heapnessthat distinguishes ordinary finite heaphood from maximal heapness as an ideal ofcompletion. On the positive side, a heap is characterized not by stepwise additionalone but by aggregation, contiguity, partial occlusion, permutation tolerance, andevaluation at a relevant sortal level of individuation. Homogeneity is not requiredfor heaphood simpliciter, though it is central to the identity of a pure heap ofa specified kind. On the critical side, familiar responses to the Sorites paradox—including sharp-boundary views, epistemicism, supervaluationism, and contextualistapproaches—manage borderline predication more directly than the tacit completiondemand that gives the paradox its strongest form. The paper also argues that merescatteredness is insufficient for heaphood and that regress to ever smaller constituentstrivializes the issue unless the relevant sortal level is fixed. The conclusion is noteliminativism about finite heaps but a reframing of the paradox: what fails is theexpectation that maximal heapness must appear at some privileged finite stage.