Călborean - 2025 - Vagueness as dispersion (CUNY Logic and Metaphysics Workshop).pdf

<p dir="ltr">Classical logic (FOL) is thought to be incompatible with the fuzzy cutoffs of vague predicates. I conceptualize vagueness as the dispersion of negative and positive cases of predicates such as “tall” across ranks defined by the preferred ordering—e.g., “having less or equal cm of height”. I distinguish vertical dispersion—both negative and positive cases of the predicate can share the same measurement—and horizontal dispersion—change happens with gradually fewer intercalations of negative and positive cases. Parallel to the non-classical approach of Cobreros et al. (2012), I introduce two classical shorthand modifiers “strictly” and “broadly”. Then, the Sorites paradox is solved by weakening the principle of tolerance to “If a person is strictly tall, anyone one less cm of height is broadly tall”, noted ∀xy.((Lxy ∧ [L]Ty) ⊃ Tx). This notational extension of FOL is conservative and can express higher-order vagueness.</p>