Sorites Without Vagueness I: Classificatory Sorites

Abstract

An abstract mathematical theory is presented for a common variety of soritical arguments, treated here in terms of responses of a system, say, a biological organism, a gadget, or a set of normative linguistic rules, to stimuli. Any characteristic of the system's responses which supervenes on stimuli is called a stimulus effect upon the system. Classificatory sorites is about the identity of or difference between the effects of stimuli that differ ‘only microscopically’. We formulate the classificatory sorites on arguably the highest possible level of generality and show that the ‘paradox’ is dissolved on grounds unrelated to vague predicates or other linguistic issues traditionally associated with it. If stimulus effects are properly defined (i.e., they are uniquely determined by stimuli), and if the space of the stimuli is endowed with appropriate (not necessarily metric) closeness and connectedness properties, then this space must contain points in every vicinity of which, ‘however small’, the stimulus effect is not constant. The effects can only be ‘tolerant’ to very small differences between stimuli if the closeness structure that is used to define very close stimuli does not render the space of stimuli appropriately connected: in this case the ‘paradox’ cannot be formulated. Nor can it be formulated if the response properties considered are not true effects, i.e., if they do not supervene on stimuli.