Open texture and its ramifications for logic and semantics
Friedrich Waismann in his 1945 paper "Verifiability" introduced a notion of open texture. A predicate P exhibits open texture if it is possible for there to be an object a such that nothing concerning the established conventions regarding the meaning of P or the non-linguistic facts determines that P holds of a, nor does anything determine that P fails to hold of a. Hence, in some contexts in which it might be uttered, the truth of a sentence containing Pa is left open by the meaning of P and the nonlinguistic facts. We offer an articulation and evaluation of the notion of open texture, along with some related themes in Waismann's series of papers on Analyticity. As we understand it, open texture is to be distinguished from vagueness and context-sensitivity. But we question whether Waismann was right to restrict open-texture to empirical predicates, leaving open the possibility that the phenomenon is found more generally, even in the terminology of science and mathematics. Our goal is to explore the extent to which Waismann's insights bear on the enterprise of natural language semantics and on the model-theoretic notion of logical consequence. We argue that the semantic indeterminacy reflected in open texture is a design feature of natural language. Hence, it behooves us as theorists to develop models that accommodate various kinds of semantic indeterminacy, including open texture.