A Refutation of Goodman's Type-Token Theory of Notation

Abstract

In Languages of Art, Nelson Goodman presents a general theory of symbolic notation. However, I show that his theory could not adequately explain possible cases of natural language notational uses, and argue that this outcome undermines, not only Goodman’s own theory, but any broadly type versus token based account of notational structure. Given this failure, an alternative representational theory is proposed, in which different visual or perceptual aspects of a given physical inscription each represent a different letter, word, or other notational item. Such a view is strongly supported by the completely conventional relation between inscriptions and notation, as shown by encryption techniques etc. In Chapter 4 of his book Languages of Art, 1 Nelson Goodman presents a general theory of symbolic notation, two of whose main syntactic requirements, of disjointness and finite differentiation, are “…met by our alphabetical, numerical, binary, telegraphic, and basic musical notations; and by a wide variety of other describable notations…” (1968, 140). However, I shall show that his theory could not adequately explain some possible cases of natural language notational uses, and argue that this outcome undermines, not only Goodman’s own theory, but any broadly type versus token based account of notational structure.