Positionality and Pictures

Abstract

LUCKILY we need not bother with the artistic dramatis personae, the talk of extrasensory perception, or the other embellishments of the preceding paper by Barker and Achinstein.' The only serious question is whether the authors succeed in defining the distinction between positional and non-positional predicates. In substance, the formulation they propose is this: a single picture or representation can be given for all instances of application of a non-positional predicate, while at least two different representations are needed to cover all instances of application of a positional predicate. For example, a single present patch of green paint will represent the color of all green things irrespective of their dates; but two present patches will be needed to represent all grue things: a green one for cases up to time t and a blue one for cases thereafter. The limitations upon what can represent what are far from obvious. We often see black-and-white diagrams in which different colors are represented by different shadings: say green by cross-hatching, blue by dotting, and so forth. Plainly symbols like these can equally well be used for grue. Vertical shading, say, for what is green up to time t or blue thereafter is as legitimate a representation of grue as the other symbols are of green and blue. Presumably Barker and Achinstein will reject such diagramming as not the natural representation they have in mind. Just what, then, constitutes representation within their meaning? To stipulate that a color must be represented by a sample of it will not do; for a present patch of paint that is a sample of green is also a sample of grue. And if we deny that grue is a single color we are in effect merely saying that grue is positional, and so begging the question. Does representation perhaps require, then, that the color of an object be represented by another object that is indiscriminable from, or matches, the first in color? This will not work either; for then a patch of green paint, since it matches very few green things, cannot represent the color of all green things.2