18 - Vagueness

Summary

A standard objection to classical logic has been its failure to come to grips with vague predicates and their associated problems and paradoxes. An analysis of the vague predicates “low,” “medium,” and “high” (as applied to brightness of light bulbs) was implicit in Lecture 3. In this lecture we want to make the idea behind this treatment more explicit, thereby suggesting an information-theoretic line of research into vagueness. At best, this line of development would allow the information-flow perspective to contribute to the study of vagueness. At the very least, it should show that vagueness is not an insurmountable problem to the perspective offered in this book.

In this lecture we explore a different family of related vague predicates, “short,” “medium,” “tall,” “taller,” and “same height as.” This family is simple enough to treat in some detail but complicated enough to exhibit three problems that are typical of vague predicates.

Information Flow Between Perspectives

The first problem is that different people, with differing circumstances, often have different standards in regard to what counts as being short or tall. In spite of the lack of any absolute standard, though, information flow is possible between people using these predicates. If Jane informs me that Mary is of medium height while she, Jane, is short, and if I consider Jane to be tall, then I know that I would consider Mary as tall as well. How is such reliable information flow possible between people with quite different standards of what counts as being tall?