Hedges: A Study in Meaning Criteria and the Logic of Fuzzy Concepts

Abstract

Logicians have, by and large, engaged in the convenient fiction that sentences of natural languages (at least declarative sentences) are either true or false or, at worst, lack a truth value, or have a third value often interpreted as ‘nonsense’. And most contemporary linguists who have thought seriously about semantics, especially formal semantics, have largely shared this fiction, primarily for lack of a sensible alternative. Yet students of language, especially psychologists and linguistic philosophers, have long been attuned to the fact that natural language concepts have vague boundaries and fuzzy edges and that, consequently, natural language sentences will very often be neither true, nor false, nor nonsensical, but rather true to a certain extent and false to a certain extent, true in certain respects and false in other respects.

This work was supported by grant GS-2939 from the National Science Foundation of the University of Michigan and by a grant from the American Council of Learned Societies. It was written while I was in residence at the Center for Advanced Study in the Behavioral Sciences at Stanford, to whom I would like to express thanks for the use of their facilities.

The original impetus for the study of hedges came from the work of Heider (1971), Alston (1964), Ross (1970), and Bolinger (1972). The formal parts are based on the development of fuzzy set theory by Lofti Zadeh, Dept. of Electrical Engineering, U. of California, Berkeley. Professor Zadeh has been kind enough to discuss this paper with me often and at great length and many of the ideas in it have come from those discussions. In addition I would like to thank the following people whose discussed these ideas with me and who contributed to what little understanding I have of the subject: Ann Borkin, Herb Clark, Alan Dershowitz, Hubert Dryfus, Charles Fillmore, Jim Fox, Dov Gabbay, Richard Grandy, Charles Guignon, Eleanor Heider, Peter Kenen, Robin Lakoff, John Lawler, Robert LeVine, David Lewis, Ruth Barcan Marcus, James Matisoff, Jim McCawley, Robert Nozick, Michael Reddy, Haj Ross, Dana Scott, and Bas van Fraassen.