Vagueness in Language: The Case Against Fuzzy Logic Revisited

When I started interacting with logicians, I was surprised to learn that fuzzy logic is still a big and active field of basic research. This surprise stemmed from my experience with fuzzy logic in my own field, linguistic semantics: In semantics, fuzzy logic was explored in the analysis of vagueness in the early seventies by Lakoff [10], but has been regarded as unsuitable for the analysis of language meaning at least since the influential work of Kamp in 1975 [8], which I summarize below. Therefore, I held the belief that fuzzy logic, though it has been useful in technical applications—I once possessed a Japanese rice-cooker that was advertised to use fuzzy logic—, was not useful for the analysis of vagueness. As I have learned since, I was just ignorant of a big chunk of modern mathematical logic, and fuzzy logic is in fact a lively paradigm of research on vagueness. The lack of interaction between linguists and logicians that my experience illustrates seems to be a more general phenomenon: From the interaction with logicians, I have learned that many fuzzy logicians also do not seem to be aware of current work in linguistics on vagueness. The different attitudes towards fuzzy logic in linguistics and in logic are, of course, most likely rationally justified on the basis of the different goals of the two fields. However, historical accidents can also happen in the development of a field of science, in which case the different traditions in two fields may turn out to have no rational basis. So, which is it in the case of fuzzy logic and linguistics? In this paper, I revisit the arguments against the use of fuzzy logic in linguistics (or more generally, against a truth-functional account of vagueness). In part, this is an exercise to explain to fuzzy logicians why linguists have shown little interest in their research paradigm. But, the paper contains more than this interdisciplinary service effort that I started out on: In fact, this seems an opportune time for revisiting the arguments against fuzzy logic in linguistics since three recent developments affect the argument. First, the formal apparatus of fuzzy logic has been made more general since the 1970s, specifically by Hájek [6], and this may make it possible to define operators in a way to make fuzzy logic more suitable for linguistic purposes. Secondly, recent research in philosophy has examined variations of fuzzy logic ([18, 19]). Since the goals of linguistic semantics