Classic epics such as Homer’s Odyssey begin in medias res. That is, the account begins in the middle of the action and the background is filled in later. Perhaps one should read Not Exactly: In Praise of Vagueness by Kees van Deemter by starting in medias res. The book is divided into three parts. The content in parts II and III is better than the introductory examples in part I may lead one to expect.
Part I of Not Exactly is entitled “Vagueness, Where One Least Expects It.” This section gives several examples of how common concepts are not as precise as one might expect at first glance. However, the vagueness in these examples is not as unexpected as the section title suggests. The book points out, for example, that all measurements are somewhat imprecise. This portion of the book is reminiscent of a precocious child whose form of humor is to take statements more literally than they were intended.
Part II, “Theories of Vagueness,” is more substantial than Part I. This section contains an interesting introduction to linguistic theories of vagueness. It also introduces classical logic and fuzzy logic. (The book is to be applauded for alluding to the limitations of fuzzy logic; too many popular books are uncritical in their presentation of the subject.) However, statistical theories of vagueness are conspicuously missing. Most surprising is the lack of any mention of Bayesian statistics.
Part III, “Working Models of Vagueness,” turns from theory to application. The section discusses computational approaches to vagueness, in particular artificial intelligence. This final section is disappointingly brief. After about 220 pages describing the problems of vagueness, one would expect a more in-depth discussion of how these difficulties are addressed in practice.
Reading Not Exactly leaves one with a vague feeling that it may have attempted to cover too much ground.
John D. Cook is a research statistician at M. D. Anderson Cancer Center and a blogger.