Not Exactly is a brave book in two ways. Its subject matter – vagueness in language, logic, computing and everyday life – does not fit well into standard categories of popular science writing. And its treatment of vagueness is often highly abstract, dealing with abstruse questions of logic that are usually discussed only in specialised philosophy journals. I’ve given it 3 stars and not 4 because for a popular science audience its concerns may be too abstract and its prose too plain. Also, its three parts do not fit together as well as they might. But – in the spirit of vagueness and its frequent companion, context-dependence – it must be said that, for clarity and originality, quite a few readers would be compelled to give it 4 stars.
For van Deemter, a computer scientist at the University of Aberdeen in Scotland, vague objects and concepts are those that admit of boundary cases. The first part of the book describes cases of vagueness in the everyday world, and is probably the weakest of the three parts. Here van Deemter discusses the vagueness in concepts such as obesity, poverty, intelligence, and scientific measurements, as well as the difficulty of keeping track of the identity of objects over time (where objects include everything from cars to human beings).
It turns out that many things are vague. But so what? We all know that politicians, journalists, and marketers use vague terms to their advantage; and the idea that human identity is ill-defined is straight out of Philosophy 101. In a book about vagueness it is useful to see examples of the phenomenon. But if the aim of the first 60 pages of the book is just to identify vagueness-related problems (rather than, say, to help solve those problems) then the point could perhaps be better made in a 10-page introduction. A possible exception is the chapter on the concept of a biological species, which Deemter dismantles in a convincing fashion.
The second part describes attempts by linguists and logicians to model the role of vagueness in language and reasoning. This is the most abstract section, and will not be everyone’s cup of tea. For sheer popular science audacity, the chapters on the sorites paradox deserve special mention. Also known as the “paradox of the heap”, the sorites paradox uses the fact that a series of imperceptibly small changes can give rise to perceptible changes. For example, the addition of a single pebble should not turn a mere collection of pebbles into a heap of pebbles; a single pebble is just too small to make such a big difference. But it follows that one can never make a heap of pebbles just by adding (say) 1000 single pebbles to mere collection, since none of those 1000 pebbles can turn the collection into a heap. This is paradoxical, since if anything makes a heap then 1000 pebbles must do so.
It turns out that the best answer to the paradox (according to van Deemter) is, roughly speaking, that the addition of each pebble makes a small but non-negligible difference to whether or not the collection becomes a heap. But the audacious part is not van Deemter’s answer but the fact that he describes in tortuous detail the different logical systems that philosophers have used to ground their various answers to the paradox – along with the arguments for and against those systems. Not many science writers would have the courage to cover such abstract material in such detail. Whether van Deemter pulls it off will depend on the reader’s tastes. But with his clear prose, vivid examples, and some engaging “dialogues intermezzo”, he gives himself every chance of being read and understood.
The third and last part, on the practical applications of vagueness, is the most appealing in conventional popular science terms. It is intriguing without being technically challenging, and describes attempts to automate such tasks as the translation of weather data into human terms, the process of making medical diagnoses, and reference (the act of drawing someone’s attention to an object).
Deemter shows why these tasks are important and why they are exasperatingly difficult to perform, largely due to the difficulty of dealing systematically with vagueness. Less successfully, he shows how game theory can be used to show why politicians make vague commitments. The game theory explanation is convincing, but it is also so obvious that it makes game theory look trivial rather than powerful. The other drawback of the third part is that it does not draw very often on the insights from the formal models that the reader has struggled through in part two.
As for the game theory case, so with many of the examples in this book: their value depends on whether the reader shares van Deemter’s enthusiasm for finding formal models of arguments or explanations that we can describe, to some extent, in an informal, intuitive way. With his dialogue intermezzos, bullet-pointed chapter summaries, and a summary of the book’s “lessons learnt”, van Deemter makes every effort to present his subject in clear, accessible terms. None of these devices disguise the main purpose of the book, which is to be very precise about vagueness. There is nothing inconsistent about this approach to the topic, but it may not be to everyone’s taste.