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Editorial: We need to think precisely about vagueness

In his book Not Exactly, Kees van Deemter argues that the very foundations of science don鈥檛 come in black and white.

Forgive the oxymoron, but how do you define vagueness?

A vague concept allows borderline cases. The potential confusion is that people think vagueness is when they don鈥檛 quite get what someone means. For people in my area of logic, it鈥檚 actually a much narrower phenomenon, such as the word 鈥済rey鈥�. Some birds are clearly grey, some are clearly not, while others are somewhere in between. The fact that such birds exist makes 鈥済rey鈥� a vague concept. The vagueness does not arise from insufficient information: some concepts are fundamentally vague.

On the other hand, if I say that I have fewer than three children, that鈥檚 not vague. In fact, it is the opposite, it is 鈥渃risp鈥�. It is true if I have zero, one or two children, and it is false if I have three or more.

Is vagueness anathema to science?

Put a magnifying glass to many scientific concepts and you find vagueness. Take the idea of 鈥渟pecies鈥�. For centuries, biologists searched for crisp distinctions between species. A common definition today is to say that two animals only belong to the same species if they can interbreed. But if A can interbreed with B, and B with C, it doesn鈥檛 always follow that A can interbreed with C.

Take the Ensatina salamander, which has six subspecies. Suppose subspecies A can interbreed with B, B with C, and so on until the end of the chain when F can no longer breed with A. Intuitively you want to say that they are all one species, but your criterion disagrees.

Should we give up on the concept?

The notion is incoherent, but biologists continue using it 鈥� with a pinch of salt. Richard Dawkins calls this tendency to think in discrete categories 鈥渢he tyranny of the discontinuous mind鈥�.

So we think in discrete categories, but reality really isn鈥檛 that way?

In the book I talk about a vintage racing car that has been repaired so many times that 70 years later only a few of the original parts remain. Is it the same car? The boundaries of objects are vague 鈥� and that goes for us, too. The average age of adult cells is 10 years. We are changing all the time.

Describing the world in terms of discrete objects is a useful fiction. Classical logic is discrete, too, based on binary dichotomies: yes/no, true/false. But that is not suited to thinking about the world鈥檚 fundamentally vague things, which include some of the things science is based on, such as measurement. There is, for example, no such thing as a 鈥減erfect鈥� metre, imperfect approximations are all we have. We should recognise we often need other forms of mathematical logic to describe the world.

How vague is everyday life?

Vagueness seeps in everywhere. We think we know what things like obesity or poverty are but they are context-based concepts. It can be a matter of life and death. We have laws prohibiting poisonous substances in food, say, but ask toxicologists what poisonous means, and all they give you is degrees of toxicity. Thresholds are arbitrary.

Is it ever important to be vague?

Doctors use vagueness all the time. For example, when researching for a project to automate messages about the condition of babies in intensive care, my colleagues found that doctors鈥� written reports say things like: 鈥渉eart rate OK most of the night, on the high side in the morning鈥�. The vagueness of the messages works in a very smart way 鈥� leaving out irrelevant details while adding a little bit of opinion. By calling the heart rate high, for example, they suggest there may be cause for worry.

For all these reasons, vagueness is crucial if you want to build computers and robots that communicate with people. If you want to understand or generate language, getting to grips with vagueness is key.

鈥淚f you want to understand or generate language, getting to grips with vagueness is key鈥�

Will the web need vagueness?

As we move toward a semantic web where the formal representations are symbolic, the challenge is to figure out how to represent vague or gradable things, such as 鈥渁ffordable鈥� housing or 鈥渁ncient鈥� monuments.

Editorial: We need to think precisely about vagueness