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We can measure temperature in degrees, but just how warm is a 'warm day'? Are you the same person today as you were yesterday? Our world is full of questions with no clear-cut answers, and our language is intrinsically vague. In this accessible study, Kees van Deemter introduces issues of vagueness as explored in philosophy, mathematical logic, linguistics and artificial intelligence, showing that it is both characteristically human and (sometimes) a virtue.