Theories of Vagueness

Theories of Vagueness

Theories of Vagueness

Theories of Vagueness


Vague expressions, such as "heap," "red" and "child," proliferate throughout natural languages, and an increasing amount of philosophical attention is being directed at theories of the logic and semantics associated with them. In this book Rosanna Keefe explores the questions of what we should want from theories of vagueness and how we should compare them. Her powerful and original study will be of interest to readers in philosophy of language and of mind, philosophical logic, epistemology and metaphysics.


The aim of this book is to formulate and defend the best possible theory of vagueness. First, I explore some general questions. What is vagueness and what are theories of vagueness? What should such theories be aiming to do? And how should we assess them?

My project is primarily one in the philosophy of logic and language. The focus is on finding the logic and semantics of vague language rather than, for example, illuminating the psychology of our use of it. But I am less concerned with formal modelling than with the philosophical rationale for any chosen type of model. Consequently, I minimise the technical discussion of complex logical material. This book should be accessible to anyone who has a grasp of elementary formal logic.

If you remove a single grain of sand from a heap of sand, you surely still have a heap of sand. But if you take a heap and remove grains one by one, you can apply that principle at each stage, which will commit you to counting even the solitary final grain as a heap. This is a sorites paradox. Arguments of a parallel form can typically be constructed for any vague term. For example, the generalisation 'anyone one hundredth of an inch shorter than a tall man is also tall' can be used to argue that a three-foot man is tall given that a sevenfoot man is, by considering a series of men each one hundredth of an inch shorter than the previous one. And a tadpole does not become a frog in the space of one hundredth of a second, which invites an argument to the conclusion that a tadpole can never become a frog. No straightforward answer to this persistent type of paradox looks promising: the premises are highly plausible, the inference seems valid but the conclusions are absurd.

The paradox is best dealt with in the context of a theory of vagueness more generally — a theory which answers a range of other questions. Consider Tek, who is a borderline case of 'tall'. We may . . .

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