The Possibility of Vagueness

We previously stated an impossibility result and suggested that the standard approaches to vagueness were incapable of providing a satisfactory response to the result. This chapter considers how a more satisfactory response to the result might proceed. This will call for a radical revision in our general understanding of vagueness and in how its logic has usually been conceived. It will be argued that the indeterminacy characteristic of vagueness can be conceived in purely logical terms without the need for any specific vagueness-theoretic vocabulary. The resulting notion of indeterminacy is seen to be global in character in that it makes sense to say that there is indeterminacy over a range of cases but not that there is indeterminacy in a single case; and a semantics for the resulting theory, in terms of the compatibility of uses, is then developed.

The Problem of Vagueness

This chapter introduces the philosophical concept of vagueness and explains its significance for contemporary philosophy. The concept is seen to give rise to two main problems: the ‘soritic problem’ of finding a solution to the paradoxes of vagueness; and the ‘semantic problem’ of finding a satisfactory semantics and logic for vague language. It discusses three of the main attempts to deal with these problems – Supervaluationism, Degree theory, and Epistemicism. It indicates why none of these theories has been regarded as satisfactory and it concludes with a general impossibility result which seems to rule out any satisfactory account of the concept.

The Phenomenon of Vagueness

The theory outlined in Chapter 2 is applied to three problems: the sorites puzzle; the Luminosity of mental states; and personal identity in the face of fission. We attempt to solve the sorites puzzle by distinguishing the principle of Tolerance from the Cut-Off principle and we argue that the plausibility of the sorites argument arises from a sort of transcendental illusion. We attempt to defend the Luminosity of the mental by showing that it is compatible with the Margin for Error principle, once that principle is properly formulated. Finally, we deal with the case of fission by taking the original person to be weakly identical, i.e. not distinct, from his offspring. This then enables us to reconnect the notions of survival and what matters to the identity of a person over time. None of these solutions would be possible without the adoption of our distinctive logic of vagueness.