Living on the slippery slope : the nature, sources and logic of vagueness

Abstract

According to the dominant approach in the theory of vagueness, the nature of the vagueness of an expression ‘F’ consists in its presenting borderline cases in an appropriately ordered series: objects which are neither definitely F nor definitely not F (where the notion of definiteness can be semantic, ontic, epistemic, psychological or primitive). In view of the various problems faced by theories of vagueness adopting the dominant approach, the thesis proposes to reconsider the naive theory of vagueness, according to which the nature of the vagueness of an expression consists in its not drawing boundaries between any neighbouring objects in an appropriately ordered series. It is argued that expressions and concepts which do present this feature play an essential role in our cognitive and practical life, allowing us to conceptualize—in a way which would otherwise be impossible—the typically coarse-grained distinctions we encounter in reality. Despite its strong initial plausibility and ability to explain many phenomena of vagueness, the naive theory is widely rejected because thought to be shown inconsistent by the sorites paradox. In reply, it is first argued that accounts of vagueness based on the dominant approach are themselves subject to higher-order sorites paradoxes. The paradox is then solved on behalf of the naive theory by rejecting the unrestricted transitivity of the consequence relation on a vague language; a family of logics apt for reasoning with vague expressions is proposed and studied (using models with partially ordered values). The characteristic philosophical and logical consequences of this novel solution are developed and defended in detail. In particular, it is shown how the analysis of what happens in the attempt of surveying a sorites series and deciding each case allows the naive theory to recover a "thin" notion of a borderline case.