The Evolution of Vagueness

Vague predicates, those that exhibit borderline cases, pose a persistent problem for philosophers and logicians. Although they are ubiquitous in natural language, when used in a logical context, vague predicates lead to contradiction. This paper will address a question that is intimately related to this problem. Given their inherent imprecision, why do vague predicates arise in the first place? Following the 1969 publication of David Lewis’ Convention, philosophers and game theorists have used signaling games to model the evolution and development of language. In this paper, I will present a variation of a standard signaling game that can help inform how and why vague predicates develop. The model in question will consider signaling games where the states of the world are contiguous. What I mean by this is that states of the world may be ordered by similarity as they are in the sorts of situations in which vague predicates typically arise. A ‘heap’ with 1 million grains is very similar to one with 999,000 grains, quite similar to one with 800,000 grains, and increasingly less similar to smaller and smaller heaps. With a small alteration, the standard Lewis signaling game can be taken as a model of the development of signaling in such situations. I will also consider an alteration to Herrnstein reinforcement learning dynamics intended to better reflect the type of generalized learning real-world actors use when states of the world are contiguous. Under these alterations, actors in these models quickly and successfully develop signaling conventions where adjacent states are categorized under one signal, as they are in prototypically vague predicates. Furthermore, the predicates developed in these simulations are vague in much the way ordinary language predicates are vague — they undoubtedly apply to certain items, and clearly do not apply to others, but for some transition period