José Pedro Correia

A vexing puzzle about vagueness, rationality, and evolution runs, in crude abbreviation, as follows: vague language use is demonstrably suboptimal if the goal is efficient, precise and cooperative information transmission; hence rational deliberation or evolutionary selection should, under this assumed goal, eradicate vagueness from language use. Since vagueness is pervasive and entrenched in all human languages, something has to give. In this paper, we focus on this problem in the context of signaling games. We provide an overview of a number of proposed ways in which vagueness may come into the picture in formal models of rational and evolutionary signaling. Most argue that vague signal use is simply the best we can get, given certain factors. Despite the plausibility of the proposals, we argue that a deeper understanding of the benefits of vagueness needs a more ecological perspective, namely one that goes beyond the local optimization of signaling strategies in a homogeneous population. As an example of one possible way to expand upon our current models, we propose two variants of a novel multi-population dynamic of imprecise imitation where, under certain conditions, populations with vague language use dominate over populations with precise language use.

In Ludwig Wittgenstein’s Philosophical Investigations, one can find a number of remarks that could be seen as antithetical to classic philosophical analysis. There are passages seemingly rejecting the ideas of concept decomposition, regression to first principles, and semantic substitution. The criticism, I argue, is aimed not at analysis in particular, but rather at some idealizations that pervade a certain picture of philosophy. This picture can be contrasted with Wittgenstein’s pragmatist view of explanations of meaning which, I believe, can inform a different attitude towards philosophical method that aligns well with a vision of philosophy as conversation. If we think of philosophy as engaging in the development and exchange of explanations of meaning, we can see how various methods can coexist insofar as they are useful, and as long as the urge to sublimate them beyond our practices can be avoided.

The ways in which languages have come to divide the visible spectrum with their color terminology, in both their variety and the apparent universal tendencies, are still largely unexplained. Building on recent work in modeling color perception and categorization, as well as the theory of signaling games, we incrementally construct a color categorization model which combines perceptual characteristics of individual agents, game-theoretic signaling interaction of these agents, and the probability of observing particular colors as an environmental constraint. We also propose a method of transparent evaluation against the data gathered in the World Color Survey. The results show that the model’s predictive power is comparable to the current state of the art. Additionally, we argue that the model we suggest is superior in terms of motivation of the principles involved, and that its explanatory relevance with respect to color categorization in languages is therefore higher. Our results suggest that the universal tendencies of color categorization cannot be explained solely in terms of the shape of the color space induced by our perceptual apparatus. We believe that only by taking the heterogeneity of the phenomenon seriously can we acquire a deeper understanding of why color categorization takes the forms we observe across languages.

Signalling games are popular models for studying the evolution of meaning, but typical approaches do not incorporate vagueness as a feature of successful signalling. Complementing recent like-minded models, we describe an aggregate population-level dynamic that describes a process of imitation of successful behaviour under imprecise perception and realization of similar stimuli. Applying this new dynamic to a generalization of Lewis’s signalling games, we show that stochastic imprecision leads to vague, yet by-and-large efficient signal use, and, moreover, that it unifies evolutionary outcomes and helps avoid sub-optimal categorization. The upshot of this is that we see ‘as-if’-generalization at an aggregate level, without agents actually generalizing. _1_ Introduction _2_ Background _2.1_ Sim-max games and conceptual spaces _2.2_ Vagueness in sim-max games and conceptual spaces _2.3_ Vagueness, functional pressure, and transmission biases _3_ Imprecise Imitation _3.1_ Replicator dynamic in behavioural strategies _3.2_ Noise-perturbed conditional imitation _4_ Exploring Imprecise Imitation _4.1_ Setting the stage _4.2_ Simulation set-up _4.3_ Measures of interest _4.4_ Results _5_ Discussion _5.1_ Levels of vagueness _5.2_ Evolutionary benefits of imprecision _5.3_ Related work _6_ Conclusion Appendix