Conceptual spaces are a frequently applied framework for representing concepts. One of its central aims is to find criteria for what makes a concept natural. A prominent demand is that natural concepts cover convex regions in conceptual spaces. The first aim of this paper is to analyse the convexity thesis and the arguments that have been advanced in its favour or against it. Based on this, I argue that most supporting arguments focus on single-domain concepts (e.g., colours, smells, shapes). Unfortunately, (...) these concepts are not the primary examples of natural concepts. Building on this observation, the second aim of the paper is to develop criteria for natural multi-domain concepts. The representation of such concepts has two main aspects: features that are associated with the concept and the probabilistic correlation pattern which the concept captures. Conceptual spaces, together with probabilistic considerations, provide a helpful framework to approach these aspects. With respect to feature representation, the existence of characteristic features (i.e., that apples have a specific taste) is essential. Moreover, natural concepts capture peaks of a probabilistic distribution over complex spaces. They carve up nature at its joints, that is, at areas with no or low probabilistic density. This last aspect is shown to be closely related to the convexity demand. (shrink)

Gärdenfors (Conceptual spaces, 2000) argues that the semantic domains that natural language deals with have a geometrical structure. He gives evidence that simple natural language adjectives usually denote natural properties, where a natural property is a convex region of such a “conceptual space.” In this paper I will show that this feature of natural categories need not be stipulated as basic. In fact, it can be shown to be the result of evolutionary dynamics of communicative strategies under very general assumptions.

I analyse conceptual change and conceptual engineering in the special case of colour concepts. The case raises the prospects of conceptual engineering because a precise standard for measuring the amelioration of the structure of concepts is available. On the other hand, the study highlights the problems with controlling conceptual engineering pointed out by Cappelen. I argue that in the case of conceptual change of colour concepts varying degrees of optimization, design and control are possible. I submit that this observation can (...) be generalized to other classes of concepts. As a result, the scope of conceptual engineering is reduced considerably; conceptual engineering appears as a limit case of conceptual change. (shrink)

We present an account of semantics that is not construed as a mapping of language to the world but rather as a mapping between individual meaning spaces. The meanings of linguistic entities are established via a “meeting of minds.” The concepts in the minds of communicating individuals are modeled as convex regions in conceptual spaces. We outline a mathematical framework, based on fixpoints in continuous mappings between conceptual spaces, that can be used to model such a semantics. If concepts are (...) convex, it will in general be possible for interactors to agree on joint meaning even if they start out from different representational spaces. Language is discrete, while mental representations tend to be continuous—posing a seeming paradox. We show that the convexity assumption allows us to address this problem. Using examples, we further show that our approach helps explain the semantic processes involved in the composition of expressions. (shrink)

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. (shrink)

Natural languages exhibit manysemantic universals, that is, properties of meaning shared across all languages. In this paper, we develop an explanation of one very prominent semantic universal, the monotonicity universal. While the existing work has shown that quantifiers satisfying the monotonicity universal are easier to learn, we provide a more complete explanation by considering the emergence of quantifiers from the perspective of cultural evolution. In particular, we show that quantifiers satisfy the monotonicity universal evolve reliably in an iterated learning paradigm (...) with neural networks as agents. (shrink)

According to standard linguistic theory, the meaning of an utterance is the product of conventional semantic meaning and general pragmatic rules on language use. We investigate how such a division of labor between semantics and pragmatics could evolve under general processes of selection and learning. We present a game‐theoretic model of the competition between types of language users, each endowed with certain lexical representations and a particular pragmatic disposition to act on them. Our model traces two evolutionary forces and their (...) interaction: (i) pressure toward communicative efficiency and (ii) transmission perturbations during the acquisition of linguistic knowledge. We illustrate the model based on a case study on scalar implicatures, which suggests that the relationship between underspecified semantics and pragmatic inference is one of coevolution. (shrink)

This paper offers a conceptual clarification of the phenomenon commonly referred to as categorical perception of color, both in adults and in infants. First, I argue against the common notion of categorical perception as involving a distortion of the perceptual color space. The effects observed in the categorical perception research concern categorical discrimination performance and the underlying processing; they need not directly reflect the relations of color similarity and difference. Moreover, the methodology of the research actually presupposes that the relations (...) of similarity and difference do not vary with languages. The observed categorical perception effects should be conceived independently of the perceptual color space. Second, I challenge the usual opinion that the existing evidence on infant “categorical perception” allows us to conclude that infants perceptually categorize color, and in particular, that they have perceptual categories that resemble the basic color categories of English. Such conclusions rest on an unjustified interpretation of the infant “categorical perception” findings in terms of adult linguistic categorical boundaries. Based on the suggested new understanding, I propose that the phenomenon, as present in infants, should be conceived and examined as a possible explanatory factor with respect to the existing patterns of color naming in languages of the world. (shrink)

Holistic accounts of meaning normally incorporate a subjective dimension that invites the criticism that they make communication impossible, for speakers are bound to differ in ways the accounts take to be relevant to meaning, and holism generalises any difference over some words to a difference about all, and this seems incompatible with the idea that successful communication requires mutual understanding. I defend holism about meaning from this criticism. I argue that the same combination of properties (subjective origins of value, holism (...) among values, and ultimate publicity of value) is exhibited by monetary value and take the emergence of equilibrium prices as a model for the emergence of public meanings. (shrink)

This article takes a cognitive approach to natural concepts. The aim is to introduce criteria that are evaluated with respect to how they support the cognitive economy of humans when using concepts in reasoning and communicating with them. I first present the theory of conceptual spaces as a tool for expressing the criteria. Then I introduce the central idea that natural concepts correspond to _convex_ regions of a conceptual space. I argue that this criterion has far-reaching consequences as regards natural (...) concepts. Partly following earlier work, I present some other criteria that further delimit the class of natural concepts. One of these is coherence, which does not seem to have been discussed previously. Finally, I show that convexity and other criteria make it possible to ensure that people mean the same thing when they communicate using concepts. Apart from its philosophical interest, the analysis presented in the article will be relevant for tasks of conceptual engineering in artificial systems that work with concepts. (shrink)

This light piece reflects on analogies between two often disjoint streams of research: the logical semantics and pragmatics of natural language and dynamic logics of general information-driven agency. The two areas show significant overlap in themes and tools, and yet, the focus seems subtly different in each, defying a simple comparison. We discuss some unusual questions that emerge when the two are put side by side, without any pretense at covering the whole literature or at reaching definitive conclusions.

Two agents endowed with different categorisations engage in bargaining to reach an understanding and agree on a common categorisation. We model the process as a simple non-cooperative game and demonstrate three results. When the initial disagreement is focused, the bargaining process has a zero-sum structure. When the disagreement is widespread, the zero-sum structure disappears and the unique equilibrium requires a retraction of consensus: two agents who individually associate a region with the same category end up rebranding it under a different (...) category. Finally, we show that this last equilibrium outcome is Pareto dominated by a cooperative solution that avoids retraction; that is, the unique equilibrium agreement may be inefficient. (shrink)

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. (shrink)