Semantic and soritical paradoxes display remarkable family resemblances. For one thing, several non-classical logics have been independently applied to both kinds of paradoxes. For another, revenge paradoxes and higher-order vagueness—among the most serious problems targeting solutions to semantic and soritical paradoxes—exhibit a rather similar dynamics. Some authors have taken these facts to suggest that truth and vagueness require a unified logical framework, or perhaps that the truth predicate is itself vague. However, a common core of semantic and soritical paradoxes has (...) not been identified yet, and no explanation of their relationships has been provided. Here we aim at filling this lacuna, in the framework of many-valued logics. We provide a unified diagnosis of semantic and soritical paradoxes, identifying their source in a general form of indiscernibility. We then develop our diagnosis into a theory of paradoxicality, which formalizes both semantic and soritical paradoxes as arguments involving specific instances of our generalized indiscernibility principle, and correctly predicts which logics can non-trivially solve them. (shrink)

Over the past few decades, cognitive science has identified several forms of reasoning that make essential use of conceptual knowledge. Despite significant theoretical and empirical progress, there is still no unified framework for understanding how concepts are used in reasoning. This paper argues that the theory of conceptual spaces is capable of filling this gap. Our strategy is to demonstrate how various inference mechanisms which clearly rely on conceptual information—including similarity, typicality, and diagnosticity-based reasoning—can be modeled using principles derived from (...) conceptual spaces. Our first topic analyzes the role of expectations in inductive reasoning and their relation to the structure of our concepts. We examine the relationship between using generic expressions in natural language and common-sense reasoning as a second topic. We propose that the strength of a generic can be described by distances between properties and prototypes in conceptual spaces. Our third topic is category-based induction. We demonstrate that the theory of conceptual spaces can serve as a comprehensive model for this type of reasoning. The final topic is analogy. We review some proposals in this area, present a taxonomy of analogical relations, and show how to model them in terms of distances in conceptual spaces. We also briefly discuss the implications of the model for reasoning with concepts in artificial systems. (shrink)

This paper studies the learnability of natural concepts in the context of the conceptual spaces framework. Previous work proposed that natural concepts are represented by the cells of optimally partitioned similarity spaces, where optimality was defined in terms of a number of constraints. Among these is the constraint that optimally partitioned similarity spaces result in easily learnable concepts. While there is evidence that systems of concepts generally regarded as natural satisfy a number of the proposed optimality constraints, the connection between (...) naturalness and learnability has been less well studied. To fill this gap, we conduct a computational study employing two standard models of concept learning. Applying these models to the learning of color concepts, we examine whether natural color concepts are more readily learned than nonnatural ones. Our findings warrant a positive answer to this question for both models employed, thus lending empirical support to the notion that learnability is a distinctive characteristic of natural concepts. (shrink)

Can the theory of conceptual spaces developed by Peter Gärdenfors and others be applied to moral issues? Martin Peterson argues that several moral principles can be construed as regions in a shared similarity space, but Kristin Shrader-Frechette and Gert-Jan Lokhorst question Peterson’s claim. They argue that the moral similarity judgments used to construct the space are underspecified and subjective. In this paper, we present new data indicating that moral principles can indeed be construed as regions in a multidimensional conceptual space (...) on the basis of moral similarity judgments. Four hundred and seventy-five students taking a course in engineering ethics completed a survey in which they were presented with ten cases featuring ethical issues related to technology and engineering. Participants were asked to judge the moral similarity of each pair of cases and to select which moral principle they believed should be applied for resolving the case. We used interval multidimensional scaling as well as individual differences scaling for analyzing the moral similarity judgments. Despite noteworthy individual variations in the judgments, the five moral principles included in the study were discernable in the aggregate multidimensional spaces, even for participants with no previous exposure to the principles. Participants tended to apply the same moral principles to cases rated as morally similar. Our overall conclusion is that moral similarity judgments, and their representation in multidimensional spaces, can help us identify moral principles that are relevant for assessing difficult moral choice situations. (shrink)

When communicating, people adapt their linguistic representations to those of their interlocutors. Previous studies have shown that this also occurs at the semantic level for vague and context-dependent terms such as quantifiers and uncertainty expressions. However, work to date has mostly focused on passive exposure to a given speaker's interpretation, without considering the possible role of active linguistic interaction. In this study, we focus on gradable adjectives big and small and develop a novel experimental paradigm that allows participants to ask (...) clarification questions to figure out their interlocutor's interpretation. We find that, when in doubt, speakers do resort to this strategy, despite its inherent cognitive cost, and that doing so results in higher semantic alignment measured in terms of communicative success. While not all question–answer pairs are equally informative, we show that speakers become better questioners as the interaction progresses. Yet, the higher semantic alignment observed when speakers are able to ask questions does not increase over time. This suggests that conversational interaction's key advantage may be to boost coordination without committing to long-term semantic updates. Our findings shed new light on the mechanisms used by speakers to achieve semantic alignment and on how language is shaped by communication. (shrink)

According to a recent proposal, natural concepts are represented in an optimally designed similarity space, adhering to principles a skilled engineer would use for creatures with our perceptual and cognitive capacities. One key principle is that natural concepts should be easily learnable. While evidence exists for parts of this optimal design proposal, there has been no direct evidence linking naturalness to learning until now. This article presents results from a computational study on perceptual color space, demonstrating that naturalness indeed facilitates (...) learning. (shrink)