Category-based induction is an inferential mechanism that uses knowledge of conceptual relations in order to estimate how likely is for a property to be projected from one category to another. During the last decades, psychologists have identified several features of this mechanism, and they have proposed different formal models of it. In this article; we propose a new mathematical model for category-based induction based on distances on conceptual spaces. We show how this model can predict most of the properties of (...) this kind of reasoning while providing a solid theoretical foundation for it. We also show that it subsumes some of the previous models proposed in the literature and that it generates new predictions. (shrink)

Recent years have witnessed a revival of interest in the method of explication as a procedure for conceptual engineering in philosophy and in science. In the philosophical literature, there has been a lively debate about the different desiderata that a good explicatum has to satisfy. In comparison, the goal of explicating the concept of explication itself has not been central to the philosophical debate. The main aim of this work is to suggest a way of filling this gap by explicating (...) ‘explication’ by means of conceptual spaces theory. Specifically, I show how different, strictly-conceptual readings of explication desiderata can be made precise as geometrical or topological constraints over the conceptual spaces related to the explicandum and the explicatum. Moreover, I show also how the richness of the geometrical representation of concepts in conceptual spaces theory allows us to achieve more fine-grained readings of explication desiderata, thereby overcoming some alleged limitations of explication as a procedure of conceptual engineering. (shrink)

This article argues that heuristics play a key role in philosophy, in generating both our verdicts on proposed counterexamples to philosophical theories and philosophical paradoxes. Heuristics are efficient ways of answering questions, quick and easy to use, but imperfectly reliable. They have been studied by psychologists and cognitive scientists such as Gigerenzer and Kahneman, but their relevance to philosophical methodology has not been properly recognized. Several heuristics are discussed at length. Thepersistence heuristiccan be summarized in the slogan ‘Small changes don’t (...) matter’. Without it, updating would present an intractable problem for both natural and artificial intelligence. But our reliance on the persistence heuristic also makes us vulnerable to paradoxes of vagueness.Disquotational heuristicsof various kinds are considered. They play central roles in our ascriptions of truth, falsity, and belief, but they also generate semantic paradoxes such as the Liar and Frege puzzles about coreference. The use of an additive heuristic for combining reasons is also discussed. Our reliance on fallible heuristics in philosophy does not make philosophical knowledge impossible, just as our reliance on fallible heuristics in perception does not make perceptual knowledge impossible. Nevertheless, it should motivate us to take a more critical attitude to our data. By identifying and analyzing the heuristics on which we rely, we may be able to work out where they make us most vulnerable to error. (shrink)

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)

The aim of this paper is to present a topological method for constructing discretizations of topological conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. The aim of this paper is to show that Alexandroff spaces, as they are called today, have many interesting properties that can be used to explicate and clarify a variety of problems in philosophy, cognitive science, and related disciplines. For instance, recently, (...) Ian Rumfitt used a special type of Alexandroff spaces to elucidate the logic of vague concepts in a new way. Moreover, Rumfitt’s class of Alexandroff spaces can be shown to provide a natural topological semantics for Susanne Bobzien’s “logic of clearness”. Mainly due to the work of Peter Gärdenfors and his collaborators, conceptual spaces have become an increasingly popular tool of dealing with a variety of problems in the fields of cognitive psychology, artificial intelligence, linguistics and philosophy. For Gärdenfors’s conceptual spaces, geometrically defined discretizations play an essential role. These tessellations can be shown to be extensionally equivalent to topological tessellations that can be constructed for Alexandroff spaces in general. Thereby, Rumfitt’s and Gärdenfors’s constructions turn out to be special cases of an approach that works for a more general class of spaces, namely, for weakly scattered Alexandroff spaces. The main aim of this paper is to show that this class of spaces provides a convenient framework for conceptual spaces as used in epistemology and related disciplines in general. Weakly scattered Alexandroff spaces are useful for elucidating problems related to the logic of vague concepts, in particular they offer a solution of the Sorites paradox. Further, they provide a semantics for the logic of clearness that overcomes certain problems of the concept of higher-order vagueness. Moreover, these spaces help find a natural place for classical syllogistics in the framework of conceptual spaces. The specialization order of Alexandroff spaces can be used to refine the all-or-nothing distinction between prototypical and non-prototypical stimuli in favor of a gradual distinction between more or less prototypical elements of conceptual spaces. The greater conceptual flexibility of the topological approach helps avoid some inherent inadequacies of the geometrical approach, for instance, the so-called “thickness problem”. Finally, it is shown that the Alexandroff spaces offer an appropriate framework to deal with digital conceptual spaces that are gaining more and more importance in the areas of artificial intelligence, computer science and related disciplines. (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)

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)

Critical discussions can often require conceptual engineering, a process in which speakers are engaged in revising each other’s concepts. We show that the analysis of conceptual engineering can benefit from integrating argumentation theory with models of conceptual representation. Argumentation theory accounts for the argumentative moves of the discussants, allowing the detection of speakers’ conceptual disagreements, for which some fallacies can be seen as cues. Models of conceptual representation, such as Conceptual spaces and the theory of meeting of minds, allow us (...) to study the cognitive side of engineering practices. However, when this integrated framework is applied to practical scenarios, conceptual engineering faces different challenges. In particular, assuming a psychological view about concepts, revisionary strategies are significantly narrowed down, if not impossible, in practice. These criticisms lead to a kind of dilemma for conceptual engineers, highlighting the necessity of further work on the definition of concept embraced by this research program. (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)

An enigma for human languages is that children learn to understand words in their mother tongue extremely fast. The cognitive sciences have not been able to fully understand the mechanisms behind this highly efficient learning process. In order to provide at least a partial answer to this problem, I have developed a cognitive model of the semantics of natural language in terms of conceptual spaces. I present a background to conceptual spaces and provide a brief summary of their main features, (...) in particular how it handles learning of concepts. I then apply the model to give a geometric account of the semantics of different word classes. In particular, I propose a “single-domain hypotheses” for the semantics of all word classes except nouns. These hypotheses provide a partial answer to the enigma of how words are learned. Next, a dynamic cognitive model of events is introduced that replaces and extends the function of thematic roles. I apply it to analyze the meanings of different kinds of verbs. I argue that the model also explains some aspects of syntactic structure. In particular, I propose that a sentence typically refers to an event. Some further applications of conceptual spaces are briefly presented. (shrink)

The overreliance on verbal models and theories in psychology has been criticized for hindering the development of reliable research programs (Harris, 1976; Yarkoni, 2020). We demonstrate how the conceptual space framework can be used to formalize verbal theories and improve their precision and testability. In the framework, scientific concepts are represented by means of geometric objects. As a case study, we present a formalization of an existing three-dimensional theory of emotion which was developed with a spatial metaphor in mind. Wundt (...) posits that the range of human emotion can be represented along three axes of basic emotions (pleasure/displeasure, excitement/inhibition, tension/relaxation), just as color vision can be represented using three basic colors. We use dimensions to represent basic emotions, points to represent emotional states, and regions to represent broader emotional concepts. We then compare our formalization to an existing structuralist formalization of Wundt’s theory. Further, we discuss the empirical predictions that our formalization generates, such as comparisons of similarity and intensity. We conclude by demonstrating how the tools developed in the conceptual space framework can be used to formulate a theory of emotion based on empirical observation. (shrink)

Nelson Goodman observed that we use only certain ‘good’ (viz. projectible) predicates during reasoning, with no obvious demarcation criterion in sight to distinguish them from the bad and gruesome ones. This apparent arbitrariness undermines the justifiability of our reasoning practices. Inspired by Quine’s 1969 paper on Natural Kinds, Peter Gärdenfors proposes a cognitive criterion based on his theory of Conceptual Spaces (CS). He argues the good predicates are those referring to natural concepts, and that we can capture naturalness in terms (...) of similarity. In contrast to Quine, he does not primarily rely on logic, but geometry. He frames his account as a descriptive project, however, and it is not obvious how it addresses the normative dimension of Goodman’s Riddle. This paper develops a charitable reconstruction of his argument, based on the idea that the instrumental success of our projectible concepts is grounded in their cognitive-pragmatic naturalness. It then explores three lines of reasoning against the argument: Evolutionarily motivated skepticism, the miracles argument, and the relation between instrumental and pragmatic success. I conclude that in its current form, the CS account fails to provide any justification of reasoning beyond appealing to its instrumental success, and that a metaphysically robust notion of naturalness helps to achieve the desired goal. (shrink)

This article presents results from a simulation‐based study of inheritance inference, that is, inference from the typicality of a property among a “base” class to its typicality among a subclass of the class. The study aims to ascertain which kinds of inheritance inferences are reliable, with attention to the dependence of their reliability upon the type of environment in which inferences are made. For example, the study addresses whether inheritance inference is reliable in the case of “exceptional subclasses” (i.e., subclasses (...) that are known to be atypical in some respect) and attends to variations in reliability that result from variations in the entropy level of the environment. A further goal of the study is to show that the reliability of inheritance inference depends crucially on which sorts of base classes are used in making inferences. One approach to inheritance inference treats the extension of any atomic predicate as a suitable base class. A second approach identifies suitable base classes with the cells of a partition (of a preselected size k) of the domain of objects that satisfies the condition of maximizing the similarity of objects that are assigned to the same class. In addition to permitting more inferences, our study shows that the second approach results in inheritance inferences that are far more reliable, particularly in the case of exceptional subclasses. (shrink)

Knowledge demands more than accuracy: epistemologists are broadly agreed that those who know are non-accidentally right, satisfying some kind of safety condition. However, it is hard to formulate any adequate account of safety, and harder still to explain exactly why we care about it. This paper approaches the problem by looking at a concrete human cognitive capacity, face recognition, to see where epistemic safety shows up in it. Drawing on new models in artificial intelligence, and making a case that human (...) face recognition is relevantly similar, I argue that safety is a natural feature of successful generalization. The concluding section of the paper applies this lesson to the problem of our intuitive recognition of knowledge. (shrink)

Similarity spaces are standardly constructed by collecting pairwise similarity judgments and subjecting those to a dimension-reduction technique such as multidimensional scaling or principal component analysis. While this approach can be effective, it has some known downsides, most notably, it tends to be costly and has limited generalizability. Recently, a number of authors have attempted to mitigate these issues through machine learning techniques. For instance, neural networks have been trained on human similarity judgments to infer the spatial representation of unseen stimuli. (...) However, these newer methods are still costly and fail to generalize widely beyond their initial training sets. This paper proposes leveraging prebuilt semantic vector spaces as a cheap alternative to collecting similarity judgments. Our results suggest that some of those spaces can be used to approximate human similarity judgments at low cost and high speed. (shrink)

We argue that concepts from the social sciences can be as natural as those from physics and chemistry, thereby answering in the positive the question of whether social metaphysics is or can be substantive. The argument takes as a starting point Douven & Gärdenfors’ (Mind & Language, 35, 313–334 2020) optimality account of natural concepts, according to which natural concepts are represented by the cells of an optimally partitioned similarity space. While the account applies straightforwardly to perceptual concepts, it does (...) not apply as straightforwardly to more abstract concepts, such as many scientific concepts. We propose an extension of Douven and Gärdenfors’ optimality account that pertains to scientific concepts as well. The proposal reuses ideas from Lewis’ Best Systems Account of laws of nature, but rather than invoking natural concepts (as Lewis does) defines natural scientific concepts as those that figure in the or a best systematization of the totality of facts. On this proposal, there is nothing especially different between concepts from the natural sciences and those from the social sciences. (shrink)

The aim of this paper is to propose a qualitative approach to the theory of conceptual spaces, in contrast to the usual metric framework. This requires qualitative notions of similarity, simple concepts, prototypes and conceptual categorisation. For this purpose, I will introduce three mathematical models for conceptual spaces. The first one is topological and has been proposed by Mormann. The other two are new and are based on atomistic orders and similarity relations. I will discuss how each of them deals (...) with the Design Principles proposed by Douven and Gärdenfors and with further Adequacy Conditions. Despite being apparently different, I will show that these three models are mathematically equivalent. Finally, I will address three objections to the present approach. The first one says that the qualitative notion of a prototype is a bad analogue of the metric one. The second one suggests that, in contrast to the Voronoi construction, the function qualitatively representing the conceptual categorisation process is arbitrary. The last one appeals to Goodman’s companionship and imperfect community problems to show that there is a flaw in defining simple concepts from similarity relations. (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)

Editor’s Introduction to the Special Issue ‘The Cognitive Ontological Dimensions of Naturalness’, including brief introductions of the individual contributions.

Both metaphysics and cognitive science raise the question of what natural concepts or properties are. A link between the two is notoriously hard to establish. I propose to take natural concepts or properties to be those that are revealed in interaction. The concept of affordances is refined and naturalized to spell out how interacting with objects grounds concepts. I will call this account “Ecological Empiricism”. I argue that the notion of naturalness within this framework turns out to be a gradable (...) – there are more or less natural properties – and dependent on the perspective taken – metaphysically natural properties are different from cognitive natural properties. From a metaphysical point of view, perfect correlations between actions and sensory input are relevant, which are best approximated by scientific measurement. For cognition, simple or basic actions are relevant. Although metaphysical and cognitive naturalness does not coincide according to Ecological Empiricism, it presents a common framework with a uniform conception of naturalness. (shrink)

The feature-matching approach pioneered by Amos Tversky remains a groundwork for psychological models of similarity and categorization but is rarely explicitly justified considering recent advances in thinking about cognition. While psychologists often view similarity as an unproblematic foundational concept that explains generalization and conceptual thought, long-standing philosophical problems challenging this assumption suggest that similarity derives from processes of higher-level cognition, including inference and conceptual thought. This paper addresses three specific challenges to Tversky’s approach: (i) the feature-selection problem, (ii) the problem (...) of cognitive implausibility, and (iii) the problem of unprincipled tweaking. It subsequently supports key insights from Tversky’s account based on recent developments in Bayesian modeling of cognition. A novel computational view of similarity as inference is proposed that addresses each challenge by considering the contrast class as constitutive of similarity and selecting for highly informative features. In so doing, this view illustrates the ongoing promise of the feature-matching approach in explaining perception, generalization and conceptual thought by grounding them in principles of probabilistic inference. (shrink)

Concepts are the building blocks of higher-order cognition and consciousness. Building on Conceptual Spaces Theory (CST) and proceeding from the assumption that concepts are inherently dynamic, this paper provides historical context to and significantly elaborates the previously offered Iterative Subdivision Model (ISDM) with the goal of pushing it toward empirical testability. The paper describes how agents in continuous interaction with their environment adopt an intentional orientation, estimate the utility of the concept(s) applicable to action in the current context, engage in (...) practical action, and adopt any new concepts that emerge: a largely pre-intellectual cycle that repeats essentially without interruption over the conceptual agent’s lifetime. This paper elaborates utility optimization by establishing three constraints on concept formation/evaluation – non-redundancy, distinctiveness, and proportionality – embedding them in a quasi-mathematical model intended for development into a formal logic. The notion of a distinctor – a quality dimension of the conceptual space in focus at any given time, used for making what we call a difference distinction – is key. The primary contribution of the revised ISDM is the way it relates concepts to action via utility optimization/actualization and the way it describes the emergence of quality dimensions through trial-by-action (trial and error), something previous presentations of CST have failed to address. (shrink)

This thesis focuses on models of conceptual change in science and philosophy. In particular, I developed a new bootstrapping methodology for studying conceptual change, centered around the formalization of several popular models of conceptual change and the collective assessment of their improved formal versions via nine evaluative dimensions. Among the models of conceptual change treated in the thesis are Carnap’s explication, Lakatos’ concept-stretching, Toulmin’s conceptual populations, Waismann’s open texture, Mark Wilson’s patches and facades, Sneed’s structuralism, and Paul Thagard’s conceptual revolutions. (...) -/- In order to analyze and compare the conception of conceptual change provided by these different models, I rely on several historical reconstructions of episodes of scientific conceptual change. The historical episodes of scientific change that figure in this work include the emergence of the morphological concept of fish in biological taxonomies, the development of scientific conceptions of temperature, the Church-Turing thesis and related axiomatizations of effective calculability, the history of the concept of polyhedron in 17th and 18th century mathematics, Hamilton’s invention of the quaternions, the history of the pre-abstract group concepts in 18th and 19th century mathematics, the expansion of Newtonian mechanics to viscous fluids forces phenomena, and the chemical revolution. I will also present five different formal and informal improvements of four specific models of conceptual change. I will first present two different improvements of Carnapian explication, a formal and an informal one. My informal improvement of Carnapian explication will consist of a more fine-grained version of the procedure that adds an intermediate, third step to the two steps of Carnapian explication. I will show how this novel three-step version of explication is more suitable than its traditional two-step relative to handle complex cases of explications. My second, formal improvement of Carnapian explication will be a full explication of the concept of explication itself within the theory of conceptual spaces. By virtue of this formal improvement, the whole procedure of explication together with its application procedures and its pragmatic desiderata will be reconceptualized as a precise procedure involving topological and geometrical constraints inside the theory of conceptual spaces. My third improved model of conceptual change will consist of a formal explication of Darwinian models of conceptual change that will make vast use of Godfrey-Smith’s population-based Darwinism for targeting explicitly mathematical conceptual change. My fourth improvement will be dedicated instead to Wilson’s indeterminate model of conceptual change. I will show how Wilson’s very informal framework can be explicated within a modified version of the structuralist model-theoretic reconstructions of scientific theories. Finally, the fifth improved model of conceptual change will be a belief-revision-like logical framework that reconstructs Thagard’s model of conceptual revolution as specific revision and contraction operations that work on conceptual structures. -/- At the end of this work, a general conception of conceptual change in science and philosophy emerges, thanks to the combined action of the three layers of my methodology. This conception takes conceptual change to be a multi-faceted phenomenon centered around the dynamics of groups of concepts. According to this conception, concepts are best reconstructed as plastic and inter-subjective entities equipped with a non-trivial internal structure and subject to a certain degree of localized holism. Furthermore, conceptual dynamics can be judged from a weakly normative perspective, bound to be dependent on shared values and goals. Conceptual change is then best understood, according to this conception, as a ubiquitous phenomenon underlying all of our intellectual activities, from science to ordinary linguistic practices. As such, conceptual change does not pose any particular problem to value-laden notions of scientific progress, objectivity, and realism. At the same time, this conception prompts all our concept-driven intellectual activities, including philosophical and metaphilosophical reflections, to take into serious consideration the phenomenon of conceptual change. An important consequence of this conception, and of the analysis that generated it, is in fact that an adequate understanding of the dynamics of philosophical concepts is a prerequisite for analytic philosophy to develop a realistic and non-idealized depiction of itself and its activities. (shrink)