In this entertaining work, Peter Grdenfors embarks on an evolutionary detective story to try and solve one of the big mysteries surrounding human existence - how has the modern human being's way of thinking come into existence. Immensely readable and full of humorous insights, the book will be valuable for students in psychology and biology, and accessible to readers of popular science.

A computational theory of induction must be able to identify the projectible predicates, that is to distinguish between which predicates can be used in inductive inferences and which cannot. The problems of projectibility are introduced by reviewing some of the stumbling blocks for the theory of induction that was developed by the logical empiricists. My diagnosis of these problems is that the traditional theory of induction, which started from a given (observational) language in relation to which all inductive rules are (...) formulated, does not go deep enough in representing the kind of information used in inductive inferences. As an interlude, I argue that the problem of induction, like so many other problems within AI, is a problem of knowledge representation. To the extent that AI-systems are based on linguistic representations of knowledge, these systems will face basically the same problems as did the logical empiricists over induction. In a more constructive mode, I then outline a non-linguistic knowledge representation based on conceptual spaces. The fundamental units of these spaces are "quality dimensions". In relation to such a representation it is possible to define "natural" properties which can be used for inductive projections. I argue that this approach evades most of the traditional problems. (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 edited book focuses on concepts and their applications using the theory of conceptual spaces, one of today’s most central tracks of cognitive science discourse. It features 15 papers based on topics presented at the Conceptual Spaces @ Work 2016 conference. The contributors interweave both theory and applications in their papers. Among the first mentioned are studies on metatheories, logical and systemic implications of the theory, as well as relations between concepts and language. Examples of the latter include explanatory models (...) of paradigm shifts and evolution in science as well as dilemmas and issues of health, ethics, and education. The theory of conceptual spaces overcomes many translational issues between academic theoretization and practical applications. The paradigm is mainly associated with structural explanations, such as categorization and meronomy. However, the community has also been relating it to relations, functions, and systems. The book presents work that provides a geometric model for the representation of human conceptual knowledge that bridges the symbolic and the sub-conceptual levels of representation. The model has already proven to have a broad range of applicability beyond cognitive science and even across a number of disciplines related to concepts and representation. (shrink)

This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...) its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are "relational" and "transitively relational", are studied in detail, and their connections with certain "supplementary postulates" of Gardenfors investigated, with a further representation theorem established. (shrink)

This article presents two learning processes in order to explain how children at an early age can transform a complex sensory input to concepts and categories. The first process constructs the perceptual structures that emerge in children’s cognitive development by detecting invariants in the sensory input. The invariant structures involve a reduction in dimensionality of the sensory information. It is argued that this process generates the primary domains of space, objects and actions and that these domains can be represented as (...) conceptual spaces. Once the primary domains have been established, the second process utilizes covariances between different dimensions of the domains in order to identify natural clusters of entities. The clusters are then are used to determine concepts as regions in the spaces. As an application, the processes are used to resolve the so-called ‘complex first paradox’ that emerges from the fact that children, in general, learn nouns earlier than adjectives, even though nouns are semantically more complex than adjectives. (shrink)

Donald proposes that early Homo evolved mimesis as a new form of cognition. This article investigates the mimesis hypothesis in relation to the evolution of teaching. The fundamental capacities that distinguish hominin teaching from that of other animals are demonstration and pantomime. A conceptual analysis of the instructional and communicative functions of demonstration and pantomime is presented. Archaeological evidence that demonstration was used for transmitting the Oldowan technology is summarized. It is argued that pantomime develops out of demonstration so that (...) the primary objective of pantomime is that the onlooker learns the motoric patterns shown in the pantomime. The communicative use of pantomime is judged to be secondary. This use of pantomime is also contrasted with other forms of gestures. A key feature of the analysis is that the meaning of a pantomime is characterized by the force patterns of the movements. These force patterns form the core of a model of the cognitive mechanism behind pantomime. Finally, the role of pantomime in the evolution of language is also discussed. (shrink)

Some fifteen years ago, research on generalized quantifiers was con sidered to be a branch of mathematical logic, mainly carried out by mathematicians. Since then an increasing number of linguists and philosophers have become interested in exploring the relevance of general quantifiers for natural language as shown by the bibliography compiled for this volume. To a large extent, the new research has been inspired by Jon Barwise and Robin Cooper's path-breaking article "Generalized Quantifiers and Natural Language" from 1981. A concrete (...) sign of this development was the workshop on this topic at Lund University, May 9-11, 1985, which was organized by Robin Cooper, Elisabet Engdahl, and the present editor. All except two of the papers in this volume derive from that workshop. Jon Barwise's paper in the volume is different from the one he presented in connection with the workshop. Mats Rooth's contribution has been added because of its close relationship with the rest of the papers. The articles have been revised for publication here and the authors have commented on each other's contributions in order to integrate the collection. The organizers of the workshop gratefully acknowledge support from the Department of Linguistics, the Department of Philosophy and the Faculty of Humanities at Lund University, the Royal Swedish Academy of Sciences (through the Wallenberg Foundation), the Swedish Institute, and the Letterstedt Foundation. (shrink)

We present a model of how counting is learned based on the ability to perform a series of specific steps. The steps require conceptual knowledge of three components: numerosity as a property of collections; numerals; and one-to-one mappings between numerals and collections. We argue that establishing one-to-one mappings is the central feature of counting. In the literature, the so-called cardinality principle has been in focus when studying the development of counting. We submit that identifying the procedural ability to count with (...) the cardinality principle is not sufficient, but only one of the several steps in the counting process. Moreover, we suggest that some of these steps may be facilitated by the external organization of the counting situation. Using the methods of situated cognition, we analyze how the balance between external and internal representations will imply different loads on the working memory and attention of the counting individual. This analysis will show that even if the counter can competently use the cardinality principle, counting will vary in difficulty depending on the physical properties of the elements of collection and on their special arrangement. The upshot is that situated factors will influence counting performance. (shrink)

The dominating models of information processes have been based on symbolic representations of information and knowledge. During the last decades, a variety of non-symbolic models have been proposed as superior. The prime examples of models within the non-symbolic approach are neural networks. However, to a large extent they lack a higher-level theory of representation. In this paper, conceptual spaces are suggested as an appropriate framework for non- symbolic models. Conceptual spaces consist of a number of 'quality dimensions' that often are (...) derived from perceptual mechanisms. It will be outlined how conceptual spaces can represent various kind of information and how they can be used to describe concept learning. The connections to prototype theory will also be presented. (shrink)

This volume is a collection of some of the most important philosophical papers by Peter Gärdenfors. Spanning a period of more than 20 years of his research, they cover a wide ground of topics, from early works on decision theory, belief revision and nonmonotonic logic to more recent work on conceptual spaces, inductive reasoning, semantics and the evolutions of thinking. Many of the papers have only been published in places that are difficult to access. The common theme of all (...) the papers is the dynamics of thought. Several of the papers have become minor classics and the volume bears witness of the wide scope of Gärdenfors’ research and of his crisp and often witty style of writing. The volume will be of interest to researchers in philosophy and other cognitive sciences. (shrink)

The world as we perceive it is structured into objects, actions and places that form parts of events. In this article, my aim is to explain why these categories are cognitively primary. From an empiricist and evolutionary standpoint, it is argued that the reduction of the complexity of sensory signals is based on the brain's capacity to identify various types of invariances that are evolutionarily relevant for the activities of the organism. The first aim of the article is to explain (...) why places, object and actions are primary cognitive categories in our constructions of the external world. It is shown that the invariances that determine these categories have their separate characteristics and that they are, by and large, independent of each other. This separation is supported by what is known about the neural mechanisms. The second aim is to show that the category of events can be analyzed as being constituted of the primary categories. The category of numbers is briefly discussed. Some implications for computational models of the categories are also presented. (shrink)

Within analytic philosophy, induction has been seen as a problem concerning inferences that have been analysed as relations between sentences. In this article, we argue that induction does not primarily concern relations between sentences, but between properties and categories. We outline a new approach to induction that is based on two theses. The first thesis is epistemological. We submit that there is not only knowledge-how and knowledge-that, but also knowledge-what. Knowledge-what concerns relations between properties and categories and we argue that (...) it cannot be reduced to knowledge-that. We support the partition of knowledge by mapping it onto the long-term memory systems: procedural, semantic and episodic memory. The second thesis is that the role of inductive reasoning is to generate knowledge-what. We use conceptual spaces to model knowledge-what and the relations between properties and categories involved in induction. (shrink)

Decision theory and the theory of rational choice have recently been the subjects of considerable research by philosophers and economists. However, no adequate anthology exists which can be used to introduce students to the field. This volume is designed to meet that need. The essays included are organized into five parts covering the foundations of decision theory, the conceptualization of probability and utility, pholosophical difficulties with the rules of rationality and with the assessment of probability, and causal decision theory. The (...) editors provide an extensive introduction to the field and introductions to each part. (shrink)

This paper offers a novel way of reconstructing conceptual change in empirical theories. Changes occur in terms of the structure of the dimensions—that is to say, the conceptual spaces—underlying the conceptual framework within which a given theory is formulated. Five types of changes are identified: (1) addition or deletion of special laws, (2) change in scale or metric, (3) change in the importance of dimensions, (4) change in the separability of dimensions, and (5) addition or deletion of dimensions. Given this (...) classification, the conceptual development of empirical theories becomes more gradual and rationalizable. Only the most extreme type—replacement of dimensions—comes close to a revolution. The five types are exemplified and applied in a case study on the development within physics from the original Newtonian mechanics to special relativity theory. (shrink)

Many animal species use tools, but human technical engagement is more complex. We argue that there is coevolution between technical engagement and advanced forms of causal cognition in the human lineage. As an analytic tool, we present a classification of different forms of causal thinking. Human causal thinking has become detached from space and time, so that instead of just reacting to perceptual input, our minds can simulate actions and forces and their causal consequences. Our main thesis is that, unlike (...) the situation for other primate species, an increasing emphasis on technical engagement made some hominins capable of reasoning about the forces involved in causal processes. This thesis is supported in three ways: We compare the casual thinking about forces of hominins with that of other primates. We analyze the causal thinking required for Stone Age hunting technologies such as throwing spears, bow hunting and the use of poisoned arrows, arguing that they may serve as examples of the expansion of casual cognition about forces. We present neurophysiological results that indicate the facilitation of advanced causal thinking. (shrink)

In Gärdenfors and Makinson :197–245, 1994) and Gärdenfors it was shown that it is possible to model nonmonotonic inference using a classical consequence relation plus an expectation-based ordering of formulas. In this article, we argue that this framework can be significantly enriched by adopting a conceptual spaces-based analysis of the role of expectations in reasoning. In particular, we show that this can solve various epistemological issues that surround nonmonotonic and default logics. We propose some formal criteria for constructing and updating (...) expectation orderings based on conceptual spaces, and we explain how to apply them to nonmonotonic reasoning about objects and properties. (shrink)

The purpose of this note is to formulate some weaker versions of the so called Ramsey test that do not entail the following unacceptable consequenceIf A and C are already accepted in K, then if A, then C is also accepted in K. and to show that these versions still lead to the same triviality result when combined with a preservation criterion.

Conceptual spaces have become an increasingly popular modeling tool in cognitive psychology. The core idea of the conceptual spaces approach is that concepts can be represented as regions in similarity spaces. While it is generally acknowledged that not every region in such a space represents a natural concept, it is still an open question what distinguishes those regions that represent natural concepts from those that do not. The central claim of this paper is that natural concepts are represented by the (...) cells of an optimally designed similarity space. (shrink)

It is argued that it is not sufficient to consider only the sentences included in the explanans and explanandum when determining whether they constitute an explanation, but these sentences must always be evaluated relative to a knowledge situation. The central criterion on an explanation is that the explanans in a non-trivial way increases the belief value of the explanandum, where the belief value of a sentence is determined from the given knowledge situation. The outlined theory of explanations is applied to (...) some well-known examples and is also compared to other theories of explanation. (shrink)

Reasoning is not just following logical rules, but a large part of human reasoning depends on our expectations about the world. To some extent, non-monotonic logic has been developed to account for the role of expectations. In this article, the focus is on expectations based on actions and their consequences. The analysis is based on a two-vector model of events where an event is represented in terms of two main components – the force of an action that drives the event, (...) and the result of its application. Actions are modelled in terms of the force domain and the results are modelled with the aid of different domains for locations or properties of objects. As a consequence, the assumption that reasoning about causal relations should be made in terms of propositional structures becomes very unnatural. Instead, the reasoning will be based on the geometric and topological properties of causes and effects modelled in conceptual spaces. (shrink)

This paper concerns voting with logical consequences, which means that anybody voting for an alternative x should vote for the logical consequences of x as well. Similarly, the social choice set is also supposed to be closed under logical consequences. The central result of the paper is that, given a set of fairly natural conditions, the only social choice functions that satisfy social logical closure are oligarchic (where a subset of the voters are decisive for the social choice). The set (...) of conditions needed for the proof include a version of Independence of Irrelevant Alternatives that also plays a central role in Arrow's impossibility theorem. (Published Online July 11 2006) Footnotes1 Much of this article was written while the author was a fellow at the Swedish Collegium for Advanced Study in the Social Sciences (SCASSS) in Uppsala. I want to thank the Collegium for providing me with excellent working conditions. Wlodek Rabinowicz and other fellows gave me valuable comments at a seminar at SCASSS when an early version of the paper was presented. I also want to thank Luc Bovens, Franz Dietrich, Christian List and an anonymous referee for their excellent comments on a later version. The final version was prepared during a stay at Oxford University for which I am grateful to the British Academy. (shrink)

Within analytic philosophy, induction has been seen as a problem concerning inferences that have been analysed as relations between sentences. In this article, we argue that induction does not primarily concern relations between sentences, but between properties and categories. We outline a new approach to induction that is based on two theses. The first thesis is epistemological. We submit that there is not only knowledge-how and knowledge-that, but also knowledge-what. Knowledge-what concerns relations between properties and categories and we argue that (...) it cannot be reduced to knowledge-that. We support the partition of knowledge by mapping it onto the long-term memory systems: procedural, semantic and episodic memory. The second thesis is that the role of inductive reasoning is to generate knowledge-what. We use conceptual spaces to model knowledge-what and the relations between properties and categories involved in induction. (shrink)

Using probability functions defined over a simple language as models of states of belief, my goal in this article has been to analyse contractions and revisions of beliefs. My first strategy was to formulate postulates for these processes. Close parallels between the postulates for contractions and the postulates for revisions have been established - the results in Section 5 show that contractions and revisions are interchangeable. As a second strategy, some suggestions for more or less explicit constructive definitions of the (...) revision process (and indirectly also of the contraction process) were then presented. However, the results in Section 6 are less conclusive than in the earlier ones. This problem area still awaits further development. (shrink)

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)

This article outlines how conceptual spaces theory applies to modeling changes of scientific frameworks when these are treated as spatial structures rather than as linguistic entities. The theory is briefly introduced and five types of changes are presented. It is then contrasted with Michael Friedman’s neo-Kantian account that seeks to render Kuhn’s “paradigm shift” as a communicatively rational historical event of conceptual development in the sciences. Like Friedman, we refer to the transition from Newtonian to relativistic mechanics as an example (...) of “deep conceptual change.” But we take the communicative rationality of radical conceptual change to be available prior to the philosophical meta-paradigms that Friedman deems indispensable for this purpose. (shrink)

The theory of belief revision deals with models of states of belief and transitions between states of belief. The goal of the theory is to describe what should happen when you update a state of belief with new information. In the most interesting case, the new information is inconsistent with what you believe. This means that some of the old beliefs have to be deleted if one wants to remain within a consistent state of belief. A guiding idea is that (...) the change should be minimal so that as few of the old beliefs as possible are given up.A central problem for the theory of belief revision is what is meant by a minimal change of a state of belief. The solution to this problem depends to a large extent on the model of a state of belief that is adopted. (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)

It is argued that early language learning in children emerges from five primary knowledge structures: Space, objects, actions, number and events. These structures constitute the basis for the semantic domains that are used to form categories that represent the meanings of early words. The domains are naturally modeled in conceptual spaces that are based on geometric notions rather than on symbolic representations. It is shown how these semantics domains can be used to generate an epigenetic model of language acquisition. The (...) four first primary knowledge systems are used for prepositions, nouns, verbs and quantifiers respectively, while events form the meanings of declarative sentences. This semantic model leads to direct recommendations for how the model can be implemented in robots and other artificial systems. (shrink)