ABSTRACT This paper explores the role of aesthetic judgements in mathematics by focussing on the relationship between the epistemic and aesthetic criteria employed in such judgements, and on the nature of the psychological experiences underpinning them. I claim that aesthetic judgements in mathematics are plausibly understood as expressions of what I will call ‘aesthetic-epistemic feelings’ that serve a genuine cognitive and epistemic function. I will then propose a naturalistic account of these feelings in terms of sub-personal processes of representing and (...) assessing the relation between cognitive processes and certain properties of the stimuli at which they are directed. (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)

Glenberg's account falls short in several respects. Besides requiring clearer explication of basic concepts, his account fails to recognize the autonomous nature of perception. His account of what is remembered, and its description, is too static. His strictures against connectionist modeling might be overcome by combining the notions of psychological space and principled learning in an embodied and situated network.

A number of ways of taxonomizing human learning have been proposed. We examine the evidence for one such proposal, namely, that there exist independent explicit and implicit learning systems. This combines two further distinctions, (1) between learning that takes place with versus without concurrent awareness, and (2) between learning that involves the encoding of instances (or fragments) versus the induction of abstract rules or hypotheses. Implicit learning is assumed to involve unconscious rule learning. We examine the evidence for implicit learning (...) derived from subliminal learning, conditioning, artificial grammar learning, instrumental learning, and reaction times in sequence learning. We conclude that unconscious learning has not been satisfactorily established in any of these areas. The assumption that learning in some of these tasks (e.g., artificial grammar learning) is predominantly based on rule abstraction is questionable. When subjects cannot report the rules that govern stimulus selection, this is often because their knowledge consists of instances or fragments of the training stimuli rather than rules. In contrast to the distinction between conscious and unconscious learning, the distinction between instance and rule learning is a sound and meaningful way of taxonomizing human learning. We discuss various computational models of these two forms of learning. (shrink)

A number of ways of taxonomizing human learning have been proposed. We examine the evidence for one such proposal, namely, that there exist independent explicit and implicit learning systems. This combines two further distinctions, between learning that takes place with versus without concurrent awareness, and between learning that involves the encoding of instances versus the induction of abstract rules or hypotheses. Implicit learning is assumed to involve unconscious rule learning. We examine the evidence for implicit learning derived from subliminal learning, (...) conditioning, artificial grammar learning, instrumental learning, and reaction times in sequence learning. We conclude that unconscious learning has not been satisfactorily established in any of these areas. The assumption that learning in some of these tasks is predominantly based on rule abstraction is questionable. When subjects cannot report the “implicitly learned” rules that govern stimulus selection, this is often because their knowledge consists of instances or fragments of the training stimuli rather than rules. In contrast to the distinction between conscious and unconscious learning, the distinction between instance and rule learning is a sound and meaningful way of taxonomizing human learning. We discuss various computational models of these two forms of learning. (shrink)

Based on evidence that learning new characters through handwriting leads to better recognition than learning through typing, some authors proposed that the graphic motor plans acquired through handwriting contribute to recognition. More recently two alternative explanations have been put forward. First, the advantage of handwriting could be due to the perceptual variability that it provides during learning. Second, a recent study suggests that detailed visual analysis might be the source of the advantage of handwriting over typing. Indeed, in that study, (...) handwriting and composition –a method requiring a detailed visual analysis but no specific graphomotor activity– led to equivalent recognition accuracy, both higher than typing. The aim of the present study was to assess whether the contribution of detailed visual analysis is observed in preschool children and to test the variability hypothesis. To that purpose, three groups of preschool children learned new symbols either by handwriting, typing, or composition. After learning, children performed first a four-alternative recognition task and then a categorization task. The same pattern of results as the one observed in adults emerged in the four-alternative recognition task, confirming the importance of the detailed visual analysis in letter-like shape learning. In addition, results failed to reveal any difference across learning methods in the categorization task. The latter results provide no evidence for the variability hypothesis which would predict better categorization after handwriting than after typing or composition. (shrink)

According to one productive and influential approach to cognition, categorization, object recognition, and higher level cognitive processes operate on a set of fixed features, which are the output of lower level perceptual processes. In many situations, however, it is the higher level cognitive process being executed that influences the lower level features that are created. Rather than viewing the repertoire of features as being fixed by low-level processes, we present a theory in which people create features to subserve the representation (...) and categorization of objects. Two types of category learning should be distinguished. Fixed space category learning occurs when new categorizations are representable with the available feature set. Flexible space category learning occurs when new categorizations cannot be represented with the features available. Whether fixed or flexible, learning depends on the featural contrasts and similarities between the new category to be represented and the individual's existing concepts. Fixed feature approaches face one of two problems with tasks that call for new features: If the fixed features are fairly high level and directly useful for categorization, then they will not be flexible enough to represent all objects that might be relevant for a new task. If the fixed features are small, subsymbolic fragments (such as pixels), then regularities at the level of the functional features required to accomplish categorizations will not be captured by these primitives. We present evidence of flexible perceptual changes arising from category learning and theoretical arguments for the importance of this flexibility. We describe conditions that promote feature creation and argue against interpreting them in terms of fixed features. Finally, we discuss the implications of functional features for object categorization, conceptual development, chunking, constructive induction, and formal models of dimensionality reduction. Key Words: concept learning; conceptual development; features; perceptual learning; stimulus encoding. (shrink)

Previous neural network models of concept learning were mainly implemented with supervised learning schemes. However, studies of human conceptual memory have shown that concepts may be learned without a teacher who provides the category name to associate with exemplars. A modular neural network architecture that realizes concept acquisition through two functionally distinct operations, categorizing and naming, is proposed as an alternative. An unsupervised algorithm realizes the categorizing module by constructing representations of categories compatible with prototype theory. The naming module associates (...) category names to the output of the categorizing module in a supervised mode. In such a modular architecture, the interface between the modules can be conceived of as an “information relay” that encodes, constrains, and propagates important information. Five experiments were conducted to analyze the relationships among internal conceptual codes and simple conceptual and lexical development. The first two experiments show a prototype effect and illustrate some basic characteristics of the system. The third experiment presents a bottom‐up model of the narrowing down of children's early lexical categories that honors mutual exclusivity. The fourth experiment introduces top‐down constraints on conceptual coding. The fifth experiment exhibits how hierarchical relationships between concepts are learned by the architecture, and also demonstrates how a spectrum of conceptual expertise may gradually emerge as a consequence of experiencing more with certain categories than with others. (shrink)

Previous neural network models of concept learning were mainly implemented with supervised learning schemes. However, studies of human conceptual memory have shown that concepts may be learned without a teacher who provides the category name to associate with exemplars. A modular neural network architecture that realizes concept acquisition through two functionally distinct operations, categorizing and naming, is proposed as an alternative. An unsupervised algorithm realizes the categorizing module by constructing representations of categories compatible with prototype theory. The naming module associates (...) category names to the output of the categorizing module in a supervised mode. In such a modular architecture, the interface between the modules can be conceived of as an “information relay” that encodes, constrains, and propagates important information. Five experiments were conducted to analyze the relationships among internal conceptual codes and simple conceptual and lexical development. The first two experiments show a prototype effect and illustrate some basic characteristics of the system. The third experiment presents a bottom‐up model of the narrowing down of children's early lexical categories that honors mutual exclusivity. The fourth experiment introduces top‐down constraints on conceptual coding. The fifth experiment exhibits how hierarchical relationships between concepts are learned by the architecture, and also demonstrates how a spectrum of conceptual expertise may gradually emerge as a consequence of experiencing more with certain categories than with others. (shrink)

This paper presents an implemented computational model of word acquisition which learns directly from raw multimodal sensory input. Set in an information theoretic framework, the model acquires a lexicon by finding and statistically modeling consistent cross‐modal structure. The model has been implemented in a system using novel speech processing, computer vision, and machine learning algorithms. In evaluations the model successfully performed speech segmentation, word discovery and visual categorization from spontaneous infant‐directed speech paired with video images of single objects. These results (...) demonstrate the possibility of using state‐of‐the‐art techniques from sensory pattern recognition and machine learning to implement cognitive models which can process raw sensor data without the need for human transcription or labeling. (shrink)

Are the following propositions true of the colors: No object can be more than one determinable or determinate color all over at the same time (Incompatibility); the colors of objects are mind-independent (Objectivism); and most human observers usually perceive the colors of objects veridically in typical conditions (Veridicality)? One reason to think not is that the empirical literature appears to support the proposition that there is mass perceptual disagreement about the colors of objects amongst human observers in typical conditions (P-Disagreement). (...) In this article, we defend Incompatibility, Objectivism, and Veridicality by calling into question whether the empirical literature really supports P-Disagreement. (shrink)

Understanding novel phrases (e.g. upside‐down daisy) and classifying objects in categories named by phrases ought to have common properties, but you'd never know it from current theories. The best candidate for both jobs is the Theory Theory, but it faces difficulties when theories are impoverished. A potential solution is a dual approach that couples theories (representations‐about categories) with fixed mentalese expressions (representations‐of categories). Both representations combine information in parallel when understanding phrases. Although there are objections to the notion that theories (...) can combine, some of them lose their force when applied to a suitable dual model. (shrink)

I examine the phenomenon of implicit learning, the process by which knowledge about the rule-governed complexities of the stimulus environment is acquired independently of conscious attempts to do so. Our research with the two seemingly disparate experimental paradigms of synthetic grammar learning and probability learning, is reviewed and integrated with other approaches to the general problem of unconscious cognition. The conclusions reached are as follows: Implicit learning produces a tacit knowledge base that is abstract and representative of the structure of (...) the environment; such knowledge is optimally acquired independently of conscious efforts to learn; and it can be used implicitly to solve problems and make accurate decisions about novel stimulus circumstances. Various epistemological issues and related problems such as intuition, neuroclinical disorders of learning and memory, and the relationship of evolutionary processes to cognitive science are also discussed. (shrink)

The distinction between rules and similarity is central to our understanding of much of cognitive psychology. Two aspects of existing research have motivated the present work. First, in different cognitive psychology areas we typically see different conceptions of rules and similarity; for example, rules in language appear to be of a different kind compared to rules in categorization. Second, rules processes are typically modeled as separate from similarity ones; for example, in a learning experiment, rules and similarity influences would be (...) described on the basis of separate models. In the present article, I assume that the rules versus similarity distinction can be understood in the same way in learning, reasoning, categorization, and language, and that a unified model for rules and similarity is appropriate. A rules process is considered to be a similarity one where only a single or a small subset of an object's properties are involved. Hence, rules and overall similarity operations are extremes in a single continuum of similarity operations. It is argued that this viewpoint allows adequate coverage of theory and empirical findings in learning, reasoning, categorization, and language, and also a reassessment of the objectives in research on rules versus similarity. Key Words: categorization; cognitive explanation; language; learning; reasoning; rules; similarity. (shrink)

We address the problem of predicting how people will spontaneously divide into groups a set of novel items. This is a process akin to perceptual organization. We therefore employ the simplicity principle from perceptual organization to propose a simplicity model of unconstrained spontaneous grouping. The simplicity model predicts that people would prefer the categories for a set of novel items that provide the simplest encoding of these items. Classification predictions are derived from the model without information either about the number (...) of categories sought or information about the distributional properties of the objects to be classified. These features of the simplicity model distinguish it from other models in unsupervised categorization (where, for example, the number of categories sought is determined via a free parameter), and we discuss how these computational differences are related to differences in modeling objectives. The predictions of the simplicity model are validated in four experiments. We also discuss the significance of simplicity in cognitive modeling more generally. (shrink)