This study applied a method of assisted introspection to investigate the phenomenology of mathematical intuition arousal. The aim was to propose an essential structure for the intuitive experience of mathematics. To achieve an intersubjective comparison of different experiences, several contemporary mathematicians were interviewed in accordance with the elicitation interview method in order to collect pinpoint experiential descriptions. Data collection and analysis was then performed using steps similar to those outlined in the descriptive phenomenological method that led to a generic structure (...) that accounts for the intuition surge in the experience of mathematics which was found to have four irreducible structural moments. The interdependence of these moments shows that a perceptualist view of intuition in mathematics, as defended by Chudnoff, is relevant to the characterization of mathematical intuition. The philosophical consequences of this generic structure and its essential features are discussed in accordance with Husserl’s philosophy of ideal objects and theory of intuition. (shrink)

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)

In this paper, I present a framework where possible relations between learning and mental models are explored. In particular, I’ll be concerned with non-symbolic gestures accompanying discourse and their role in inducing the construction of models and therefore deep comprehension and learning in the listener. Also, I’ll be concerned with cognitive and socio-cognitive conflicts and their roles in inducing construction of alternative models of a problem and therefore in learning to reason. Human ability to learn is of great importance for (...) individuals interested in change. Indeed, to learn both declarative and procedural knowledge means to change, and in order to be able to intervene on change in a desired way it is necessary to have a theory of the mental representations and processes involved in learning and a theory of the communication and contexts that favour learning. (shrink)

This article proposes a unified framework for understanding creative problem solving, namely, the explicit–implicit interaction theory. This new theory of creative problem solving constitutes an attempt at providing a more unified explanation of relevant phenomena (in part by reinterpreting/integrating various fragmentary existing theories of incubation and insight). The explicit–implicit interaction theory relies mainly on 5 basic principles, namely, (a) the coexistence of and the difference between explicit and implicit knowledge, (b) the simultaneous involvement of implicit and explicit processes in most (...) tasks, (c) the redundant representation of explicit and implicit knowledge, (d) the integration of the results of explicit and implicit processing, and (e) the iterative (and possibly bidirectional) processing. A computational implementation of the theory is developed based on the CLARION cognitive architecture and applied to the simulation of relevant human data. This work represents an initial step in the development of process-based theories of creativity encompassing incubation, insight, and various other related.. (shrink)

This book argues for the need to put into practice a profound and comprehensive intellectual revolution, affecting to a greater or lesser extent all branches of scientific and technological research, scholarship and education. This intellectual revolution differs, however, from the now familiar kind of scientific revolution described by Kuhn. It does not primarily involve a radical change in what we take to be knowledge about some aspect of the world, a change of paradigm. Rather it involves a radical change in (...) the fundamental, overall intellectual aims and methods of inquiry. At present inquiry is devoted to the enhancement of knowledge. This needs to be transformed into a kind of rational inquiry having as its basic aim to enhance personal and social wisdom. This new kind of inquiry gives intellectual priority to the personal and social problems we encounter in our lives as we strive to realize what is desirable and of value – problems of knowledge and technology being intellectually subordinate and secondary. For this new kind of inquiry, it is what we do and what we are that ultimately matters: our knowledge is but an aspect of our life and being. (shrink)

Geometrical and physical intuition, both untutored andcultivated, is ubiquitous in the research, teaching,and development of mathematics. A number ofmathematical ``monsters'', or pathological objects, havebeen produced which – according to somemathematicians – seriously challenge the reliability ofintuition. We examine several famous geometrical,topological and set-theoretical examples of suchmonsters in order to see to what extent, if at all,intuition is undermined in its everyday roles.

The purpose of this article is to integrate two outstanding problems within the philosophy of science. The first concerns what role aesthetics plays in scientific thinking. The second is the problem of how logically testable ideas are generated (the so-called "psychology of research" versus "logic of (dis)proof" problem). I argue that aesthetic sensibility is the basis for what scientists often call intuition, and that intuition in turn embodies (in a literal physiological sense) ways of thinking that have their own meta-logic. (...) Thus, aesthetics is a form of cognition. Scientists think not in equations or words or other logical abstractions, but emotionally and sensually, using visual and aural images, kinesthetic and other proprioceptive feelings, sensations, patterns, and analogies. These aesthetic forms of thinking have their own logics that I call "synosia", from the root words synaesthesia (a combining of senses) and gnosis, "to know". Synosia denotes understanding that integrates feeling that one knows with feeling what one knows. Eminent scientists universally describe an explicitly secondary process in which such personal knowledge must be "translated" into a formal language, such as words or equations, in order to be communicated to other people. Many of the unsolved problems that philosophers of science (as well as psychologists and artificial intelligence researchers) have had in making sense of scientific thinking have arisen from confusing the form and content of the final translations with the hidden means by which scientific insights are actually achieved. (shrink)

Prior to the twentieth century, theories of knowledge were inherently perceptual. Since then, developments in logic, statis- tics, and programming languages have inspired amodal theories that rest on principles fundamentally different from those underlying perception. In addition, perceptual approaches have become widely viewed as untenable because they are assumed to implement record- ing systems, not conceptual systems. A perceptual theory of knowledge is developed here in the context of current cognitive science and neuroscience. During perceptual experience, association areas in the (...) brain capture bottom-up patterns of activation in sensory-motor areas. Later, in a top-down manner, association areas partially reactivate sensory-motor areas to implement perceptual symbols. The stor- age and reactivation of perceptual symbols operates at the level of perceptual components – not at the level of holistic perceptual expe- riences. Through the use of selective attention, schematic representations of perceptual components are extracted from experience and stored in memory (e.g., individual memories of green, purr, hot). As memories of the same component become organized around a com- mon frame, they implement a simulator that produces limitless simulations of the component (e.g., simulations of purr). Not only do such simulators develop for aspects of sensory experience, they also develop for aspects of proprioception (e.g., lift, run) and introspec- tion (e.g., compare, memory, happy, hungry). Once established, these simulators implement a basic conceptual system that represents types, supports categorization, and produces categorical inferences. These simulators further support productivity, propositions, and ab- stract concepts, thereby implementing a fully functional conceptual system. Productivity results from integrating simulators combinato- rially and recursively to produce complex simulations. Propositions result from binding simulators to perceived individuals to represent type-token relations. Abstract concepts are grounded in complex simulations of combined physical and introspective events. Thus, a per- ceptual theory of knowledge can implement a fully functional conceptual system while avoiding problems associated with amodal sym- bol systems. Implications for cognition, neuroscience, evolution, development, and artificial intelligence are explored. (shrink)

Music is at the centre of what it means to be human – it is the sounds of human bodies and minds moving in creative, story-making ways. We argue that music comes from the way in which knowing bodies (Merleau-Ponty) prospectively explore the environment using habitual 'patterns of action' which we have identified as our innate ‘communicative musicality’. To support our argument, we present short case studies of infant interactions using micro analyses of video and audio recordings to show the (...) timings and shapes of intersubjective vocalisations and body movements of adult and child while they improvise shared narratives of meaning. Following a survey of the history of discoveries of infant abilities, we propose that the gestural narrative structures of voice and body seen as infants communicate with loving caregivers are the building blocks of what become particular cultural instances of the art of music, and of dance, theatre and other temporal arts. Children enter into a musical culture where their innate communicative musicality can be encouraged and strengthened through sensitive, respectful, playful, culturally informed teaching in companionship. The central importance of our abilities for music as part of what sustains our well-being is supported by evidence that communicative musicality strengthens emotions of social resilience to aid recovery from mental stress and illness. Drawing on the experience of the first author as a counsellor, we argue that the strength of one person’s communicative musicality can support the vitality of another’s through the application of skilful techniques that encourage an intimate, supportive, therapeutic, spirited companionship. Turning to brain science, we focus on hemispheric differences and the affective neuroscience of Jaak Panksepp. We emphasise that the psychobiological purpose of our innate musicality grows from the integrated rhythms of energy in the brain for prospective, sensation-seeking affective guidance of vitality of movement. We conclude with a Coda that recalls the philosophy of the Scottish Enlightenment, which built on the work of Heraclitus and Spinoza. This view places the shared experience of sensations of living – our communicative musicality – as inspiration for rules of logic formulated in symbols of language. (shrink)

After a brief presentation of Feynman diagrams, we criticizise the idea that Feynman diagrams can be considered to be pictures or depictions of actual physical processes. We then show that the best interpretation of the role they play in quantum field theory and quantum electrodynamics is captured by Hughes' Denotation, Deduction and Interpretation theory of models, where “models” are to be interpreted as inferential, non-representational devices constructed in given social contexts by the community of physicists.

The for-profit sector is an active, viable and financially successful piece of the landscape of education and assumed to continue growing. “Edupreneurs” or private, for-profit education companies provide desirable and affordable educational products and services for students, or better, customers. At the tertiary level, for-profit higher education is defined “private institution[s] in which the individual or agency in control receives compensation other than wages, rent, or other expenses for the assumption of risk”. In other words, public higher education and private (...) not-for-profit colleges and universities on the one hand are not entitled to benefit private interests and net earnings cannot be distributed to owners or shareholders. On the other hand, for-profit institutions set their goal to make a profit for their owners or shareholders. According to John Sperling, For-profit universities offer several advantages over non-profit institutions, among which are the for-profit’s accountability for educational effectiveness, operational efficiency, cost benefits, and the time it takes them to respond to changes in the education needs. Fueled by the trends of internationalization, globalization, commercialization, and privatization in the education sector, for-profit education expands worldwide. This research intends to feature the Chinese echoes to the trend of For-profit education. The purpose of the study is three-fold. To begin with, the author aims to portray the scope and size of Chinese for-profit education sector, and make a tentative classification for “Edupreneurs” operating in Chinese education and training market. Next, the author aims to show the panorama of Chinese for-profit education, looking into the yesterday, today, and tomorrow of Chinese “Edupreneurs”. Last but not least, the researcher proposes to promote educational cooperation between Germany and China. Germany is blessed with excellent educational resources and services, and among one of the most popular destinations for international student mobility. Nevertheless, Germany has been avoiding the private surge, and thus a for-profit surge so far, even when faced with severe budget cuts and funding problems. Is this a voluntary or reluctant rejection, under the current educational system lacking self-management and autonomy? A quest for combining educational provision and consumption between Germany and China will then be incorporated in this study. Qualitative research methods are used to collect data. The primary source of data comes from semi-structured interviews with middle or senior administrators of selected for-profit educational companies. Other sources include direct observation made by the researcher during the periods of visiting the interviewees and companies; official documents ; internal documents; company fact book; company website; journalism, and others. (shrink)

What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, and ‘beautiful’? By applying empirical methods developed by social psychologists, we demonstrate that mathematicians' appraisals of proofs vary on four dimensions: aesthetics, intricacy, utility, and precision. We pay particular attention to mathematical beauty and show that, contrary to the classical view, beauty and simplicity are almost entirely unrelated in mathematics.

Can philosophy still be fruitful, and what kind of philosophy can be such? In particular, what kind of philosophy can be legitimized in the face of sciences? The aim of this paper is to answer these questions, listing the characteristics philosophy should have to be fruitful and legitimized in the face of sciences. Since the characteristics in question demand that philosophy search for new knowledge and new rules of discovery, a philosophy with such characteristics may be called the ‘heuristic view’. (...) According to the heuristic view, philosophy is an inquiry into the world which is continuous with the sciences. It differs from them only because it deals with questions which are beyond the present sciences, and in order to deal with them must try unexplored routes. By so doing, when successful, it may even give birth to new sciences. In listing the characteristics that philosophy should have, the paper systematically compares them with classical analytic philosophy, because the latter has been the dominant philosophical tradition in the last century. (shrink)

The 20th century philosophy of science began on a positivistic note. Its focal point was scientific explanation and the hypothetico-deductive (HD) framework of explanation was proposed as the standard of what is meant by “science.” HD framework, its inductive and statistical variants, and other logic-based approaches to modeling scientific explanation were developed long before the dawn of the information age. Since that time, the volume of observational data and power of high performance computing have increased by several orders of magnitude (...) and reshaped the practice and concept of science, and indeed, the philosophy of science. A new observational-inductive (OI) framework for scientific research is emerging due to recent developments in sensors, data systems, computers, and knowledge discovery techniques. We examine the nature of these changes and their impact on the question of what is meant by “science” after discussing five examples of the OI framework, and conclude that the HD and OI frameworks are complementary and synergistic. (shrink)

Umerez’s analysis made me aware of the fundamental differences in the culture of physics and molecular biology and the culture of semiotics from which the new field of biosemiotics arose. These cultures also view histories differently. Considering the evolutionary span and the many hierarchical levels of organization that their models must cover, models at different levels will require different observables and different meanings for common words, like symbol, interpretation, and language. These models as well as their histories should be viewed (...) as complementary rather than competitive. The relation of genetic language and human language is the central issue. They are separated by 4 billion years and require entirely different models. Nevertheless, these languages have in common a unique unlimited expressive power that allows open-ended evolution and creative thought. Understanding the nature of this expressive power and how it arises remains a basic unsolved problem of biosemiotics. (shrink)

This article looks at recent work in cognitive science on mathematical cognition from the perspective of history and philosophy of mathematical practice. The discussion is focused on the work of Lakoff and Núñez, because this is the first comprehensive account of mathematical cognition that also addresses advanced mathematics and its history. Building on a distinction between mathematics as it is presented in textbooks and as it presents itself to the researcher, it is argued that the focus of cognitive analyses of (...) historical developments of mathematics has been primarily on the former, even if they claim to be about the latter. (shrink)

The necessary but not sufficient conditions for biological informational concepts like signs, symbols, memories, instructions, and messages are (1) an object or referent that the information is about, (2) a physical embodiment or vehicle that stands for what the information is about (the object), and (3) an interpreter or agent that separates the referent information from the vehicle’s material structure, and that establishes the stands-for relation. This separation is named the epistemic cut, and explaining clearly how the stands-for relation is (...) realized is named the symbol-matter problem. (4) A necessary physical condition is that all informational vehicles are material boundary conditions or constraints acting on the lawful dynamics of local systems. It is useful to define a dependency hierarchy of information types: (1) syntactic information (i.e., communication theory), (2) heritable information acquired by variation and natural selection, (3) non-heritable learned or creative information, and (4) measured physical information in the context of natural laws. High information storage capacity is most reliably implemented by discrete linear sequences of non-dynamic vehicles, while the execution of information for control and construction is a non-holonomic dynamic process. The first epistemic cut occurs in self-replication. The first interpretation of base sequence information is by protein folding; the last interpretation of base sequence information is by natural selection. Evolution has evolved senses and nervous systems that acquire non-heritable information, and only very recently after billions of years, the competence for human language. Genetic and human languages are the only known complete general purpose languages. They have fundamental properties in common, but are entirely different in their acquisition, storage and interpretation. (shrink)

The mind maps symbols and the extra-symbolic relationships amongst them to specific meanings. When symbols of various levels are placed in a hierarchical ordering, one may look at such ordered classes as distinct worlds where one class represents objects and the other represents the objects’ corresponding meanings. However, such an explanation can only be partial because the number of potential levels in such an ordering is infinite and, therefore, it engenders problems of recursion and infinite regress. There are also logical (...) problems in the form of paradoxes that emanate from the consideration of sets of sets. Given that most prior studies only consider symbols that are classical objects in associative relationships, we argue that there is a need to also consider objects with shifting boundaries and quantum objects. We believe that objects belonging to each of these three classes—that is classical objects, objects with shifting boundaries, and quantum objects—play a role in the workings of the mind. (shrink)

For a variety of reasons, learning should be studied as a cultural phenomenon. The task of the first part of this article is to clear up the terminological questions about various ideal types of learning cultures, and how ideal type analysis may be used to study value and knowledge transfer and knowledge acquirement in various types of organisations. The important task of the second part is to analyse how implementation of environmental management systems, like BS-7750, contribute to a certain learning (...) practice. Moreover the task is to evaluate and discuss supplementing or alternative modes of learning to just formalisation of knowledge transfer. (shrink)

This paper examines the contemporary philosophical and cognitive relevance of Charles Peirce's diagrammatic logic of existential graphs (EGs), the ‘moving pictures of thought’. The first part brings to the fore some hitherto unknown details about the reception of EGs in the early 1900s that took place amidst the emergence of modern conceptions of symbolic logic. In the second part, philosophical aspects of EGs and their contributions to contemporary logical theory are pointed out, including the relationship between iconic logic and images, (...) the problem of the meaning of logical constants, the cognitive economy of iconic logic, the failure of the Frege–Russell thesis, and the failure of the Language of Thought hypothesis. (shrink)

Computer science only became established as a field in the 1950s, growing out of theoretical and practical research begun in the previous two decades. The field has exhibited immense creativity, ranging from innovative hardware such as the early mainframes to software breakthroughs such as programming languages and the Internet. Martin Gardner worried that "it would be a sad day if human beings, adjusting to the Computer Revolution, became so intellectually lazy that they lost their power of creative thinking" (Gardner, 1978, (...) p. vi-viii). On the contrary, computers and the theory of computation have provided great opportunities for creative work. This chapter examines several key aspects of creativity in computer science, beginning with the question of how problems arise in computer science. We then discuss the use of analogies in solving key problems in the history of computer science. Our discussion in these sections is based on historical examples, but the following sections discuss the nature of creativity using information from a contemporary source, a set of interviews with practicing computer scientists collected by the Association of Computing Machinery’s on-line student magazine, Crossroads. We then provide a general comparison of creativity in computer science and in the natural sciences. (shrink)

This is a critical analysis of the first part of Go¨del’s 1951 Gibbs lecture on certain philosophical consequences of the incompleteness theorems. Go¨del’s discussion is framed in terms of a distinction between objective mathematics and subjective mathematics, according to which the former consists of the truths of mathematics in an absolute sense, and the latter consists of all humanly demonstrable truths. The question is whether these coincide; if they do, no formal axiomatic system (or Turing machine) can comprehend the mathematizing (...) potentialities of human thought, and, if not, there are absolutely unsolvable mathematical problems of diophantine form. (shrink)

The research on which the present paper makes a point in aimed at designing a cognitive model of Albert Einstein's discovery that is based on fundamental Einstein's publications and placed, ideally, at a meso-level, between macro-historical and micro-cognitive reconstructions (e.g. protocol analysis). As in a cognitive-historical analysis, we will trace some discovery heuristics in the construction of representations, that are on a continuum with those we employ in ordinary problem solving. Firstly, some theory-specific, reflexive heuristics—named orientative heuristics—are traced: inner perfection, (...) explain-or-assume, explanatory correspondence, and covariance/invariance. Then, other well-known abstractive heuristics as analogical and imagistic reasoning, thought experiment, limiting case analysis (e.g. Nersessian 1992) are shown occurring in Einstein's key-publications. A sketch of a socio-cognitive model for his discovery is then presented following two suggestions: (a) an idea of Van Fraassen about discovery phases, and (b) the Humean distinction between beliefs and ideas. (shrink)

Many scientific discoveries have depended on external diagrams or visualizations. Many scientists also report to use an internal mental representation or mental imagery to help them solve problems and reason. How do scientists connect these internal and external representations? We examined working scientists as they worked on external scientific visualizations. We coded the number and type of spatial transformations (mental operations that scientists used on internal or external representations or images) and found that there were a very large number of (...) comparisons, either between different visualizations or between a visualization and the scientists’ internal mental representation. We found that when scientists compared visualization to visualization, the comparisons were based primarily on features. However, when scientists compared a visualization to their mental representation, they were attempting to align the two representations. We suggest that this alignment process is how scientists connect internal and external representations. (shrink)

Recent years have seen a growing acknowledgement within the mathematical community that mathematics is cognitively/socially constructed. Yet to anyone doing mathematics, it seems totally objective. The sensation in pursuing mathematical research is of discovering prior (eternal) truths about an external (abstract) world. Although the community can and does decide which topics to pursue and which axioms to adopt, neither an individual mathematician nor the entire community can choose whether a particular mathematical statement is true or false, based on the given (...) axioms. Moreover, all the evidence suggests that all practitioners work with the same ontology. (My number 7 is exactly the same as yours.) How can we reconcile the notion that people construct mathematics, with this apparent choice-free, predetermined objectivity? I believe the answer is to be found by examining what mathematical thinking is (as a mental activity) and the way the human brain acquired the capacity for mathematical thinking. (shrink)

The Greeks had a ready answer for what happens when the mind suddenly finds the answer to a question for which it had been searching: insight was regarded as a gift of the Muses, its origins were divine. It served to highlight the Greeks'' belief that there are some things which are not meant to be scientifically explained. The essence of insight is that it comes from some supernatural source: unpredicted and unfettered. In other words, the origins of insight are (...) unconscious, and hence, unexplainable. Wittgenstein felt that, as long as there continues to be a noun expression like to have a moment of insight which functions in the same way as the expression to have a hunger pang, thereby inducing us to treat moment of insight as the name of an experience, then people will keep stumbling over the same puzzling difficulties and find themselves staring at something which no explanation seems capable of clearing up. To the founders of AI, this argument reeked of obscurantism. The moment of insight, they felt, is indeed a mystery, but it is one that begs to be explained in causal terms. Indeed, the problem of insight served as one of the leading problems in the evolution of AI. Hence anyone interested in the foundations of AI is compelled to examine the manner in which the early pioneers of the field sought to explain the eureka experience. In this paper I will look at some of the key conceptual developments which paved the way for Newell and Simon''s theory of GPS: the fundamental changes in the notion of the unconscious — the emergence of the cognitive unconscious — which took place in the nineteenth- and early twentieth-century. In so doing, I hope to clarify what Wittgenstein may have had in mind in his strictures against mechanist attempts to analyse the nature of insight. (shrink)

In the context of superintelligent AI systems, the term “oracle” has two meanings. One refers to modular systems queried for domain-specific tasks. Another usage, referring to a class of systems which may be useful for addressing the value alignment and AI control problems, is a superintelligent AI system that only answers questions. The aim of this manuscript is to survey contemporary research problems related to oracles which align with long-term research goals of AI safety. We examine existing question answering systems (...) and argue that their high degree of architectural heterogeneity makes them poor candidates for rigorous analysis as oracles. On the other hand, we identify computer algebra systems as being primitive examples of domain-specific oracles for mathematics and argue that efforts to integrate computer algebra systems with theorem provers, systems which have largely been developed independent of one another, provide a concrete set of problems related to the notion of provable safety that has emerged in the AI safety community. We review approaches to interfacing CASs with theorem provers, describe well-defined architectural deficiencies that have been identified with CASs, and suggest possible lines of research and practical software projects for scientists interested in AI safety. (shrink)

Scientific creativity, i.e. the production of new and socially effective empirical knowledge, can itself be subjected to empirical analysis. Research on the determinants of creative work in science suggests that the internal and external world of creative scientists is characterised by a series of tensions or "oppositions of forces" which "normally" cannot be integrated. Conversely, creative work in science can be understood as the provision of new answers to scientific problems where conventional answers are no longer sufficient to reduce incongruities (...) between cognitive, affective and social standards of satisfactory problem solution. (shrink)

Turing’s paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure comprehensively hosting causality at the physical level and beyond. On the other, it can give an insight into the way in which higher order information arises and leads to loss of computational control—while demonstrating how the control can be re-established, in special circumstances, via suitable type reductions. (...) We examine the classical computational framework more closely than is usual, drawing out lessons for the wider application of information–theoretical approaches to characterizing the real world. The problem which arises across a range of contexts is the characterizing of the balance of power between the complexity of informational structure and the means available to bring this information back into the computational fold. We proceed via appropriate mathematical modelling to a more coherent view of the computational structure of information, relevant to a wide spectrum of areas of investigation. (shrink)

The richness of humanity is the diversity of its cultures, but now as never before the destructive power of modern technology and threatening ecological disasters make it necessary that we all recognize we are many peoples of one world. Complementing the diversity of our different cultures, the growth of a common, scientific knowledge inspires the hope that we may achieve and share a secondary culture of ideas. Computers, which can help represent explicitly the best ideas of modern science, can aid (...) in the diffusion of such powerful ideas to create a popular, secondary, scientific culture.We propose that a primary objective of learning environment design should be the development of thinkable models in the minds of students; further, since thinkable models represent a level of knowledge deeper than superficial terminology and specific graphical forms, such may be an objective suitable for various people in different cultures. To pursue these notions in some detail, a taxonomy of models is developed and the issue of how representations relate to human modes of perception and action is raised. The notions are explored first through the contrasting of a half-dozen approaches to the Pythagorean Theorem; then through describing polylingual word worlds and the Rosetta disk project.Common experiences produce common models —not only public models but the cognitive structures built from those shared experiences; and shared models will permit enhanced communication and understanding. If sharing experiences through play with computer based learning environments in different languages permits children to develop common models of the world, this will ultimately enhance mutual understanding between people in different places. This objective is now within reach. (shrink)

Interactive computer systems can support their users in problem solving, both in Performing their work tasks and in using the systems themselves. Not only is direct support for heuristics beneficial, but to do so modifies the form of computer support provided. This Paper defines and explores the use of problem solving heuristics in user interface design.

I DO not have to apologize for entering upon a discussion of intelligence and intelligence tests; it is a field which comes within the purview of philosophy as well as psychology. Any method of testing intelligence is therefore of common interest, especially as the methodology employed is usually based upon some definite theory as to its nature. The very word intelligence covers a wide range of meanings and psychologists seem to select sections of this range at will in accordance with (...) their particular interest. It may include most of the behavioural activities of man, or be narrowed down so that it refers to certain quantitative or relational aspects of experience. To take the case of the factor analyst, after his concept of intelligence has been analysed and classified into g's and s's, it becomes not a description of the mind, but rather a closed cognitive model of it. (shrink)

In recent years, there have been some attempts to defend the legitimacy of a non-inductive generative logic of discovery whose strategy is to analyze a variety of constraints on the actual generation of explanatory hypotheses. These proposed new theories, however, are only weakly generative (relying on sophisticated processes of elimination) rather than strongly generative (embodying processes of correction).This paper develops a strongly generative theory which holds that we can come to know something new only as a variant of what we (...) already know — and that the novelty of this variant is not thereby eliminated nor beyond our powers of characterization, a double requirement that is vital for resolving the Meno paradox. In this light, the discovery of a new hypothesis is taken as the correction of an antecedent hypothesis in response to the discrepancies between the predictions generated by that antecedent hypothesis and the desired result (e.g. the actual data to be explained). This process comprises two parallel operations: the first, which demonstrates the positive role of the facts in generating new explanations, involves a mapping between multiple hypotheses and sets of predictions generated from those hypotheses, for the purpose of taking the actual data as a determinable variant of neighboring sets of predictions. This mapping permits the facts to indicate how corrective adjustments in the working hypothesis should be made; the second operation, which demonstrates the positive role of explanations in generating new facts, involves a mapping between differently construed versions of the actual data and the conceptualizations derived from those perceptual versions, for the purpose of taking the working hypothesis as a determinable variant of these neighboring conceptualizations. This mapping permits a given hypothesis to generate predictions increasingly closer to the actual facts. (shrink)