In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. (...) The second yields a strong, finitary, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically computable Tarskian truth values to the formulas of PA under the interpretation. We situate our investigation within a broad analysis of quantification vis a vis: * Hilbert's epsilon-calculus * Goedel's omega-consistency * The Law of the Excluded Middle * Hilbert's omega-Rule * An Algorithmic omega-Rule * Gentzen's Rule of Infinite Induction * Rosser's Rule C * Markov's Principle * The Church-Turing Thesis * Aristotle's particularisation * Wittgenstein's perspective of constructive mathematics * An evidence-based perspective of quantification. By showing how these are formally inter-related, we highlight the fragility of both the persisting, theistic, classical/Platonic interpretation of quantification grounded in Hilbert's epsilon-calculus; and the persisting, atheistic, constructive/Intuitionistic interpretation of quantification rooted in Brouwer's belief that the Law of the Excluded Middle is non-finitary. We then consider some consequences for mathematics, mathematics education, philosophy, and the natural sciences, of an agnostic, evidence-based, finitary interpretation of quantification that challenges classical paradigms in all these disciplines. (shrink)

In the twentieth century, science and art had a grand paradigmatic shift each other. This study aims at comparing the epistemologies of surrealism and quantum mechanics that emerged in the 1930s and interpreting the paintings from a physical viewpoint, with a focus on the Copenhagen interpretation. In terms of epistemologies, the arbitrary relationship between an object and an image advocated by Magritte may correspond to the indeterminacy between physical entities and measurement. This study analysed the paintings of Magritte from the (...) point of view of the features of the Copenhagen interpretation categories of wave–particle duality, indeterminacy, probabilistic interpretation and quantum hypothesis. Based on such discussions, this study gives some implications for enhancing creativity through an interdisciplinary approach. (shrink)

This introduction to the special issue on "Aesthetics of Science" reviews recent philosophical research on aesthetic aspects of science. Topics represented in this research include the aesthetic properties of scientific images, theories, and experiments; the relation of science and art; the role of aesthetic criteria in scientific practice and their effect on the development of science; aesthetic aspects of mathematics; the contrast between a classic and a Romantic aesthetic; and the relation between emotion, cognition, and rationality.

This article discusses the epistemology of design as a process, arguing specifically that sketching and drawing are essential modes of thinking and reasoning. It demonstrates that the commonly accepted notion of a spontaneous and intuitive vision in the mind’s eye—encapsulated in the cliché of the napkin sketch—obscures the exploratory inferences that are made while scribbling with a pencil on a sheet of paper. The draughtsperson, along with their work tools, modes of notation, specific techniques, and epistemic strategies as well as (...) the resulting design artefacts form milieus of reflection that facilitate complex processes of exploration. Case studies, including the genesis of the Mini by Alec Issigonis, samples of work by Alvar Aalto, and a reinterpretation of student sketches from a classical design study by Gabriela Goldschmidt, serve to illustrate how drawing inferences with pencil and paper occurs. (shrink)

In response to the increasingly acknowledged power of metaphor upon everyday and scientific thinking, the present essay aims to revitalize the metaphoric process in commonsense psychology from the interaction view perspective. As prerequisites, a historical review of the "man-the-scientist" metaphor inherited in commonsense psychology, and a situation analysis of its dormant state are attempted. With metaphorical imagination, a holistic-paradigmatic view of personal theories is postulated on the basis of new knowledge in the philosophy and history of science, namely, the Duhem (...) - Quine (holism) thesis and Kuhn's paradigmatic perspective of scientific activities. To optimize the metaphoric process, deliberations are made on the similarities as well as the differences between the principal subject (i.e. everyday activities) and the subsidiary subject (i.e. scientific activities). It is shown that the "man-the-scientist" metaphoric process can be far-reaching and dialectic in nature, resulting in fresh perspectives for understanding both everyday and scientific activities. The focus of the present essay lies in elaborating a more sophisticated view on personal theories, and in calling for a non-reductionist approach to the investigation of commonsense psychology. (shrink)

Creativity is commonly thought of as a positive advance for society that transcends the status quo knowledge. Humans display an inordinate capacity for it in a broad range of activities, with art being only one. Most work on creativity’s neural substrates measures general creativity, and that is done with laboratory tasks, whereas specific creativity in art is gleaned from acquired brain damage, largely in observing established visual artists, and some in visual de novo artists (became artists after the damage). The (...) verb “to create” has been erroneously equated with creativity; creativity, in the classic sense, does not appear to be enhanced following brain damage, regardless of etiology. The turning to communication through art in lieu of language deficits reflects a biological survival strategy. Creativity in art, and in other domains, is most likely dependent on intact and healthy knowledge and semantic conceptual systems, which are represented in several pathways in the cortex. It is adversely affected when these systems are dysfunctional, for congenital reasons (savant autism) or because of acquired brain damage (stroke, dementia, Parkinson’s), whereas inherent artistic talent and skill appear less affected. Clues to the neural substrates of general creativity and specific art creativity can be gleaned from considering that art is produced spontaneously mainly by humans, that there are unique neuroanatomical and neurofunctional organizations in the human brain, and that there are biological antecedents of innovation in animals. (shrink)

This paper examines creative strategies employed inscientific modelling. It is argued that being creativepresents not a discrete event, but rather an ongoingeffort consisting of many individual `creative acts''.These take place over extended periods of time andcan be carried out by different people, working ondifferent aspects of the same project. The example ofextended extragalactic radio sources shows that, inorder to model a complicated phenomenon in itsentirety, the modelling task is split up into smallerproblems that result in several sub-models. This is away (...) of using cognitive resources efficiently and in away which overcomes their limitations. Another aspectof modelling that requires creativity is theemployment of visualisation in order to reassemble,i.e. recreate the unity of, the various sub-models bymeans of visualisation. This illustrates how thecreative effort required to deal with the complexityof the complicated phenomenon of radio sources ischannelled in order to use cognitive resourcesefficiently and to stay within their capacity. (shrink)

The authoranalyzes the types of metaphors that are used to describe the Internetin issues of Wired magazine from before and after the dot-com collapse to understand the perceptions and expectations of some of the actors involved in the shaping of the Internet. In addition, the metaphors deployed in economics and geophysiology are used to demonstrate how metaphors can influence public debate, policy, and theory. The author argues that metaphors do not simply have a descriptive function but that they also carry (...) normative connotations. Language, alongside social practices and material objects, is an important tool in attempts to construct the future. Six overlapping metaphorical themes are identified: revolution, evolution, salvation, progress, universalism, and the “American dream.” A critical analysis of these metaphors, informed by a critique of the metaphors used in economics and geophysiology, leads the author to challenge the universalist claims made by some Internet enthusiasts for the inclusive potential of the Internet. (shrink)

In this article, I limn the remarkable ascent of Albert Einstein and Wassily Kandinsky into our cultural pantheon. I depict how both figures mastered and transcended their respective fields, and how they called into question long-established disciplinary assumptions and practices. I also demonstrate how the creative works of Einstein and Kandinsky constructed, and were constructed by, the reality we now call "modern.".

This chapter contains sections titled: Highlights of Past Literature Current Work Future Work.

Despite the recent upsurge of interest in the investigation of creativity, the question of how to measure creativity is arguably underdiscussed. The aim of this paper is to address this gap, proposing a multidimensional account of creativity which identifies problem-solving, evaluation, and naivety as measurable features that are common among creative processes. The benefits that result from the adoption of this model are twofold: integrating discussions on creativity in various domains and offering the tools to assess creativity across systems of (...) different kinds. By situating creativity within this framework, I aim to contribute to a non-anthropocentric, more comprehensive understanding of the notion, and to debates on natural and artificial creativity. (shrink)

The current view of theoretical statements in science is that they should be literal and precise; ambiguous and metaphorical statements are useful only as pre-theoretical, exegetical, and heuristic devices and as pedagogical tools. In this paper we argue that this view is mistaken. Literal, precise statements apply to those experiential phenomena which can be defined either conventionally by criterial attribution or by internal atomic constitution. Experiential phenomena which are defined relationally and/or functionally, like nursing, in virtue of their nature, require (...) metaphorical description and explanation. In such cases, metaphor is theory-constitutive. Using insights from the philosophies of language and mind, and examples from nursing practice, education, and our own empirical research, we explore the nature of metaphor and its role in theory constitution. We argue that the apparent resistance of certain experiential phenomena to literal description and explanation is not necessarily indicative of pre-theoretic linguistic imprecision. We suggest, rather, that such resistance provides useful insights into the nature of such experiential phenomena. We also suggest that the aim of scientific theory should be methodological or epistemological precision and not merely linguistic precision. (shrink)

Physics textbooks often present items of disciplinary knowledge in a sequential order of topics of the theory under instruction. Such presentation is usually univocal, that is, isolated from alternative claims and contributions regarding the subject matter in the pertinent scientific discourse. We argue that comparing and contrasting the contributions of scientists addressing similar or the same subject could not only enrich the picture of scientific enterprise, but also possess a special appealing power promoting genuine understanding of the concept considered. This (...) approach draws on the historical tradition from Plutarch in distant past and Koyré in the recent history and philosophy of science. It gains a new support in the discipline–culture structuring of the physics curriculum, seeking cultural content knowledge of the subject matter. Here, we address two prominent individuals of Italian Renaissance, Leonardo and Galileo, in their dealing with issues relevant for introductory science courses. Although both figures addressed similar subjects of scientific content, their products were essentially different. Considering this difference is educationally valuable, illustrating the meaning of what students presently learn in the content knowledge of mechanics, optics and astronomy, as well as the nature of science and scientific knowledge. (shrink)

In the nineteenth and twentieth centuries many mathematicians referred to intuition as the indispensable research tool for obtaining new results. In this essay we will analyse a group of mathematicians who interacted with Luitzen Egbertus Jan Brouwer in order to compare their conceptions of intuition. We will see how to the same word “intuition” very different meanings corresponded: they varied from geometrical vision, to a unitary view of a demonstration, to the perception of time, to the faculty of considering concepts (...) that habitually occur in our thinking separately. Furthermore, we will discover that these different meanings had a philosophical, very relevant counterside: they passed from a racial characterization of mathematics to a pluralistic view of it. (shrink)

The function of metaphor in science has been labeled as decorative, persuasive, heuristic, instrumental, facilitating or obstructing. It has sometimes been regarded as inspiring, provoking, perverting or destroying rational thought. Metaphor’s positive role has been noted by philosophers, historians of chemistry, and science education researchers. It has been hailed as a descriptive and explanatory device that stimulates and shapes concept development. I discuss how metaphor functions in science generally, then refine this idea through an examination metaphor’s role in chemical thinking (...) in three contexts: the history and philosophy of chemistry, laboratory research practice, and chemical education. I aim to show how metaphor is already operative in the chemist’s use of the concept of chemical element and that this understanding characterizes chemical thinking in general. The chapter concludes with a discussion of a specifically chemical understanding of metaphor. (shrink)