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An essay on the psychology of invention in the mathematical field

[New York]: Dover Publications (1945)

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  1. Audience role in mathematical proof development.Zoe Ashton - 2020 - Synthese 198 (Suppl 26):6251-6275.
    The role of audiences in mathematical proof has largely been neglected, in part due to misconceptions like those in Perelman and Olbrechts-Tyteca which bar mathematical proofs from bearing reflections of audience consideration. In this paper, I argue that mathematical proof is typically argumentation and that a mathematician develops a proof with his universal audience in mind. In so doing, he creates a proof which reflects the standards of reasonableness embodied in his universal audience. Given this framework, we can better understand (...)
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  • A Piagetian perspective on mathematical construction.Michael A. Arbib - 1990 - Synthese 84 (1):43 - 58.
    In this paper, we offer a Piagetian perspective on the construction of the logico-mathematical schemas which embody our knowledge of logic and mathematics. Logico-mathematical entities are tied to the subject's activities, yet are so constructed by reflective abstraction that they result from sensorimotor experience only via the construction of intermediate schemas of increasing abstraction. The axiom set does not exhaust the cognitive structure (schema network) which the mathematician thus acquires. We thus view truth not as something to be defined within (...)
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  • Philosophia Naturalis Rediviva: Natural Philosophy for the Twenty-First Century.Bruce J. MacLennan - 2018 - Philosophies 3 (4):38--0.
    A revitalized practice of natural philosophy can help people to live a better life and promote a flourishing ecosystem. Such a philosophy is natural in two senses. First, it is natural by seeking to understand the whole of nature, including mental phenomena. Thus, a comprehensive natural philosophy should address the phenomena of sentience by embracing first- and second-person methods of investigation. Moreover, to expand our understanding of the world, natural philosophy should embrace a full panoply of explanations, similar to Aristotle’s (...)
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  • CRITIQUE OF IMPURE REASON: Horizons of Possibility and Meaning.Steven James Bartlett - 2021 - Salem, USA: Studies in Theory and Behavior.
    PLEASE NOTE: This is the corrected 2nd eBook edition, 2021. ●●●●● _Critique of Impure Reason_ has now also been published in a printed edition. To reduce the otherwise high price of this scholarly, technical book of nearly 900 pages and make it more widely available beyond university libraries to individual readers, the non-profit publisher and the author have agreed to issue the printed edition at cost. ●●●●● The printed edition was released on September 1, 2021 and is now available through (...)
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  • Wigner’s Puzzle for Mathematical Naturalism.Sorin Bangu - 2009 - International Studies in the Philosophy of Science 23 (3):245-263.
    I argue that a recent version of the doctrine of mathematical naturalism faces difficulties arising in connection with Wigner's old puzzle about the applicability of mathematics to natural science. I discuss the strategies to solve the puzzle and I show that they may not be available to the naturalist.
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  • Thought without language: Thought without awareness?Lawrence Weiskrantz - 1997 - In Thought and Language. New York: Cambridge University Press. pp. 127-.
  • The creative mind versus the creative computer.Robert W. Weisberg - 1994 - Behavioral and Brain Sciences 17 (3):555-557.
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  • Creativity: Myths? Mechanisms.Michel Treisman - 1994 - Behavioral and Brain Sciences 17 (3):554-555.
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  • The use of protocol analysis in philosophy.Steven Bartlett - 1978 - Metaphilosophy 9 (3-4):324-336.
    A description of the author's application of protocol analysis in the teaching of philosophy.
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  • Individual differences, developmental changes, and social context.Dean Keith Simonton - 1994 - Behavioral and Brain Sciences 17 (3):552-553.
  • Rethinking creative intelligence: comparative psychology and the concept of creativity.Henry Shevlin - 2020 - European Journal for Philosophy of Science 11 (1):1-21.
    The concept of creativity is a central one in folk psychological explanation and has long been prominent in philosophical debates about the nature of art, genius, and the imagination. The scientific investigation of creativity in humans is also well established, and there has been increasing interest in the question of whether the concept can be rigorously applied to non-human animals. In this paper, I argue that such applications face serious challenges of both a conceptual and methodological character, reflecting deep controversies (...)
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  • Respecting the phenomenology of human creativity.Victor A. Shames & John F. Kihlstrom - 1994 - Behavioral and Brain Sciences 17 (3):551-552.
  • Thoughts beyond words: When language overshadows insight.Jonathan W. Schooler, Stellan Ohlsson & Kevin Brooks - 1993 - Journal of Experimental Psychology: General 122 (2):166.
  • Imagery and creativity.Klaus Rehkämper - 1994 - Behavioral and Brain Sciences 17 (3):550-550.
  • The generative-rules definition of creativity.Joseph O'Rourke - 1994 - Behavioral and Brain Sciences 17 (3):547-547.
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  • ""Neither" True" nor" False" nor Meaningless: Meditation on the Pragmatics of Knowing Becoming.Floyd Merrell - 2004 - Contemporary Pragmatism 1 (1):61-81.
    Meinongian 'objects' are evoked in an effort to critique and expand upon traditional theories of reference. The argument stems from an account of Peirce's categories of meaning in light of vague, contradictory, inconsistent, general, incomplete, and incompleteable signs. In addition to signs as either 'true', 'false', or meaningless, the function of imaginary numbers reveals the possibility of a sign's being both 'true' and 'false' or neither 'true' nor 'false', over time, and dialogically speaking. This demands a tolerance for vagueness, ambiguity, (...)
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  • Living signs in a rigidly patterned world: How healthy can it be?Floyd Merrell - 2003 - Semiotica 2003 (147):107-134.
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  • Self-Knowledge as Non-Dual Awareness: A Comparative Study of Plotinus and Indian Advaita Philosophy.Binita Mehta - 2017 - International Journal of the Platonic Tradition 11 (2):117-148.
    _ Source: _Volume 11, Issue 2, pp 117 - 148 The paper examines the problem of self-knowledge from the perspectives of Plotinus and the Indian Advaita school. Analyzing the subject-object relation, I show that according to both Plotinus and Advaita thinkers, full self-knowledge demands complete absence of otherness. Plotinus argues that if self-consciousness is divided into subject-object relation then one will know oneself as contemplated but not as contemplating and no real self-knowledge obtains in this case. Śaṅkara, who constitutes an (...)
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  • Duhem and the origins of statics: Ramifications of the crisis of 1903–04.R. N. D. Martin - 1990 - Synthese 83 (3):337 - 355.
    Much speculation on the sources of Duhem's historical interests fails to account for the major shifts in these interests: neither his belief in the continuous development of physics nor his Catholicism, when his Church was encouraging the study of generally Aristotelian scholastic thought, led to any interest in mediaeval science before 1904. Equally, his own claim that he was merely testing his views on the nature of physical theory is easily squared only with earlier work with no trace of mediaeval (...)
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  • Phenomenology and mathematical practice.Mary Leng - 2002 - Philosophia Mathematica 10 (1):3-14.
    A phenomenological approach to mathematical practice is sketched out, and some problems with this sort of approach are considered. The approach outlined takes mathematical practices as its data, and seeks to provide an empirically adequate philosophy of mathematics based on observation of these practices. Some observations are presented, based on two case studies of some research into the classification of C*-algebras. It is suggested that an anti-realist account of mathematics could be developed on the basis of these and other studies, (...)
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  • Principles Supporting the Perceptional Teaching of Physics: A “Practical Teaching Philosophy”.Kaarle Kurki-Suonio - 2011 - Science & Education 20 (3-4):211-243.
  • The Role of Creativity in Expertise and Skilled Action.Spencer Ivy - 2022 - Synthese 200 (456):1-22.
    Perhaps a part of what makes expertise so inspiring to the curious researcher is the possibility of appropriating the structural components of skilled action to draw a roadmap towards their achievement that anyone might be able to follow. Accordingly, the purpose of this essay is to shed light upon the role that creativity plays in the production and environment of skilled action to that foregoing end. In doing so, I suggest that the lessons to be learned from recent empirical research (...)
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  • Conscious thought processes and creativity.Maria F. Ippolito - 1994 - Behavioral and Brain Sciences 17 (3):546-547.
  • Syntax-directed discovery in mathematics.David S. Henley - 1995 - Erkenntnis 43 (2):241 - 259.
    It is shown how mathematical discoveries such as De Moivre's theorem can result from patterns among the symbols of existing formulae and that significant mathematical analogies are often syntactic rather than semantic, for the good reason that mathematical proofs are always syntactic, in the sense of employing only formal operations on symbols. This radically extends the Lakatos approach to mathematical discovery by allowing proof-directed concepts to generate new theorems from scratch instead of just as evolutionary modifications to some existing theorem. (...)
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  • Conceptualizing creativity and innovation as affective processes: Steve Jobs, Lars von Trier, and responsible innovation.Lars Geer Hammershøj - 2018 - Philosophy of Management 17 (1):115-131.
    The aim of this article is to contribute to responsible innovation by developing a conceptual framework for the processes of creativity and innovation. The hypothesis is that creative and innovative processes are similar in that both are affective in nature. I develop this conceptual framework through an interpretation of the insights of Henri Poincaré’s notion of the ‘four stages’ in the creative process and Joseph Schumpeter’s notion of the entrepreneur. Building on this framework, I analyze the creative and innovative practices (...)
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  • Creativity as a question of bildung.Lars Geer Hammershøj - 2009 - Journal of Philosophy of Education 43 (4):545-558.
    The aim of the article is to contribute to the conceptualization of creativity in education. The article makes use of the self-Bildung perspective, which is an up-to-date version of the Neo-humanistic notion of the formation of the personality in order to interpret the original notion of the 'four stages' of the creative process. The conclusion is that in this perspective creativity can be understood as a state of transcendence and a practice of taste. Finally, the article seeks to sketch out (...)
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  • Creativity as a Question of Bildung.Lars Geer Hammershøj - 2009 - Journal of Philosophy of Education 43 (4):545-558.
    The aim of the article is to contribute to the conceptualization of creativity in education. The article makes use of the self-Bildung perspective, which is an up-to-date version of the Neo-humanistic notion of the formation of the personality in order to interpret the original notion of the ‘four stages’ of the creative process. The conclusion is that in this perspective creativity can be understood as a state of transcendence and a practice of taste. Finally, the article seeks to sketch out (...)
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  • Creativity theory: Detail and testability.K. J. Gilhooly - 1994 - Behavioral and Brain Sciences 17 (3):544-545.
  • Intuition and visualization in mathematical problem solving.Valeria Giardino - 2010 - Topoi 29 (1):29-39.
    In this article, I will discuss the relationship between mathematical intuition and mathematical visualization. I will argue that in order to investigate this relationship, it is necessary to consider mathematical activity as a complex phenomenon, which involves many different cognitive resources. I will focus on two kinds of danger in recurring to visualization and I will show that they are not a good reason to conclude that visualization is not reliable, if we consider its use in mathematical practice. Then, I (...)
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  • Art for art's sake.Alan Garnham - 1994 - Behavioral and Brain Sciences 17 (3):543-544.
    This piece is a commentary on a precis of Maggie Boden's book "The creative mind" published in Behavioral and Brain Sciences.
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  • The birth of an idea.Liane M. Gabora - 1994 - Behavioral and Brain Sciences 17 (3):543-543.
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  • Creativity, madness, and extra strong Al.K. W. M. Fulford - 1994 - Behavioral and Brain Sciences 17 (3):542-543.
  • Creative thinking presupposes the capacity for thought.James H. Fetzer - 1994 - Behavioral and Brain Sciences 17 (3):539-540.
  • Creativity, combination, and cognition.Terry Dartnall - 1994 - Behavioral and Brain Sciences 17 (3):537-537.
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  • Précis of The creative mind: Myths and mechanisms.Margaret A. Boden - 1994 - Behavioral and Brain Sciences 17 (3):519-531.
    What is creativity? One new idea may be creative, whereas another is merely new: What's the difference? And how is creativity possible? These questions about human creativity can be answered, at least in outline, using computational concepts. There are two broad types of creativity, improbabilist and impossibilist. Improbabilist creativity involves novel combinations of familiar ideas. A deeper type involves METCS: the mapping, exploration, and transformation of conceptual spaces. It is impossibilist, in that ideas may be generated which – with respect (...)
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  • Creativity: A framework for research.Margaret A. Boden - 1994 - Behavioral and Brain Sciences 17 (3):558-570.
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  • Picturing Knowledge: Historical and Philosophical Problems Concerning the Use of Art in Science.Brian Scott Baigrie (ed.) - 1996 - University of Toronto Press.
    List of Illustrations Introduction 1 The Didactic and the Elegant: Some Thoughts on Scientific and Technological Illustrations in the Middle Ages and Renaissance 3 2 Temples of the Body and Temples of the Cosmos: Vision and Visualization in the Vesalian and Copernican Revolutions 40 3 Descartes’s Scientific Illustrations and ’la grande mecanique de la nature’ 86 4 Illustrating Chemistry 135 5 Representations of the Natural System in the Nineteenth Century 164 6 Visual Representation in Archaeology: Depicting the Missing-Link in Human (...)
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  • Free Will: The Scandal in Philosophy.Bob Doyle - 2011 - Cambridge, MA, USA: I-Phi Press.
    A sourcebook/textbook on the problem of free will and determinism. Contains a history of the free will problem, a taxonomy of current free will positions, the standard argument against free will, the physics, biology, and neuroscience of free will, the most plausible and practical solution of the problem, and reviews of the work of the leading determinist Ted Honderich, the leading libertarian Robert Kane, the well-known compatibilist Daniel Dennett, and the determinism-agnostic Alfred Mele.
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  • The Argument of Mathematics.Andrew Aberdein & Ian J. Dove (eds.) - 2013 - Dordrecht, Netherland: Springer.
    Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. -/- The book begins by first challenging the (...)
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  • What is Mathematics: Gödel's Theorem and Around (Edition 2015).Karlis Podnieks - manuscript
    Introduction to mathematical logic. Part 2.Textbook for students in mathematical logic and foundations of mathematics. Platonism, Intuition, Formalism. Axiomatic set theory. Around the Continuum Problem. Axiom of Determinacy. Large Cardinal Axioms. Ackermann's Set Theory. First order arithmetic. Hilbert's 10th problem. Incompleteness theorems. Consequences. Connected results: double incompleteness theorem, unsolvability of reasoning, theorem on the size of proofs, diophantine incompleteness, Loeb's theorem, consistent universal statements are provable, Berry's paradox, incompleteness and Chaitin's theorem. Around Ramsey's theorem.
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  • Unpacking the logic of mathematical statements.Annie Selden - 1995 - Educational Studies in Mathematics 29:123-151.
    This study focuses on undergraduate students' ability to unpack informally written mathematical statements into the language of predicate calculus. Data were collected between 1989 and 1993 from 61students in six small sections of a “bridge" course designed to introduce proofs and mathematical reasoning. We discuss this data from a perspective that extends the notion of concept image to that of statement image and introduces the notion of proof framework to indicate the top-level logical structure of a proof. For simplified informal (...)
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  • Non-deductive Logic in Mathematics: The Probability of Conjectures.James Franklin - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Springer. pp. 11--29.
    Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...)
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  • The multifaceted role of imagination in science and religion. A critical examination of its epistemic, creative and meaning-making functions.Ingrid Malm Lindberg - 2021 - Dissertation, Uppsala University
    The main purpose of this dissertation is to examine critically and discuss the role of imagination in science and religion, with particular emphasis on its possible epistemic, creative, and meaning-making functions. In order to answer my research questions, I apply theories and concepts from contemporary philosophy of mind on scientific and religious practices. This framework allows me to explore the mental state of imagination, not as an isolated phenomenon but, rather, as one of many mental states that co-exist and interplay (...)
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  • The role of inversion in the genesis, development and the structure of scientific knowledge.Nagarjuna G. - manuscript
    The main thrust of the argument of this thesis is to show the possibility of articulating a method of construction or of synthesis--as against the most common method of analysis or division--which has always been (so we shall argue) a necessary component of scientific theorization. This method will be shown to be based on a fundamental synthetic logical relation of thought, that we shall call inversion--to be understood as a species of logical opposition, and as one of the basic monadic (...)
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  • The CEMI Field Theory Gestalt Information and the Meaning of Meaning.Johnjoe McFadden - 2013 - Journal of Consciousness Studies 20 (3-4):3-4.
    In earlier papers I described the conscious electromagnetic information (CEMI) field theory, which claimed that the substrate of consciousness is the brain’s electromagnetic (EM) field. I here further explore this theory by examining the properties and dynamics of the information underlying meaning in consciousness. I argue that meaning suffers from a binding problem, analogous to the binding problem described for visual perception, and describe how the gestalt (holistic) properties of meaning give rise to this binding problem. To clarify the role (...)
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