Representation And Productive Ambiguity In Mathematics And The Sciences
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Representation And Productive Ambiguity In Mathematics And The Sciences
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Author : Emily R. Grosholz
language : en
Publisher: Clarendon Press
Release Date : 2007-08-30
Representation And Productive Ambiguity In Mathematics And The Sciences written by Emily R. Grosholz and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-30 with Mathematics categories.
Emily Grosholz offers an original investigation of demonstration in mathematics and science, examining how it works and why it is persuasive. Focusing on geometrical demonstration, she shows the roles that representation and ambiguity play in mathematical discovery. She presents a wide range of case studies in mechanics, topology, algebra, logic, and chemistry, from ancient Greece to the present day, but focusing particularly on the seventeenth and twentieth centuries. She argues that reductive methods are effective not because they diminish but because they multiply and juxtapose modes of representation. Such problem-solving is, she argues, best understood in terms of Leibnizian 'analysis' - the search for conditions of intelligibility. Discovery and justification are then two aspects of one rational way of proceeding, which produces the mathematician's formal experience. Grosholz defends the importance of iconic, as well as symbolic and indexical, signs in mathematical representation, and argues that pragmatic, as well as syntactic and semantic, considerations are indispensable for mathematical reasoning. By taking a close look at the way results are presented on the page in mathematical (and biological, chemical, and mechanical) texts, she shows that when two or more traditions combine in the service of problem solving, notations and diagrams are sublty altered, multiplied, and juxtaposed, and surrounded by prose in natural language which explains the novel combination. Viewed this way, the texts yield striking examples of language and notation that are irreducibly ambiguous and productive because they are ambiguous. Grosholtz's arguments, which invoke Descartes, Locke, Hume, and Kant, will be of considerable interest to philosophers and historians of mathematics and science, and also have far-reaching consequences for epistemology and philosophy of language.
Representation And Productive Ambiguity In Mathematics And The Sciences
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Author : Emily Grosholz
language : en
Publisher:
Release Date : 2023
Representation And Productive Ambiguity In Mathematics And The Sciences written by Emily Grosholz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Mathematics categories.
Focusing on geometrical demonstration, the author shows the roles that representation and ambiguity play in mathematical discovery. She presents a wide range of case studies in mechanics, topology, algebra, logic, and chemistry, focusing particularly on the 17th and 20th centuries.
The Argument Of Mathematics
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Author : Andrew Aberdein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-01
The Argument Of Mathematics written by Andrew Aberdein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-01 with Philosophy categories.
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 assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics.
Realizing Reason
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Author : Danielle Macbeth
language : en
Publisher:
Release Date : 2014-03
Realizing Reason written by Danielle Macbeth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03 with Mathematics categories.
Danielle Macbeth offers a new account of mathematical practice as a mode of inquiry into objective truth, and argues that understanding the nature of mathematical practice provides us with the resources to develop a radically new conception of ourselves and our capacity for knowledge of objective truth.
Luciano Floridi S Philosophy Of Technology
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Author : Hilmi Demir
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-15
Luciano Floridi S Philosophy Of Technology written by Hilmi Demir and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-15 with Philosophy categories.
Information and communication technologies of the 20th century have had a significant impact on our daily lives. They have brought new opportunities as well as new challenges for human development. The Philosopher: Luciano Floridi claims that these new technologies have led to a revolutionary shift in our understanding of humanity’s nature and its role in the universe. Florodi’s philosophical analysis of new technologies leads to a novel metaphysical framework in which our understanding of the ultimate nature of reality shifts from a materialist one to an informational one. In this world, all entities, be they natural or artificial, are analyzed as informational entities. This book provides critical reflection to this idea, in four different areas: Information Ethics and The Method of Levels of Abstraction The Information Revolution and Alternative Categorizations of Technological Advancements Applications: Education, Internet and Information Science Epistemic and Ontic Aspects of the Philosophy of Information
New Perspectives On Mathematical Practices
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Author : Bart van Kerkhove
language : en
Publisher: World Scientific
Release Date : 2009
New Perspectives On Mathematical Practices written by Bart van Kerkhove and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics. It contains a well-balanced mixture of contributions by internationally established experts, such as Jeremy Gray and Jens Hoyrup; upcoming scholars, such as Erich Reck and Dirk Schlimm; and young, promising researchers at the beginning of their careers. The book is situated within a relatively new and broadly naturalistic tradition in the philosophy of mathematics. In this alternative philosophical current, which has been dramatically growing in importance in the last few decades, unlike in the traditional schools, proper attention is paid to scientific practices as informing for philosophical accounts.
Heuristic Reasoning
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Author : Emiliano Ippoliti
language : en
Publisher: Springer
Release Date : 2014-09-05
Heuristic Reasoning written by Emiliano Ippoliti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-05 with Technology & Engineering categories.
How can we advance knowledge? Which methods do we need in order to make new discoveries? How can we rationally evaluate, reconstruct and offer discoveries as a means of improving the ‘method’ of discovery itself? And how can we use findings about scientific discovery to boost funding policies, thus fostering a deeper impact of scientific discovery itself? The respective chapters in this book provide readers with answers to these questions. They focus on a set of issues that are essential to the development of types of reasoning for advancing knowledge, such as models for both revolutionary findings and paradigm shifts; ways of rationally addressing scientific disagreement, e.g. when a revolutionary discovery sparks considerable disagreement inside the scientific community; frameworks for both discovery and inference methods; and heuristics for economics and the social sciences.
Rethinking Logic Logic In Relation To Mathematics Evolution And Method
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Author : Carlo Cellucci
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-09
Rethinking Logic Logic In Relation To Mathematics Evolution And Method written by Carlo Cellucci and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-09 with Philosophy categories.
This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. trigger
From A Heuristic Point Of View
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Author : Cesare Cozzo
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2014-07-03
From A Heuristic Point Of View written by Cesare Cozzo and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-03 with Science categories.
How do we get new knowledge? Following the maverick tradition in the philosophy of science, Carlo Cellucci gradually came to the conclusion that logic can only fulfill its role in mathematics, science and philosophy if it helps us to answer this question. He argues that mathematical logic is inadequate and that we need a new logic, framed in a naturalistic conception of knowledge and philosophy – the heuristic conception. This path from logic to a naturalistic conception of knowledge and philosophy explains the title, From a Heuristic Point of View, which recalls the celebrated collection of essays, From a Logical Point of View, by Willard Van Orman Quine, the father of modern naturalized epistemology. The word ‘heuristic’ points to Cellucci’s favorite theme and the main difference between him and Quine: the emphasis on discovery and building a ‘logic’ for generating new knowledge. This book is a collection of essays from leading figures in this field who discuss, criticize, or expand on the main topics in Cellucci’s work, dealing with some of the most challenging questions in logic, science and philosophy.
Reflections On Poetry And The World
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Author : Emily Grosholz
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2020-12-18
Reflections On Poetry And The World written by Emily Grosholz and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-18 with Literary Collections categories.
This collection brings together 40 years of essays about poetry and literature written by Emily Grosholz. The first section includes essays about some of her favorite poets and thinkers in the United States, England, France and Germany. The second section brings poetry into relation with ethics, politics and practical deliberation, and the third considers it alongside science and imagination. The last section is an homage to The Hudson Review, for whom she has served as an Advisory Editor for many years. As a philosopher, Emily Grosholz has written and thought about feminism, racism, and mathematics and science, which has led her to admire all the more the distinct wisdom of poetry. These essays show how poetry reorganized language and memory, eros and experience, and time and place, and how and why it deepens our understanding of life.