Download or read book Visualization Explanation and Reasoning Styles in Mathematics written by P. Mancosu and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.

Download or read book Visual Thinking in Mathematics written by Marcus Giaquinto and published by Oxford University Press. This book was released on 2007-07-05 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis.

Download or read book Truth Existence and Explanation written by Mario Piazza and published by Springer. This book was released on 2018-10-24 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains more than 15 essays that explore issues in truth, existence, and explanation. It features cutting-edge research in the philosophy of mathematics and logic. Renowned philosophers, mathematicians, and younger scholars provide an insightful contribution to the lively debate in this interdisciplinary field of inquiry. The essays look at realism vs. anti-realism as well as inflationary vs. deflationary theories of truth. The contributors also consider mathematical fictionalism, structuralism, the nature and role of axioms, constructive existence, and generality. In addition, coverage also looks at the explanatory role of mathematics and the philosophical relevance of mathematical explanation. The book will appeal to a broad mathematical and philosophical audience. It contains work from FilMat, the Italian Network for the Philosophy of Mathematics. These papers collected here were also presented at their second international conference, held at the University of Chieti-Pescara, May 2016.

Download or read book New Perspectives on Mathematical Practices written by Bart Van Kerkhove and published by World Scientific. This book was released on 2009 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Because Without Cause written by Marc Lange and published by Oxford University Press. This book was released on 2017 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Not all scientific explanations work by describing causal connections between events or the world's overall causal structure. In addition, mathematicians regard some proofs as explaining why the theorems being proved do in fact hold. This book proposes new philosophical accounts of many kinds of non-causal explanations in science and mathematics.

Download or read book Advances in Experimental Philosophy of Logic and Mathematics written by Andrew Aberdein and published by Bloomsbury Publishing. This book was released on 2019-05-02 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the results of applying empirical methods to the philosophy of logic and mathematics. Much of the work that has earned experimental philosophy a prominent place in twenty-first century philosophy is concerned with ethics or epistemology. But, as this book shows, empirical methods are just as much at home in logic and the philosophy of mathematics. Chapters demonstrate and discuss the applicability of a wide range of empirical methods including experiments, surveys, interviews, and data-mining. Distinct themes emerge that reflect recent developments in the field, such as issues concerning the logic of conditionals and the role played by visual elements in some mathematical proofs. Featuring leading figures from experimental philosophy and the fields of philosophy of logic and mathematics, this collection reveals that empirical work in these disciplines has been quietly thriving for some time and stresses the importance of collaboration between philosophers and researchers in mathematics education and mathematical cognition.

Download or read book Visualization in the Age of Computerization written by Annamaria Carusi and published by Routledge. This book was released on 2014-08-21 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Digitalization and computerization are now pervasive in science. This has deep consequences for our understanding of scientific knowledge and of the scientific process, and challenges longstanding assumptions and traditional frameworks of thinking of scientific knowledge. Digital media and computational processes challenge our conception of the way in which perception and cognition work in science, of the objectivity of science, and the nature of scientific objects. They bring about new relationships between science, art and other visual media, and new ways of practicing science and organizing scientific work, especially as new visual media are being adopted by science studies scholars in their own practice. This volume reflects on how scientists use images in the computerization age, and how digital technologies are affecting the study of science.

Download or read book The Golden Age of Data Visualization written by Kim Marriott and published by CRC Press. This book was released on 2024-09-04 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: We are living in the Golden Age of Data Visualization. The COVID-19 pandemic has demonstrated how we increasingly use data visualizations to make sense of the world. Business analysts fill their presentations with charts, journalists use infographics to engage their readers, we rely on the dials and gauges on our household appliances, and we use mapping apps on our smartphones to find our way. This book explains how and why this has happened. It details the evolution of information graphics, the kinds of graphics at the core of data visualization—maps, diagrams, charts, scientific and medical images—from prehistory to the present day. It explains how the cultural context, production and presentation technologies, and data availability have shaped the history of data visualization. It considers the perceptual and cognitive reasons why data visualization is so effective and explores the little-known world of tactile graphics—raised-line drawings used by people who are blind. The book also investigates the way visualization has shaped our modern world. The European Renaissance and the Scientific Revolution relied on maps and technical and scientific drawings, and graphics influence how we think about abstract concepts like time and social connection. This book is written for data visualization researchers and professionals and anyone interested in data visualization and the way we use graphics to understand and think about the world.

Download or read book Bloomsbury Semiotics Volume 2 Semiotics in the Natural and Technical Sciences written by Jamin Pelkey and published by Bloomsbury Publishing. This book was released on 2023-01-12 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bloomsbury Semiotics offers a state-of-the-art overview of the entire field of semiotics by revealing its influence on a wide range of disciplinary perspectives. With four volumes spanning theory, method and practice across the disciplines, this definitive reference work emphasizes and strengthens common bonds shared across intellectual cultures, and facilitates the discovery and recovery of meaning across fields. It comprises: Volume 1: History and Semiosis Volume 2: Semiotics in the Natural and Technical Sciences Volume 3: Semiotics in the Arts and Social Sciences Volume 4: Semiotic Movements Written by leading international experts, the chapters provide comprehensive overviews of the history and status of semiotic inquiry across a diverse range of traditions and disciplines. Together, they highlight key contemporary developments and debates along with ongoing research priorities. Providing the most comprehensive and united overview of the field, Bloomsbury Semiotics enables anyone, from students to seasoned practitioners, to better understand and benefit from semiotic insight and how it relates to their own area of study or research. Volume 2: Semiotics in the Natural and Technical Sciences presents the state-of-the art in semiotic approaches to disciplines ranging from mathematics and biology to neuroscience and medicine, from evolutionary linguistics and animal behaviour studies to computing, finance, law, architecture, and design. Each chapter casts a vision for future research priorities, unanswered questions, and fresh openings for semiotic participation in these and related fields.

Download or read book From Logic to Practice written by Gabriele Lolli and published by Springer. This book was released on 2014-11-28 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together young researchers from a variety of fields within mathematics, philosophy and logic. It discusses questions that arise in their work, as well as themes and reactions that appear to be similar in different contexts. The book shows that a fairly intensive activity in the philosophy of mathematics is underway, due on the one hand to the disillusionment with respect to traditional answers, on the other to exciting new features of present day mathematics. The book explains how the problem of applicability once again plays a central role in the development of mathematics. It examines how new languages different from the logical ones (mostly figural), are recognized as valid and experimented with and how unifying concepts (structure, category, set) are in competition for those who look at this form of unification. It further shows that traditional philosophies, such as constructivism, while still lively, are no longer only philosophies, but guidelines for research. Finally, the book demonstrates that the search for and validation of new axioms is analyzed with a blend of mathematical historical, philosophical, psychological considerations.

Download or read book Selected Essays on Pre and Early Modern Mathematical Practice written by Jens Høyrup and published by Springer Nature. This book was released on 2019-09-20 with total page 963 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a broad selection of articles mainly published during the last two decades on a variety of topics within the history of mathematics, mostly focusing on particular aspects of mathematical practice. This book is of interest to, and provides methodological inspiration for, historians of science or mathematics and students of these disciplines.

Download or read book The Philosophy of Mathematical Practice written by Paolo Mancosu and published by OUP Oxford. This book was released on 2008-06-19 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, and developments at the intersection of history and philosophy of mathematics. But anyone familiar with contemporary philosophy of mathematics will be aware of the need for new approaches that pay closer attention to mathematical practice. This book is the first attempt to give a coherent and unified presentation of this new wave of work in philosophy of mathematics. The new approach is innovative at least in two ways. First, it holds that there are important novel characteristics of contemporary mathematics that are just as worthy of philosophical attention as the distinction between constructive and non-constructive mathematics at the time of the foundational debates. Secondly, it holds that many topics which escape purely formal logical treatment - such as visualization, explanation, and understanding - can nonetheless be subjected to philosophical analysis. The Philosophy of Mathematical Practice comprises an introduction by the editor and eight chapters written by some of the leading scholars in the field. Each chapter consists of short introduction to the general topic of the chapter followed by a longer research article in the area. The eight topics selected represent a broad spectrum of contemporary philosophical reflection on different aspects of mathematical practice: diagrammatic reasoning and representation systems; visualization; mathematical explanation; purity of methods; mathematical concepts; the philosophical relevance of category theory; philosophical aspects of computer science in mathematics; the philosophical impact of recent developments in mathematical physics.

Download or read book Mathematical Knowledge and the Interplay of Practices written by José Ferreirós and published by Princeton University Press. This book was released on 2015-12-22 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, José Ferreirós uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, Ferreirós shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. He argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. Ferreirós demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, Mathematical Knowledge and the Interplay of Practices challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

Download or read book Platonism Naturalism and Mathematical Knowledge written by James Robert Brown and published by Routledge. This book was released on 2013-06-17 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does this engaging book present the Platonist-Naturalist debate over mathematics in a comprehensive fashion, but it also sheds considerable light on non-mathematical aspects of a dispute that is central to contemporary philosophy.

Download or read book An Introduction to the Philosophy of Mathematics written by Mark Colyvan and published by Cambridge University Press. This book was released on 2012-06-14 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.

Download or read book Explanation Beyond Causation written by Alexander Reutlinger and published by Oxford University Press. This book was released on 2018-05-31 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explanations are important to us in many contexts: in science, mathematics, philosophy, and also in everyday and juridical contexts. But what is an explanation? In the philosophical study of explanation, there is long-standing, influential tradition that links explanation intimately to causation: we often explain by providing accurate information about the causes of the phenomenon to be explained. Such causal accounts have been the received view of the nature of explanation, particularly in philosophy of science, since the 1980s. However, philosophers have recently begun to break with this causal tradition by shifting their focus to kinds of explanation that do not turn on causal information. The increasing recognition of the importance of such non-causal explanations in the sciences and elsewhere raises pressing questions for philosophers of explanation. What is the nature of non-causal explanations - and which theory best captures it? How do non-causal explanations relate to causal ones? How are non-causal explanations in the sciences related to those in mathematics and metaphysics? This volume of new essays explores answers to these and other questions at the heart of contemporary philosophy of explanation. The essays address these questions from a variety of perspectives, including general accounts of non-causal and causal explanations, as well as a wide range of detailed case studies of non-causal explanations from the sciences, mathematics, and metaphysics.

Download or read book The Architecture of Modern Mathematics written by J. Ferreiros and published by OUP Oxford. This book was released on 2006-04-27 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research, and how a number of historical accounts can be deepened by embracing philosophical questions.