Mathematics and Scientific Representation

Author: Christopher Pincock

Publisher: OUP USA

ISBN: 0199757100

Category: Mathematics

Page: 330

View: 6604

Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. Pincock tackles this perennial question by asking how mathematics contributes to the success of our best scientific representations.

The Oxford Handbook of Philosophy of Science

Author: Commonwealth Professor of Philosophy and Co-Director of the Center for the Study of Knowledge and Data Paul Humphreys,Paul Humphreys

Publisher: Oxford University Press

ISBN: 0199368813

Category: Philosophy and science

Page: 944

View: 8408

This handbook provides both an overview of state-of-the-art scholarship in philosophy of science, as well as a guide to new directions in the discipline. Section I contains broad overviews of the main lines of research and the state of established knowledge in six principal areas of the discipline, including computational, physical, biological, psychological and social sciences, as well as general philosophy of science. Section II covers what are considered to be the traditional topics in the philosophy of science, such as causation, probability, models, ethics and values, and explanation. Section III identifies new areas of investigation that show promise of becoming important areas of research, including the philosophy of astronomy and astrophysics, data, complexity theory, neuroscience, simulations, post-Kuhnian philosophy, post-empiricist epistemology, and emergence. Most chapters are accessible to scientifically educated non-philosophers as well as to professional philosophers, and the contributors - all leading researchers in their field -- bring diverse perspectives from the North American, European, and Australasian research communities. This volume is an essential resource for scholars and students.

Scientific Representation

Paradoxes of Perspective

Author: Bas C. van Fraassen

Publisher: OUP Oxford

ISBN: 0191613746

Category: Philosophy

Page: 422

View: 3426

Bas C. van Fraassen presents an original exploration of how we represent the world. Science represents natural phenomena by means of theories, as well as in many concrete ways by such means as pictures, graphs, table-top models, and computer simulations. Scientific Representation begins with an inquiry into the nature of representation in general, drawing on such diverse sources as Plato's dialogues, the development of perspectival drawing in the Renaissance, and the geometric styles of modelling in modern physics. Starting with Mach's and Poincaré's analyses of measurement and the 'problem of coordination', van Fraassen then presents a view of measurement outcomes as representations. With respect to the theories of contemporary science he defends an empiricist structuralist version of the 'picture theory' of science, through an inquiry into the paradoxes that came to light in twentieth-century philosophies of science. Van Fraassen concludes with an analysis of the complex relationship between appearance and reality in the scientific world-picture.

The Philosophy of Science

Author: Alexander Rosenberg

Publisher: Psychology Press

ISBN: 0415939275

Category: Science

Page: N.A

View: 2009

Beyond Mimesis and Convention

Representation in Art and Science

Author: Roman Frigg,Matthew Hunter

Publisher: Springer Science & Business Media

ISBN: 9789048138517

Category: Science

Page: 266

View: 9255

Representation is a concern crucial to the sciences and the arts alike. Scientists devote substantial time to devising and exploring representations of all kinds. From photographs and computer-generated images to diagrams, charts, and graphs; from scale models to abstract theories, representations are ubiquitous in, and central to, science. Likewise, after spending much of the twentieth century in proverbial exile as abstraction and Formalist aesthetics reigned supreme, representation has returned with a vengeance to contemporary visual art. Representational photography, video and ever-evolving forms of new media now figure prominently in the globalized art world, while this "return of the real" has re-energized problems of representation in the traditional media of painting and sculpture. If it ever really left, representation in the arts is certainly back. Central as they are to science and art, these representational concerns have been perceived as different in kind and as objects of separate intellectual traditions. Scientific modeling and theorizing have been topics of heated debate in twentieth century philosophy of science in the analytic tradition, while representation of the real and ideal has never moved far from the core humanist concerns of historians of Western art. Yet, both of these traditions have recently arrived at a similar impasse. Thinking about representation has polarized into oppositions between mimesis and convention. Advocates of mimesis understand some notion of mimicry (or similarity, resemblance or imitation) as the core of representation: something represents something else if, and only if, the former mimics the latter in some relevant way. Such mimetic views stand in stark contrast to conventionalist accounts of representation, which see voluntary and arbitrary stipulation as the core of representation. Occasional exceptions only serve to prove the rule that mimesis and convention govern current thinking about representation in both analytic philosophy of science and studies of visual art. This conjunction can hardly be dismissed as a matter of mere coincidence. In fact, researchers in philosophy of science and the history of art have increasingly found themselves trespassing into the domain of the other community, pilfering ideas and approaches to representation. Cognizant of the limitations of the accounts of representation available within the field, philosophers of science have begun to look outward toward the rich traditions of thinking about representation in the visual and literary arts. Simultaneously, scholars in art history and affiliated fields like visual studies have come to see images generated in scientific contexts as not merely interesting illustrations derived from "high art", but as sophisticated visualization techniques that dynamically challenge our received conceptions of representation and aesthetics. "Beyond Mimesis and Convention: Representation in Art and Science" is motivated by the conviction that we students of the sciences and arts are best served by confronting our mutual impasse and by recognizing the shared concerns that have necessitated our covert acts of kleptomania. Drawing leading contributors from the philosophy of science, the philosophy of literature, art history and visual studies, our volume takes its brief from our title. That is, these essays aim to put the evidence of science and of art to work in thinking about representation by offering third (or fourth, or fifth) ways beyond mimesis and convention. In so doing, our contributors explore a range of topics-fictionalism, exemplification, neuroaesthetics, approximate truth-that build upon and depart from ongoing conversations in philosophy of science and studies of visual art in ways that will be of interest to both interpretive communities. To put these contributions into context, the remainder of this introduction aims to survey how our communities have discretely arrived at a place wherein the perhaps-surprising collaboration between philosophy of science and art history has become not only salubrious, but a matter of necessity.

Plato's Problem

An Introduction to Mathematical Platonism

Author: M. Panza,A. Sereni

Publisher: Springer

ISBN: 1137298138

Category: Mathematics

Page: 306

View: 980

What is mathematics about? And how can we have access to the reality it is supposed to describe? The book tells the story of this problem, first raised by Plato, through the views of Aristotle, Proclus, Kant, Frege, Gödel, Benacerraf, up to the most recent debate on mathematical platonism.

The Oxford Handbook of the History of Mathematics

Author: Eleanor Robson,Jacqueline Stedall

Publisher: Oxford University Press on Demand

ISBN: 0199213127

Category: History

Page: 918

View: 3471

Comprising thirty-six self-contained, multifaceted chapters structured around methodological issues in the history of mathematics, this Handbook aims to be exemplary rather than exhaustive by taking a new look at what mathematics has been in history, and what it means to write history of mathematics. It provides a picture of the discipline that reflects the scholarship of recent decades, stating open problems and thus helping toset agendas for subsequent research. Aimed at a broad academic audience including mathematicians, historians of science, and general historians, the relevance of each subject to general history is stressed, and specific linksmade to the wider academic literature.

The Routledge Companion to Philosophy of Science

Author: Martin Curd,Stathis Psillos

Publisher: Routledge

ISBN: 1134259034

Category: Philosophy

Page: 656

View: 5995

This indispensable reference source and guide to the major themes, debates, problems and topics in philosophy of science contains fifty-five specially commissioned entries by a leading team of international contributors. Organized into four parts it covers: historical and philosophical context debates concepts the individual sciences. The Companion covers everything students of philosophy of science need to know - from empiricism, explanation and experiment to causation, observation, prediction and more - and contains many helpful features including: a section on the individual sciences, including chapters on the philosophy of biology, chemistry, physics and psychology, further reading and cross-referencing at the end of each chapter.

Towards a Philosophy of Real Mathematics

Author: David Corfield

Publisher: Cambridge University Press

ISBN: 9781139436397

Category: Philosophy

Page: N.A

View: 8991

In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done.

Correspondence, Invariance and Heuristics

Essays in Honour of Heinz Post

Author: S. French,H. Kamminga

Publisher: Springer Science & Business Media

ISBN: 9401711852

Category: Science

Page: 364

View: 1682

This volume is presented in honour of Heinz Post, who founded a distinc tive and distinguished school of philosophy of science at Chelsea College, University of London. The 'Chelsea tradition' in philosophy of science takes the content of science seriously, as exemplified by the papers presented here. The unifying theme of this work is that of 'Correspondence, Invariance and Heuristics', after the title of a classic and seminal paper by Heinz Post, published in 1971, which is reproduced in this volume with the kind permission of the editors and publishers of Studies in History and Philosophy of Science. Described by Paul Feyerabend in Against Method as "brilliant" and " . . . a partial antidote against the view which I try to defend" (1975, p. 61, fn. 17), this paper, peppered with illustrative examples from the history of science, brings to the fore some of Heinz Post's central concerns: the heuristic criteria used by scientists in constructing their theories, the intertheoretic relationships which these criteria reflect and, in particular, the nature of the correspondence that holds between a theory and its predecessors (and its suc cessors). The appearance of this volume more than twenty years later is an indica tion of the fruitfulness of Post's contribution: philosophers of science continue to explore the issues raised in his 1971 paper.

Reconstructing Reality

Models, Mathematics, and Simulations

Author: Margaret Morrison

Publisher: Oxford University Press, USA

ISBN: 0199380279

Category: Philosophy

Page: 334

View: 7345

This text examines issues related to the way modelling and simulation enable us to reconstruct aspects of the world we are investigating. It also investigates the processes by which we extract concrete knowledge from those reconstructions and how that knowledge is legitimated.

Science after the Practice Turn in the Philosophy, History, and Social Studies of Science

Author: Léna Soler,Sjoerd Zwart,Michael Lynch,Vincent Israel-Jost

Publisher: Routledge

ISBN: 1317935357

Category: Philosophy

Page: 346

View: 3020

In the 1980s, philosophical, historical and social studies of science underwent a change which later evolved into a turn to practice. Analysts of science were asked to pay attention to scientific practices in meticulous detail and along multiple dimensions, including the material, social and psychological. Following this turn, the interest in scientific practices continued to increase and had an indelible influence in the various fields of science studies. No doubt, the practice turn changed our conceptions and approaches of science, but what did it really teach us? What does it mean to study scientific practices? What are the general lessons, implications, and new challenges? This volume explores questions about the practice turn using both case studies and theoretical analysis. The case studies examine empirical and mathematical sciences, including the engineering sciences. The volume promotes interactions between acknowledged experts from different, often thought of as conflicting, orientations. It presents contributions in conjunction with critical commentaries that put the theses and assumptions of the former in perspective. Overall, the book offers a unique and diverse range of perspectives on the meanings, methods, lessons, and challenges associated with the practice turn.

The Continuum Companion to the Philosophy of Science

Author: Steven French,Juha Saatsi

Publisher: A&C Black

ISBN: 1441187618

Category: Science

Page: 452

View: 7144

A one volume reference guide To The latest research in Philosophy of Science, written by an international team of leading scholars in the field.

Models, Simulations, and Representations

Author: Paul Humphreys,Cyrille Imbert

Publisher: Routledge

ISBN: 1136668497

Category: Philosophy

Page: 306

View: 5031

Although scientific models and simulations differ in numerous ways, they are similar in so far as they are posing essentially philosophical problems about the nature of representation. This collection is designed to bring together some of the best work on the nature of representation being done by both established senior philosophers of science and younger researchers. Most of the pieces, while appealing to existing traditions of scientific representation, explore new types of questions, such as: how understanding can be developed within computational science; how the format of representations matters for their use, be it for the purpose of research or education; how the concepts of emergence and supervenience can be further analyzed by taking into account computational science; or how the emphasis upon tractability--a particularly important issue in computational science--sheds new light on the philosophical analysis of scientific reasoning.

Psychology of Science

Implicit and Explicit Processes

Author: Robert W. Proctor,E.J. Capaldi

Publisher: Oxford University Press

ISBN: 0199753628

Category: Medical

Page: 523

View: 9480

Symposium held at Purdue Univ. in June 4-5, 2010.

The Philosophy of Mathematical Practice

Author: Paolo Mancosu

Publisher: Oxford University Press on Demand

ISBN: 0199296456

Category: Philosophy

Page: 447

View: 4419

This book gives a coherent and unified presentation of a new direction of work in philosophy of mathematics. This new approach in philosophy of mathematics requires extensive attention to mathematical practice and provides philosophical analyses of important novel characteristics of contemporary (twentieth century) mathematics and of many aspects of mathematical activity-such as visualization, explanation, understanding etc.-- which escape purely formal logicaltreatment.The book consists of a lengthy introduction by the editor and of eight chapters written by some of the very best scholars in this area. Each chapter consists of a short introduction to the general topic of the chapter and of a longer research article in the very same area. Theeight topics selected represent a broad spectrum of the contemporary philosophical reflection on different aspects of mathematical practice: Diagrammatic reasoning and representational systems; Visualization; Mathematical Explanation; Purity of Methods; Mathematical Concepts; Philosophical relevance of category theory; Philosophical aspects of computer science in mathematics; Philosophical impact of recent developments in mathematical physics.

Philosophy of Science

The Central Issues

Author: Martin Curd,Jan A. Cover,Christopher Pincock,Chris Pincock

Publisher: W. W. Norton

ISBN: 9780393919035

Category: Philosophy

Page: 1393

View: 1930

A flexible and comprehensive introduction to the main currents in philosophy of science.

Models as Make-Believe

Imagination, Fiction and Scientific Representation

Author: Adam Toon

Publisher: Springer

ISBN: 1137292237

Category: Science

Page: 148

View: 5808

Scientists often try to understand the world by building simplified and idealised models of it. Adam Toon develops a new approach to scientific models by comparing them to the dolls and toy trucks of children's imaginative games, and offers a unified framework to solve difficult metaphysical problems and help to make sense of scientific practice.

Scientific Concepts and Investigative Practice

Author: Uljana Feest,Friedrich Steinle

Publisher: Walter de Gruyter

ISBN: 3110253615

Category: Philosophy

Page: 308

View: 8670

Recent philosophy and history of science have seen a surge of interest in the role of concepts in scientific research. Combining philosophical and historical scholarship, the articles in this volume investigate the ways in which scientists form and use concepts, rather than in what the concepts themselves represent. The fields treated range from mathematics to virology and genetics, from nuclear physics to psychology, from technology to present-day neural engineering.

From Discrete to Continuous

The Broadening of Number Concepts in Early Modern England

Author: K. Neal

Publisher: Springer Science & Business Media

ISBN: 940170077X

Category: Mathematics

Page: 175

View: 546

In the early modern period, a crucial transformation occurred in the classical conception of number and magnitude. Traditionally, numbers were merely collections of discrete units that measured some multiple. Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible. This traditional idea of discrete number versus continuous magnitude was challenged in the early modern period in several ways. This detailed study explores how the development of algebraic symbolism, logarithms, and the growing practical demands for an expanded number concept all contributed to a broadening of the number concept in early modern England. An interest in solving practical problems was not, in itself, enough to cause a generalisation of the number concept. It was the combined impact of novel practical applications together with the concomitant development of such mathematical advances as algebraic notation and logarithms that produced a broadened number concept.