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Books > Science & Mathematics > Mathematics > Philosophy of mathematics

The Structure of Time (Hardcover): W.H. Newton-Smith The Structure of Time (Hardcover)
W.H. Newton-Smith
R3,428 Discovery Miles 34 280 Ships in 12 - 17 working days

Originally published in 1980. What is time? How is its structure determined? The enduring controversy about the nature and structure of time has traditionally been a diametrical argument between those who see time as a container into which events are placed, and those for whom time cannot exist without events. This controversy between the absolutist and the relativist theories of time is a central theme of this study. The author's impressive arguments provide grounds for rejecting both these theories, firstly by establishing that 'empty' time is possible, and secondly by showing, through a discussion of the structure of time which involves considering whether time might be cyclical, branching, beginning or non-beginning, that the absolutist theory of time is untenable. This book then advances two new theories, and succeeds in shifting the traditional debate about time to a consideration of time as a theoretical structure and as a theoretical framework.

Logic from A to Z - The Routledge Encyclopedia of Philosophy Glossary of Logical and Mathematical Terms (Paperback): John B.... Logic from A to Z - The Routledge Encyclopedia of Philosophy Glossary of Logical and Mathematical Terms (Paperback)
John B. Bacon, Michael Detlefsen, David Charles McCarty
R1,165 Discovery Miles 11 650 Ships in 12 - 17 working days


First published in the most ambitious international philosophy project for a generation; the Routledge Encyclopedia of Philosophy.
Logic from A to Z is a unique glossary of terms used in formal logic and the philosophy of mathematics.
Over 500 entries include key terms found in the study of:
* Logic: Argument, Turing Machine, Variable
* Set and model theory: Isomorphism, Function
* Computability theory: Algorithm, Turing Machine
* Plus a table of logical symbols.
Extensively cross-referenced to help comprehension and add detail, Logic from A to Z provides an indispensable reference source for students of all branches of logic.

Mathematical Reasoning - Analogies, Metaphors, and Images (Hardcover): Lyn D English Mathematical Reasoning - Analogies, Metaphors, and Images (Hardcover)
Lyn D English
R5,134 R4,310 Discovery Miles 43 100 Save R824 (16%) Ships in 12 - 17 working days

How we reason with mathematical ideas continues to be a fascinating and challenging topic of research--particularly with the rapid and diverse developments in the field of cognitive science that have taken place in recent years. Because it draws on multiple disciplines, including psychology, philosophy, computer science, linguistics, and anthropology, cognitive science provides rich scope for addressing issues that are at the core of mathematical learning.
Drawing upon the interdisciplinary nature of cognitive science, this book presents a broadened perspective on mathematics and mathematical reasoning. It represents a move away from the traditional notion of reasoning as "abstract" and "disembodied," to the contemporary view that it is "embodied" and "imaginative." From this perspective, mathematical reasoning involves reasoning with structures that emerge from our bodily experiences as we interact with the environment; these structures extend beyond finitary propositional representations. Mathematical reasoning is imaginative in the sense that it utilizes a number of powerful, illuminating devices that structure these concrete experiences and transform them into models for abstract thought. These "thinking tools"--analogy, metaphor, metonymy, and imagery--play an important role in mathematical reasoning, as the chapters in this book demonstrate, yet their potential for enhancing learning in the domain has received little recognition.
This book is an attempt to fill this void. Drawing upon backgrounds in mathematics education, educational psychology, philosophy, linguistics, and cognitive science, the chapter authors provide a rich and comprehensive analysis of mathematical reasoning. New and exciting perspectives are presented on the nature of mathematics (e.g., "mind-based mathematics"), on the array of powerful cognitive tools for reasoning (e.g., "analogy and metaphor"), and on the different ways these tools can facilitate mathematical reasoning. Examples are drawn from the reasoning of the preschool child to that of the adult learner.

Mathematical Reasoning - Analogies, Metaphors, and Images (Paperback): Lyn D English Mathematical Reasoning - Analogies, Metaphors, and Images (Paperback)
Lyn D English
R1,822 Discovery Miles 18 220 Ships in 12 - 17 working days

How we reason with mathematical ideas continues to be a fascinating and challenging topic of research--particularly with the rapid and diverse developments in the field of cognitive science that have taken place in recent years. Because it draws on multiple disciplines, including psychology, philosophy, computer science, linguistics, and anthropology, cognitive science provides rich scope for addressing issues that are at the core of mathematical learning.
Drawing upon the interdisciplinary nature of cognitive science, this book presents a broadened perspective on mathematics and mathematical reasoning. It represents a move away from the traditional notion of reasoning as "abstract" and "disembodied," to the contemporary view that it is "embodied" and "imaginative." From this perspective, mathematical reasoning involves reasoning with structures that emerge from our bodily experiences as we interact with the environment; these structures extend beyond finitary propositional representations. Mathematical reasoning is imaginative in the sense that it utilizes a number of powerful, illuminating devices that structure these concrete experiences and transform them into models for abstract thought. These "thinking tools"--analogy, metaphor, metonymy, and imagery--play an important role in mathematical reasoning, as the chapters in this book demonstrate, yet their potential for enhancing learning in the domain has received little recognition.
This book is an attempt to fill this void. Drawing upon backgrounds in mathematics education, educational psychology, philosophy, linguistics, and cognitive science, the chapter authors provide a rich and comprehensive analysis of mathematical reasoning. New and exciting perspectives are presented on the nature of mathematics (e.g., "mind-based mathematics"), on the array of powerful cognitive tools for reasoning (e.g., "analogy and metaphor"), and on the different ways these tools can facilitate mathematical reasoning. Examples are drawn from the reasoning of the preschool child to that of the adult learner.

Empowering Mathematics Learners: Yearbook 2017, Association Of Mathematics Educators (Hardcover): Berinderjeet Kaur, Ngan Hoe... Empowering Mathematics Learners: Yearbook 2017, Association Of Mathematics Educators (Hardcover)
Berinderjeet Kaur, Ngan Hoe Lee
R3,732 Discovery Miles 37 320 Ships in 10 - 15 working days

This book contributes towards the literature in the field of mathematics education, specifically on aspects of empowering learners of mathematics. The book, comprising eighteen chapters, written by renowned researchers in mathematics education, provides readers with approaches and applicable classroom strategies to empower learners of mathematics.The chapters in the book can be classified into four sections. The four sections focus on how learners could be empowered in their learning, cognitive and affective processes, through mathematical content, purposefully designed mathematical tasks, whilst developing 21st century competencies.

Theories of Mathematical Learning (Hardcover): Leslie P. Steffe, Pearla Nesher, Paul Cobb, Bharath Sriraman, Brian Greer Theories of Mathematical Learning (Hardcover)
Leslie P. Steffe, Pearla Nesher, Paul Cobb, Bharath Sriraman, Brian Greer
R5,146 R4,034 Discovery Miles 40 340 Save R1,112 (22%) Ships in 12 - 17 working days

Chemists, working with only mortars and pestles, could not get very far unless they had mathematical models to explain what was happening "inside" of their elements of experience -- an example of what could be termed mathematical learning.
This volume contains the proceedings of Work Group 4: Theories of Mathematics, a subgroup of the Seventh International Congress on Mathematical Education held at Universite Laval in Quebec. Bringing together multiple perspectives on mathematical thinking, this volume presents elaborations on principles reflecting the progress made in the field over the past 20 years and represents starting points for understanding mathematical learning today. This volume will be of importance to educational researchers, math educators, graduate students of mathematical learning, and anyone interested in the enterprise of improving mathematical learning worldwide.

The Nature of Mathematical Thinking (Paperback): Robert J. Sternberg, Talia Ben-Zeev The Nature of Mathematical Thinking (Paperback)
Robert J. Sternberg, Talia Ben-Zeev
R1,903 Discovery Miles 19 030 Ships in 12 - 17 working days

Why do some children seem to learn mathematics easily and others slave away at it, learning it only with great effort and apparent pain? Why are some people good at algebra but terrible at geometry? How can people who successfully run a business as adults have been failures at math in school? How come some professional mathematicians suffer terribly when trying to balance a checkbook? And why do school children in the United States perform so dismally in international comparisons? These are the kinds of real questions the editors set out to answer, or at least address, in editing this book on mathematical thinking. Their goal was to seek a diversity of contributors representing multiple viewpoints whose expertise might converge on the answers to these and other pressing and interesting questions regarding this subject.
The chapter authors were asked to focus on their own approach to mathematical thinking, but also to address a common core of issues such as the nature of mathematical thinking, how it is similar to and different from other kinds of thinking, what makes some people or some groups better than others in this subject area, and how mathematical thinking can be assessed and taught. Their work is directed to a diverse audience -- psychologists interested in the nature of mathematical thinking and abilities, computer scientists who want to simulate mathematical thinking, educators involved in teaching and testing mathematical thinking, philosophers who need to understand the qualitative aspects of logical thinking, anthropologists and others interested in how and why mathematical thinking seems to differ in quality across cultures, and laypeople and others who have to think mathematically and want to understand how they are going to accomplish that feat.

Naturalizing Logico-Mathematical Knowledge - Approaches from Philosophy, Psychology and Cognitive Science (Hardcover): Sorin... Naturalizing Logico-Mathematical Knowledge - Approaches from Philosophy, Psychology and Cognitive Science (Hardcover)
Sorin Bangu
R4,315 Discovery Miles 43 150 Ships in 12 - 17 working days

This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato's dialogues, and virtually all major philosophers have expressed interest in it. The essays in this collection tackle this important philosophical query from the perspective of the modern sciences of cognition, namely cognitive psychology and neuroscience. Naturalizing Logico-Mathematical Knowledge contributes to consolidating a new, emerging direction in the philosophy of mathematics, which, while keeping the traditional concerns of this sub-discipline in sight, aims to engage with them in a scientifically-informed manner. A subsequent aim is to signal the philosophers' willingness to enter into a fruitful dialogue with the community of cognitive scientists and psychologists by examining their methods and interpretive strategies.

Wittgenstein and Naturalism (Hardcover): Kevin M. Cahill, Thomas Raleigh Wittgenstein and Naturalism (Hardcover)
Kevin M. Cahill, Thomas Raleigh
R4,608 Discovery Miles 46 080 Ships in 12 - 17 working days

Wittgenstein was centrally concerned with the puzzling nature of the mind, mathematics, morality and modality. He also developed innovative views about the status and methodology of philosophy and was explicitly opposed to crudely "scientistic" worldviews. His later thought has thus often been understood as elaborating a nuanced form of naturalism appealing to such notions as "form of life", "primitive reactions", "natural history", "general facts of nature" and "common behaviour of mankind". And yet, Wittgenstein is strangely absent from much of the contemporary literature on naturalism and naturalising projects. This is the first collection of essays to focus explicitly on the relationship between Wittgenstein and naturalism. The volume is divided into four sections, each of which addresses a different aspect of naturalism and its relation to Wittgenstein's thought. The first section considers how naturalism could or should be understood. The second section deals with some of the main problematic domains-consciousness, meaning, mathematics-that philosophers have typically sought to naturalise. The third section explores ways in which the conceptual nature of human life might be continuous in important respects with animals. The final section is concerned with the naturalistic status and methodology of philosophy itself. This book thus casts a fresh light on many classical philosophical issues and brings Wittgensteinian ideas to bear on a number of current debates-for example experimental philosophy, neo-pragmatism and animal cognition/ethics-in which naturalism is playing a central role.

Hidden Questions, Clinical Musings (Hardcover): M.Robert Gardner Hidden Questions, Clinical Musings (Hardcover)
M.Robert Gardner
R2,934 R2,422 Discovery Miles 24 220 Save R512 (17%) Ships in 12 - 17 working days

In Hidden Questions, Clinical Musings, M. Robert Gardner chronicles an odyssey of self-discovery that has taken him beneath and beyond the categoies and conventions of traditional psychoanalysis. His essays offer a vision of psychoanalytic inquiry that blends art and science, a vision in which the subtly intertwining not-quite-conscious questions of analysand and analyst, gradually discerned, open to ever-widening vistas of shared meaning. Gardner is wonderfully illuminating in exploring the associations, images, and dreams that have fueled his own analytic inquiries, but he is no less compelling in writing about the different perceptual modalities and endlessly variegated strategies that can be summoned to bring hidden questions to light.

This masterfully assembled collection exemplifies the lived experience of psychoanalysis of one of its most gifted and reflective practitioners. In his vivid depictions of analysis oscillating between the poles of art and science, word and image, inquiry and self-inquiry, Gardner offers precious insights into tensions that are basic to the analytic endeavor. Evincing rare virtuosity of form and content, these essays are evocative clinical gems, radiating the humility, gentle skepticism, and abiding wonder of this lifelong self-inquirer. Gardner's most uncommon musings are a gift to the reader.

The Emergence of Mathematical Meaning - interaction in Classroom Cultures (Hardcover): Paul Cobb, Heinrich Bauersfeld The Emergence of Mathematical Meaning - interaction in Classroom Cultures (Hardcover)
Paul Cobb, Heinrich Bauersfeld
R6,608 R5,311 Discovery Miles 53 110 Save R1,297 (20%) Ships in 12 - 17 working days

This book grew out of a five-year collaboration between groups of American and German mathematics educators. The central issue addressed accounting for the messiness and complexity of mathematics learning and teaching as it occurs in classroom situations. The individual chapters are based on the view that psychological and sociological perspectives each tell half of a good story. To unify these concepts requires a combined approach that takes individual students' mathematical activity seriously while simultaneously seeing their activity as necessarily socially situated. Throughout their collaboration, the chapter authors shared a single set of video recordings and transcripts made in an American elementary classroom where instruction was generally compatible with recent reform recommendations. As a consequence, the book is much more than a compendium of loosely related papers.
The combined approach taken by the authors draws on interactionism and ethnomethodology. Thus, it constitutes an alternative to Vygotskian and Soviet activity theory approaches. The specific topics discussed in individual chapters include small group collaboration and learning, the teacher's practice and growth, and language, discourse, and argumentation in the mathematics classroom. This collaborative effort is valuable to educators and psychologists interested in situated cognition and the relation between sociocultural processes and individual psychological processes.

Figures of Thought - Mathematics and Mathematical Texts (Hardcover, New): David Reed Figures of Thought - Mathematics and Mathematical Texts (Hardcover, New)
David Reed
R4,299 Discovery Miles 42 990 Ships in 12 - 17 working days

Rarely has the history and philosophy of mathematics been written about by mathematicians, and the analysis of mathematical texts themselves has been an area almost entirely unexplored. "Figures of Thought" looks at ways in which mathematical works can be read as texts and demonstrates that such readings provide a rich source of philosophical issues regarding mathematics: issues which traditional approaches to the history and philosophy of mathematics have neglected. David Reed offers the first sustained and critical attempt to find a consistent argument or narrative thread in mathematical texts. He selects mathematicians from a range of historical periods and compares their approaches to organizing and arguing texts, using an extended commentary of Euclid's "Elements" as a central structuring framework. In doing so, he develops new interpretations of mathematicians' work throughout history, from Descartes to Grothendieck and traces the implications of such an approach for the understanding of the history and development of mathematics.

Wittgenstein's Philosophy of Mathematics (Hardcover, annotated edition): Pasquale Frascolla Wittgenstein's Philosophy of Mathematics (Hardcover, annotated edition)
Pasquale Frascolla
R4,299 Discovery Miles 42 990 Ships in 12 - 17 working days

This volume presents Wittgenstein's views on mathematics, which he progressively elaborated during a lifetime's reflections on the subject. Divided into three parts, it corresponds to the three distinct phases in the development of Wittgenstein's philosophy of mathematics. The first part is devoted to the "Tractatus" and contains a systematic construction of the representation of arithmetic in logical operations. The second part is concerned with the so-called "intermediate phase" (1929-33), which is characterized by strong verification and by a conception of the relation between the particular and the general in mathematics which forms the basis of Wittgenstein's later reflections on rule-following. The final section deals with the writings on mathematics in the decade 1934-44. The main themes of Wittgenstein's later philosophy of mathematics are understood as consequences of his considerations of rule-following.

Mathematics in Aristotle (Paperback): Thomas Heath Mathematics in Aristotle (Paperback)
Thomas Heath
R1,218 Discovery Miles 12 180 Ships in 12 - 17 working days

Originally published in 1949. This meticulously researched book presents a comprehensive outline and discussion of Aristotle's mathematics with the author's translations of the greek. To Aristotle, mathematics was one of the three theoretical sciences, the others being theology and the philosophy of nature (physics). Arranged thematically, this book considers his thinking in relation to the other sciences and looks into such specifics as squaring of the circle, syllogism, parallels, incommensurability of the diagonal, angles, universal proof, gnomons, infinity, agelessness of the universe, surface of water, meteorology, metaphysics and mechanics such as levers, rudders, wedges, wheels and inertia. The last few short chapters address 'problems' that Aristotle posed but couldn't answer, related ethics issues and a summary of some short treatises that only briefly touch on mathematics.

Curves for the Mathematically Curious - An Anthology of the Unpredictable, Historical, Beautiful, and Romantic (Paperback):... Curves for the Mathematically Curious - An Anthology of the Unpredictable, Historical, Beautiful, and Romantic (Paperback)
Julian Havil
R553 R508 Discovery Miles 5 080 Save R45 (8%) Ships in 10 - 15 working days

Ten amazing curves personally selected by one of today's most important math writers Curves for the Mathematically Curious is a thoughtfully curated collection of ten mathematical curves, selected by Julian Havil for their significance, mathematical interest, and beauty. Each chapter gives an account of the history and definition of one curve, providing a glimpse into the elegant and often surprising mathematics involved in its creation and evolution. In telling the ten stories, Havil introduces many mathematicians and other innovators, some whose fame has withstood the passing of years and others who have slipped into comparative obscurity. You will meet Pierre Bezier, who is known for his ubiquitous and eponymous curves, and Adolphe Quetelet, who trumpeted the ubiquity of the normal curve but whose name now hides behind the modern body mass index. These and other ingenious thinkers engaged with the challenges, incongruities, and insights to be found in these remarkable curves-and now you can share in this adventure. Curves for the Mathematically Curious is a rigorous and enriching mathematical experience for anyone interested in curves, and the book is designed so that readers who choose can follow the details with pencil and paper. Every curve has a story worth telling.

Proof and Knowledge in Mathematics (Hardcover, New): Michael Detlefsen Proof and Knowledge in Mathematics (Hardcover, New)
Michael Detlefsen
R4,297 Discovery Miles 42 970 Ships in 12 - 17 working days

This volume of essays tackles the main problem that arises when considering an epistemology for mathematics, the nature and sources of mathematical justification. Focusing both on particular and general issues, the essays from leading philosophers of mathematics raise important issues for our current understanding of mathematics. Is mathematical justification "a priori" or "a posteriori"? What role, if any, does logic play in mathematical reasoning or inference? And how epistemologically important is the formalizability of proof? The companion volume "Proof, Knowledge and Formalization" is also available from Routledge. Contributors include Michael Detlefsen, Michael D. Resnik, Stewart Shapiro, Mark Steiner, Pirmin Stekeler-Weithofer, Shelley Stillwell, William J. Tait and Steven J. Wagner. This book should be of interest to advanced students and lecturers of philosophy of logic and maths.

The Cambridge Companion to Frege (Hardcover): Tom Ricketts, Michael Potter The Cambridge Companion to Frege (Hardcover)
Tom Ricketts, Michael Potter
R2,736 Discovery Miles 27 360 Ships in 12 - 17 working days

Gottlob Frege (1848 1925) was unquestionably one of the most important philosophers of all time. He trained as a mathematician, and his work in philosophy started as an attempt to provide an explanation of the truths of arithmetic, but in the course of this attempt he not only founded modern logic but also had to address fundamental questions in the philosophy of language and philosophical logic. Frege is generally seen (along with Russell and Wittgenstein) as one of the fathers of the analytic method, which dominated philosophy in English-speaking countries for most of the twentieth century. His work is studied today not just for its historical importance but also because many of his ideas are still seen as relevant to current debates in the philosophies of logic, language, mathematics and the mind. The Cambridge Companion to Frege provides a route into this lively area of research.

On Constructive Interpretation of Predictive Mathematics (1990) (Hardcover): Charles Parsons On Constructive Interpretation of Predictive Mathematics (1990) (Hardcover)
Charles Parsons
R2,892 Discovery Miles 28 920 Ships in 12 - 17 working days

First published in 1990, this book consists of a detailed exposition of results of the theory of "interpretation" developed by G. Kreisel - the relative impenetrability of which gives the elucidation contained here great value for anyone seeking to understand his work. It contains more complex versions of the information obtained by Kreisel for number theory and clustering around the no-counter-example interpretation, for number-theorectic forumulae provide in ramified analysis. It also proves the omega-consistency of ramified analysis. The author also presents proofs of Schutte's cut-elimination theorems which are based on his consistency proofs and essentially contain them - these went further than any published work up to that point, helping to squeeze the maximum amount of information from these proofs.

Universality in Chaos, 2nd edition (Paperback, 2 Revised Edition): P. Cvitanovic Universality in Chaos, 2nd edition (Paperback, 2 Revised Edition)
P. Cvitanovic
R2,879 Discovery Miles 28 790 Ships in 12 - 17 working days

Nature provides many examples of physical systems that are described by deterministic equations of motion, but that nevertheless exhibit nonpredictable behavior. The detailed description of turbulent motions remains perhaps the outstanding unsolved problem of classical physics. In recent years, however, a new theory has been formulated that succeeds in making quantitative predictions describing certain transitions to turbulence. Its significance lies in its possible application to large classes (often very dissimilar) of nonlinear systems.
Since the publication of Universality in Chaos in 1984, progress has continued to be made in our understanding of nonlinear dynamical systems and chaos. This second edition extends the collection of articles to cover recent developments in the field, including the use of statistical mechanics techniques in the study of strange sets arising in dynamics. It concentrates on the universal aspects of chaotic motions, the qualitative and quantitative predictions that apply to large classes of physical systems. Much like the previous edition, this book will be an indispensable reference for researchers and graduate students interested in chaotic dynamics in the physical, biological, and mathematical sciences as well as engineering.

Resonance: From Probability To Epistemology And Back (Hardcover): Krzysztof Burdzy Resonance: From Probability To Epistemology And Back (Hardcover)
Krzysztof Burdzy
R4,012 Discovery Miles 40 120 Ships in 10 - 15 working days

Resonance examines some building blocks of epistemology as a prelude to the careful analysis of the foundations of probability. The concept of resonance is introduced to shed light on the philosophical problems of induction, consciousness, intelligence and free will. The same concept is later applied to provide support for a new philosophical theory of probability.Although based on existing ideas and theories, the epistemological concept of resonance is investigated for the first time in this book. The best-known philosophical theories of probability, frequency and subjective, are shown to be unrealistic and dissociated from the two main branches of statistics: frequency statistics and Bayesian statistics.Written in an accessible style, this book can be enjoyed by philosophers, statisticians and mathematicians, and also by anyone looking to expand their understanding of the disciplines of epistemology and probability.

Exploring the Invisible - Art, Science, and the Spiritual - Revised and Expanded Edition (Hardcover, Revised edition): Lynn... Exploring the Invisible - Art, Science, and the Spiritual - Revised and Expanded Edition (Hardcover, Revised edition)
Lynn Gamwell; Foreword by Neil De Grasse Tyson
R1,597 Discovery Miles 15 970 Ships in 12 - 17 working days

How science changed the way artists understand reality Exploring the Invisible shows how modern art expresses the first secular, scientific worldview in human history. Now fully revised and expanded, this richly illustrated book describes two hundred years of scientific discoveries that inspired French Impressionist painters and Art Nouveau architects, as well as Surrealists in Europe, Latin America, and Japan. Lynn Gamwell describes how the microscope and telescope expanded the artist's vision into realms unseen by the naked eye. In the nineteenth century, a strange and exciting world came into focus, one of microorganisms in a drop of water and spiral nebulas in the night sky. The world is also filled with forces that are truly unobservable, known only indirectly by their effects-radio waves, X-rays, and sound-waves. Gamwell shows how artists developed the pivotal style of modernism-abstract, non-objective art-to symbolize these unseen worlds. Starting in Germany with Romanticism and ending with international contemporary art, she traces the development of the visual arts as an expression of the scientific worldview in which humankind is part of a natural web of dynamic forces without predetermined purpose or meaning. Gamwell reveals how artists give nature meaning by portraying it as mysterious, dangerous, or beautiful. With a foreword by Neil deGrasse Tyson and a wealth of stunning images, this expanded edition of Exploring the Invisible draws on the latest scholarship to provide a global perspective on the scientists and artists who explore life on Earth, human consciousness, and the space-time universe.

From Mathematics to Philosophy (Routledge Revivals) (Hardcover): Hao Wang From Mathematics to Philosophy (Routledge Revivals) (Hardcover)
Hao Wang
R5,342 Discovery Miles 53 420 Ships in 12 - 17 working days

First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more general method of approach called substantial factualism which the author asserts allows for the development of a more comprehensive philosophical position by not trivialising or distorting substantial facts of human knowledge.

Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences - Volume Two (Paperback): Ivor Grattan-Guiness Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences - Volume Two (Paperback)
Ivor Grattan-Guiness
R1,801 Discovery Miles 18 010 Ships in 12 - 17 working days

First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.

Causality (Hardcover, 2nd Revised edition): Judea Pearl Causality (Hardcover, 2nd Revised edition)
Judea Pearl
R1,675 Discovery Miles 16 750 Ships in 12 - 17 working days

Written by one of the preeminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, economics, philosophy, cognitive science, and the health and social sciences. Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations. The book will open the way for including causal analysis in the standard curricula of statistics, artificial intelligence, business, epidemiology, social sciences, and economics. Students in these fields will find natural models, simple inferential procedures, and precise mathematical definitions of causal concepts that traditional texts have evaded or made unduly complicated. The first edition of Causality has led to a paradigmatic change in the way that causality is treated in statistics, philosophy, computer science, social science, and economics. Cited in more than 5,000 scientific publications, it continues to liberate scientists from the traditional molds of statistical thinking. In this revised edition, Judea Pearl elucidates thorny issues, answers readers questions, and offers a panoramic view of recent advances in this field of research. Causality will be of interests to students and professionals in a wide variety of fields. Anyone who wishes to elucidate meaningful relationships from data, predict effects of actions and policies, assess explanations of reported events, or form theories of causal understanding and causal speech will find this book stimulating and invaluable."

Research in History and Philosophy of Mathematics - The CSHPM 2019-2020 Volume (Hardcover, 1st ed. 2022): Maria Zack, Dirk... Research in History and Philosophy of Mathematics - The CSHPM 2019-2020 Volume (Hardcover, 1st ed. 2022)
Maria Zack, Dirk Schlimm
R5,227 R4,401 Discovery Miles 44 010 Save R826 (16%) Ships in 12 - 17 working days

This volume contains eleven papers that have been collected by the Canadian Society for History and Philosophy of Mathematics/Societe canadienne d'histoire et de philosophie des mathematiques. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics, as well as the teaching of the history of mathematics. Topics considered include The mathematics and astronomy in Nathaniel Torperly's only published work, Diclides Coelometricae, seu valvae astronomicae universal Connections between the work of Urbain Le Verrier, Carl Gustav Jacob Jacobi, and Augustin-Louis Cauchy on the algebraic eigenvalue problem An evaluation of Ken Manders' argument against conceiving of the diagrams in Euclid's Elements in semantic terms The development of undergraduate modern algebra courses in the United States Ways of using the history of mathematics to teach the foundations of mathematical analysis Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.

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