Download or read book A Critical Analysis of the Reasons Given in Methods Books and in Textbooks of Plane Geometry for Preferring Deductive Proofs to Discovery by Experimentation written by Roy Lee Hiburn and published by . This book was released on 1960 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Guide Sheets in Geometry for the Use of Teachers in Grades 7 9 in the Schools of Ceylon written by Daya Ananda Perera and published by . This book was released on 1961 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Abstracts of Masters Theses written by Ohio State University. Graduate School and published by . This book was released on with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Master s Theses in Education written by T. A. Lamke and published by . This book was released on 1961 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Scientific Method written by William Whewell and published by Hackett Publishing. This book was released on 1989-01-01 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes the author's seminal studies of the logic of induction, arguments for his realist view that science discovers necessary truths about nature, and exercises in the epistemology and ontology of science.
Download or read book Proof and Proving in Mathematics Education written by Gila Hanna and published by Springer Science & Business Media. This book was released on 2012-06-14 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: *THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.
Download or read book How to Solve it written by George Pólya and published by Princeton University Press. This book was released on 2014 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams."--Back cover.
Download or read book Democracy and Education written by John Dewey and published by Createspace Independent Publishing Platform. This book was released on 1916 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: . Renewal of Life by Transmission. The most notable distinction between living and inanimate things is that the former maintain themselves by renewal. A stone when struck resists. If its resistance is greater than the force of the blow struck, it remains outwardly unchanged. Otherwise, it is shattered into smaller bits. Never does the stone attempt to react in such a way that it may maintain itself against the blow, much less so as to render the blow a contributing factor to its own continued action. While the living thing may easily be crushed by superior force, it none the less tries to turn the energies which act upon it into means of its own further existence. If it cannot do so, it does not just split into smaller pieces (at least in the higher forms of life), but loses its identity as a living thing. As long as it endures, it struggles to use surrounding energies in its own behalf. It uses light, air, moisture, and the material of soil. To say that it uses them is to say that it turns them into means of its own conservation. As long as it is growing, the energy it expends in thus turning the environment to account is more than compensated for by the return it gets: it grows. Understanding the word "control" in this sense, it may be said that a living being is one that subjugates and controls for its own continued activity the energies that would otherwise use it up. Life is a self-renewing process through action upon the environment.
Download or read book Logical Reasoning written by Bradley Harris Dowden and published by Bradley Dowden. This book was released on 1993 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed to engage students' interest and promote their writing abilities while teaching them to think critically and creatively. Dowden takes an activist stance on critical thinking, asking students to create and revise arguments rather than simply recognizing and criticizing them. His book emphasizes inductive reasoning and the analysis of individual claims in the beginning, leaving deductive arguments for consideration later in the course.
Download or read book The History of Mathematical Proof in Ancient Traditions written by Karine Chemla and published by Cambridge University Press. This book was released on 2012-07-05 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.
Download or read book Mathematics and Plausible Reasoning written by George Polya and published by Lushena Books. This book was released on 2023-02-22 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two volume classic comprises two titles: "Patterns of Plausible Inference" and "Induction and Analogy in Mathematics". This is a guide to the practical art of plausible reasoning, particularly in mathematics, but also in every field of human activity. Using mathematics as the example par excellence, Polya shows how even the most rigorous deductive discipline is heavily dependent on techniques of guessing, inductive reasoning, and reasoning by analogy. In solving a problem, the answer must be guessed at before a proof can be given, and guesses are usually made from a knowledge of facts, experience, and hunches. The truly creative mathematician must be a good guesser first and a good prover afterward; many important theorems have been guessed but no proved until much later. In the same way, solutions to problems can be guessed, and a god guesser is much more likely to find a correct solution. This work might have been called "How to Become a Good Guesser."-From the Dust Jacket.
Download or read book Bulletin of the Atomic Scientists written by and published by . This book was released on 1959-02 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Bulletin of the Atomic Scientists is the premier public resource on scientific and technological developments that impact global security. Founded by Manhattan Project Scientists, the Bulletin's iconic "Doomsday Clock" stimulates solutions for a safer world.
Download or read book Against Method written by Paul Feyerabend and published by Verso. This book was released on 1993 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern philosophy of science has paid great attention to the understanding of scientific 'practice', in contrast to concentration on scientific 'method'. Paul Feyerabend's acclaimed work, which has contributed greatly to this new emphasis, shows the deficiencies of some widespread ideas about the nature of knowledge. He argues that the only feasible explanations of scientific successes are historical explanations, and that anarchism must now replace rationalism in the theory of knowledge. The third edition of this classic text contains a new preface and additional reflections at various points in which the author takes account both of recent debates on science and on the impact of scientific products and practices on the human community. While disavowing populism or relativism, Feyerabend continues to insist that the voice of the inexpert must be heard. Thus many environmental perils were first identified by non-experts against prevailing assumptions in the scientific community. Feyerabend's challenging reassessment of scientific claims and understandings are as pungent and timely as ever.
Download or read book CRITIQUE OF IMPURE REASON written by Steven James Bartlett and published by Studies in Theory and Behavior. This book was released on 2021-09-01 with total page 886 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Critique of Impure Reason: Horizons of Possibility and Meaning comprises a major and important contribution to philosophy. It inaugurates a revolutionary paradigm shift in philosophical thought by providing compelling and long-sought-for solutions to a wide range of philosophical problems. In the process, the massive work fundamentally transforms the way in which the concepts of reference, meaning, and possibility are understood. The book includes a Foreword by the celebrated German philosopher and physicist Carl Friedrich von Weizsäcker. In Kant’s Critique of Pure Reason we find an analysis of the preconditions of experience and of knowledge. In contrast, but yet in parallel, the new Critique focuses upon the ways—unfortunately very widespread and often unselfconsciously habitual—in which many of the concepts that we employ conflict with the very preconditions of meaning and of knowledge. This is a book about the boundaries of frameworks and about the unrecognized conceptual confusions in which we become entangled when we attempt to transgress beyond the limits of the possible and meaningful. We tend either not to recognize or not to accept that we all-too-often attempt to trespass beyond the boundaries of the frameworks that make knowledge possible and the world meaningful. The Critique of Impure Reason proposes a bold, ground-breaking, and startling thesis: that a great many of the major philosophical problems of the past can be solved through the recognition of a viciously deceptive form of thinking to which philosophers as well as non-philosophers commonly fall victim. For the first time, the book advances and justifies the criticism that a substantial number of the questions that have occupied philosophers fall into the category of “impure reason,” violating the very conditions of their possible meaningfulness. The purpose of the study is twofold: first, to enable us to recognize the boundaries of what is referentially forbidden—the limits beyond which reference becomes meaningless—and second, to avoid falling victims to a certain broad class of conceptual confusions that lie at the heart of many major philosophical problems. As a consequence, the boundaries of possible meaning are determined. Bartlett, the author or editor of more than 20 books, is responsible for identifying this widespread and delusion-inducing variety of error, metalogical projection. It is a previously unrecognized and insidious form of erroneous thinking that undermines its own possibility of meaning. It comes about as a result of the pervasive human compulsion to seek to transcend the limits of possible reference and meaning. Based on original research and rigorous analysis combined with extensive scholarship, the Critique of Impure Reason develops a self-validating method that makes it possible to recognize, correct, and eliminate this major and pervasive form of fallacious thinking. In so doing, the book provides at last provable and constructive solutions to a wide range of major philosophical problems. CONTENTS AT A GLANCE Preface Foreword by Carl Friedrich von Weizsäcker Acknowledgments Avant-propos: A philosopher’s rallying call Introduction A note to the reader A note on conventions PART I WHY PHILOSOPHY HAS MADE NO PROGRESS AND HOW IT CAN 1 Philosophical-psychological prelude 2 Putting belief in its place: Its psychology and a needed polemic 3 Turning away from the linguistic turn: From theory of reference to metalogic of reference 4 The stepladder to maximum theoretical generality PART II THE METALOGIC OF REFERENCE A New Approach to Deductive, Transcendental Philosophy 5 Reference, identity, and identification 6 Self-referential argument and the metalogic of reference 7 Possibility theory 8 Presupposition logic, reference, and identification 9 Transcendental argumentation and the metalogic of reference 10 Framework relativity 11 The metalogic of meaning 12 The problem of putative meaning and the logic of meaninglessness 13 Projection 14 Horizons 15 De-projection 16 Self-validation 17 Rationality: Rules of admissibility PART III PHILOSOPHICAL APPLICATIONS OF THE METALOGIC OF REFERENCE Major Problems and Questions of Philosophy and the Philosophy of Science 18 Ontology and the metalogic of reference 19 Discovery or invention in general problem-solving, mathematics, and physics 20 The conceptually unreachable: “The far side” 21 The projections of the external world, things-in-themselves, other minds, realism, and idealism 22 The projections of time, space, and space-time 23 The projections of causality, determinism, and free will 24 Projections of the self and of solipsism 25 Non-relational, agentless reference and referential fields 26 Relativity physics as seen through the lens of the metalogic of reference 27 Quantum theory as seen through the lens of the metalogic of reference 28 Epistemological lessons learned from and applicable to relativity physics and quantum theory PART IV HORIZONS 29 Beyond belief 30 Critique of Impure Reason: Its results in retrospect SUPPLEMENT The Formal Structure of the Metalogic of Reference APPENDIX I: The Concept of Horizon in the Work of Other Philosophers APPENDIX II: Epistemological Intelligence References Index About the author
Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Download or read book Humanizing Mathematics and its Philosophy written by Bharath Sriraman and published by Birkhäuser. This book was released on 2017-11-07 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume: Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians? Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data processing and scientific computing? The essays also offer glimpses into Reuben’s fertile mind and his lasting influence on the mathematical community, as well as revealing the diverse roots, obstacles and philosophical dispositions that characterize the working lives of mathematicians. With contributions from a veritable “who’s who” list of 20th century luminaries from mathematics and philosophy, as well as from Reuben himself, this volume will appeal to a wide variety of readers from curious undergraduates to prominent mathematicians.
Download or read book The Principles of Mathematics written by Bertrand Russell and published by W. W. Norton & Company. This book was released on 1996 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical--that what is commonly called mathematics is simply later deductions from logical premises.
