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Books > Science & Mathematics > Mathematics > Philosophy of mathematics

The Routledge Companion to Philosophy of Physics (Hardcover): Eleanor Knox, Alastair Wilson The Routledge Companion to Philosophy of Physics (Hardcover)
Eleanor Knox, Alastair Wilson
R6,653 Discovery Miles 66 530 Ships in 12 - 19 working days

The Routledge Companion to Philosophy of Physics is a comprehensive and authoritative guide to the state of the art in the philosophy of physics. It comprisess 54 self-contained chapters written by leading philosophers of physics at both senior and junior levels, making it the most thorough and detailed volume of its type on the market - nearly every major perspective in the field is represented. The Companion's 54 chapters are organized into 12 parts. The first seven parts cover all of the major physical theories investigated by philosophers of physics today, and the last five explore key themes that unite the study of these theories. I. Newtonian Mechanics II. Special Relativity III. General Relativity IV. Non-Relativistic Quantum Theory V. Quantum Field Theory VI. Quantum Gravity VII. Statistical Mechanics and Thermodynamics VIII. Explanation IX. Intertheoretic Relations X. Symmetries XI. Metaphysics XII. Cosmology The difficulty level of the chapters has been carefully pitched so as to offer both accessible summaries for those new to philosophy of physics and standard reference points for active researchers on the front lines. An introductory chapter by the editors maps out the field, and each part also begins with a short summary that places the individual chapters in context. The volume will be indispensable to any serious student or scholar of philosophy of physics.

Recursive Functions and Metamathematics - Problems of Completeness and Decidability, Goedel's Theorems (Hardcover, 1999... Recursive Functions and Metamathematics - Problems of Completeness and Decidability, Goedel's Theorems (Hardcover, 1999 ed.)
Roman Murawski
R5,014 R4,667 Discovery Miles 46 670 Save R347 (7%) Ships in 12 - 19 working days

Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then G del's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science.

Metametaphysics and the Sciences - Historical and Philosophical Perspectives (Paperback): Frode Kjosavik, Camilla Serck-Hanssen Metametaphysics and the Sciences - Historical and Philosophical Perspectives (Paperback)
Frode Kjosavik, Camilla Serck-Hanssen
R1,415 Discovery Miles 14 150 Ships in 12 - 19 working days

This collection addresses metaphysical issues at the intersection between philosophy and science. A unique feature is the way in which it is guided both by history of philosophy, by interaction between philosophy and science, and by methodological awareness. In asking how metaphysics is possible in an age of science, the contributors draw on philosophical tools provided by three great thinkers who were fully conversant with and actively engaged with the sciences of their day: Kant, Husserl, and Frege. Part I sets out frameworks for scientifically informed metaphysics in accordance with the meta-metaphysics outlined by these three self-reflective philosophers. Part II explores the domain for co-existent metaphysics and science. Constraints on ambitious critical metaphysics are laid down in close consideration of logic, meta-theory, and specific conditions for science. Part III exemplifies the role of language and science in contemporary metaphysics. Quine's pursuit of truth is analysed; Cantor's absolute infinitude is reconstrued in modal terms; and sense is made of Weyl's take on the relationship between mathematics and empirical aspects of physics. With chapters by leading scholars, Metametaphysics and the Sciences is an in-depth resource for researchers and advanced students working within metaphysics, philosophy of science, and the history of philosophy.

Philosophy's Loss of Logic to Mathematics - An Inadequately Understood Take-Over (Hardcover, 1st ed. 2018): Woosuk Park Philosophy's Loss of Logic to Mathematics - An Inadequately Understood Take-Over (Hardcover, 1st ed. 2018)
Woosuk Park
R2,643 Discovery Miles 26 430 Ships in 10 - 15 working days

This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege's logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand Tarski's and Goedel's work, explaining why the problems they discussed are still unsolved. Finally, the book reports on some of the most influential positions in contemporary philosophy of mathematics, i.e., Maddy's mathematical naturalism and Shapiro's mathematical structuralism. Last but not least, the book introduces Biancani's Aristotelian philosophy of mathematics as this is considered important to understand current philosophical issue in the applications of mathematics. One of the main purposes of the book is to stimulate readers to reconsider the Aristotelian position, which disappeared almost completely from the scene in logic and mathematics in the early twentieth century.

The Oxford Handbook of the History of Mathematics (Hardcover, New): Eleanor Robson, Jacqueline Stedall The Oxford Handbook of the History of Mathematics (Hardcover, New)
Eleanor Robson, Jacqueline Stedall
R4,461 Discovery Miles 44 610 Ships in 12 - 19 working days

This Handbook explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practice it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematical practitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence is drawn upon as well as an unusual array of textual sources. Further, the ways in which people have chosen to express themselves are as historically meaningful as the contents of the mathematics they have produced. Mathematics is not a fixed and unchanging entity. New questions, contexts, and applications all influence what counts as productive ways of thinking. Because the history of mathematics should interact constructively with other ways of studying the past, the contributors to this book come from a diverse range of intellectual backgrounds in anthropology, archaeology, art history, philosophy, and literature, as well as history of mathematics more traditionally understood.
The thirty-six self-contained, multifaceted chapters, each written by a specialist, are arranged under three main headings: 'Geographies and Cultures', 'Peoples and Practices', and 'Interactions and Interpretations'. Together they deal with the mathematics of 5000 years, but without privileging the past three centuries, and an impressive range of periods and places with many points of cross-reference between chapters. The key mathematical cultures of North America, Europe, the Middle East, India, and China are all represented here as well as areas which are not often treated in mainstream history of mathematics, such as Russia, the Balkans, Vietnam, and South America. This Handbook will be a vital reference for graduates and researchers in mathematics, historians of science, and general historians.

Presuppostion & Transcendental Inference (Paperback): Humphrey Palmer Presuppostion & Transcendental Inference (Paperback)
Humphrey Palmer
R761 Discovery Miles 7 610 Ships in 12 - 19 working days

Originally published in 1985. This book is about a single famous line of argument, pioneered by Descartes and deployed to full effect by Kant. That argument was meant to refute scepticism once and for all, and make the world safe for science. 'I think, so I exist' is valid reasoning, but circular as proof. In similar vein, Kant argues from our having a science of geometry to Space being our contribution to experience: a different conclusion, arrived at by a similar fallacy. Yet these arguments do show something: that certain sets of opinions, if professed, show an inbuilt inconsistency. It is this second-strike capacity that has kept transcendental arguments going for so long. Attempts to re-build metaphysics by means of such transcendental reasoning have been debated. This book offers an introduction to the field, and ventures its own assessment, in non-technical language, without assuming previous training in logic or philosophy.

Monthly Problem Gems (Hardcover): Hongwei Chen Monthly Problem Gems (Hardcover)
Hongwei Chen
R5,544 Discovery Miles 55 440 Ships in 12 - 19 working days

This book is an outgrowth of a collection of sixty-two problems offered in the The American Mathematical Monthly (AMM) the author has worked over the last two decades. Each selected problem has a central theme, contains gems of sophisticated ideas connected to important current research, and opens new vistas in the understanding of mathematics. The AMM problem section provides one of the most challenging and interesting problem sections among the various journals and online sources currently available. The published problems and solutions have become a treasure trove rife with mathematical gems. The author presents either his published solution in the AMM or an alternative solution to the published one to present and develop problem-solving techniques. A rich glossary of important theorems and formulas is included for easy reference. The reader may regard this book as a starter set for AMM problems, providing a jumping of point to new ideas, and extending their personal lexicon of problems and solutions. This collection is intended to encourage the reader to move away from routine exercises toward creative solutions, as well as offering the reader a systematic illustration of how to organize the transition from problem solving to exploring, investigating and discovering new results.

Leibniz's Legacy and Impact (Paperback): Julia Weckend, Lloyd Strickland Leibniz's Legacy and Impact (Paperback)
Julia Weckend, Lloyd Strickland
R1,419 Discovery Miles 14 190 Ships in 12 - 19 working days

This volume tells the story of the legacy and impact of the great German polymath Gottfried Wilhelm Leibniz (1646-1716). Leibniz made significant contributions to many areas, including philosophy, mathematics, political and social theory, theology, and various sciences. The essays in this volume explores the effects of Leibniz's profound insights on subsequent generations of thinkers by tracing the ways in which his ideas have been defended and developed in the three centuries since his death. Each of the 11 essays is concerned with Leibniz's legacy and impact in a particular area, and between them they show not just the depth of Leibniz's talents but also the extent to which he shaped the various domains to which he contributed, and in some cases continues to shape them today. With essays written by experts such as Nicholas Jolley, Pauline Phemister, and Philip Beeley, this volume is essential reading not just for students of Leibniz but also for those who wish to understand the game-changing impact made by one of history's true universal geniuses.

Understanding Perspectivism - Scientific Challenges and Methodological Prospects (Paperback): Michela Massimi, Casey D. McCoy Understanding Perspectivism - Scientific Challenges and Methodological Prospects (Paperback)
Michela Massimi, Casey D. McCoy
R1,401 Discovery Miles 14 010 Ships in 12 - 19 working days

This edited collection is the first of its kind to explore the view called perspectivism in philosophy of science. The book brings together an array of essays that reflect on the methodological promises and scientific challenges of perspectivism in a variety of fields such as physics, biology, cognitive neuroscience, and cancer research, just as a few examples. What are the advantages of using a plurality of perspectives in a given scientific field and for interdisciplinary research? Can different perspectives be integrated? What is the relation between perspectivism, pluralism, and pragmatism? These ten new essays by top scholars in the field offer a polyphonic journey towards understanding the view called 'perspectivism' and its relevance to science.

Monthly Problem Gems (Paperback): Hongwei Chen Monthly Problem Gems (Paperback)
Hongwei Chen
R945 Discovery Miles 9 450 Ships in 12 - 19 working days

This book is an outgrowth of a collection of sixty-two problems offered in the The American Mathematical Monthly (AMM) the author has worked over the last two decades. Each selected problem has a central theme, contains gems of sophisticated ideas connected to important current research, and opens new vistas in the understanding of mathematics. The AMM problem section provides one of the most challenging and interesting problem sections among the various journals and online sources currently available. The published problems and solutions have become a treasure trove rife with mathematical gems. The author presents either his published solution in the AMM or an alternative solution to the published one to present and develop problem-solving techniques. A rich glossary of important theorems and formulas is included for easy reference. The reader may regard this book as a starter set for AMM problems, providing a jumping of point to new ideas, and extending their personal lexicon of problems and solutions. This collection is intended to encourage the reader to move away from routine exercises toward creative solutions, as well as offering the reader a systematic illustration of how to organize the transition from problem solving to exploring, investigating and discovering new results.

Truth, Existence and Explanation - FilMat 2016 Studies in the Philosophy of Mathematics (Hardcover, 1st ed. 2018): Mario... Truth, Existence and Explanation - FilMat 2016 Studies in the Philosophy of Mathematics (Hardcover, 1st ed. 2018)
Mario Piazza, Gabriele Pulcini
R3,393 Discovery Miles 33 930 Ships in 10 - 15 working days

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.

Aspects of a Theory of Singular Reference - Prolegomena to a Dialectical Logic of Singular Terms (Paperback): William J.... Aspects of a Theory of Singular Reference - Prolegomena to a Dialectical Logic of Singular Terms (Paperback)
William J. Greenberg
R703 Discovery Miles 7 030 Ships in 12 - 19 working days

Originally published in 1985. This study concerns the problem of treating identity as a relation between an object and itself. It addresses the Russellian and Fregean solutions and goes on to present in the first part a surfacist account of belief-context ambiguity requiring neither differences in relative scope nor distinctions between sense and reference. The second part offers an account of negative existentials, necessity and identity-statements which resolves problems unlike the Russell-Frege analyses. This is a detailed work in linguistics and philosophy.

An Introduction to Many-valued Logics (Paperback): Robert Ackermann An Introduction to Many-valued Logics (Paperback)
Robert Ackermann
R1,085 Discovery Miles 10 850 Ships in 12 - 19 working days

Originally published in 1967. An introduction to the literature of nonstandard logic, in particular to those nonstandard logics known as many-valued logics. Part I expounds and discusses implicational calculi, modal logics and many-valued logics and their associated calculi. Part II considers the detailed development of various many-valued calculi, and some of the important metathereoms which have been proved for them. Applications of the calculi to problems in the philosophy are also surveyed. This work combines criticism with exposition to form a comprehensive but concise survey of the field.

Nondeductive Inference (Paperback): Robert Ackermann Nondeductive Inference (Paperback)
Robert Ackermann
R1,083 Discovery Miles 10 830 Ships in 12 - 19 working days

Originally published in 1966. An introduction to current studies of kinds of inference in which validity cannot be determined by ordinary deductive models. In particular, inductive inference, predictive inference, statistical inference, and decision making are examined in some detail. The last chapter discusses the relationship of these forms of inference to philosophical notions of rationality. Special features of the monograph include a discussion of the legitimacy of various criteria for successful predictive inference, the development of an intuitive model which exhibits the difficulties of choosing probability measures over infinite sets, and a comparison of rival views on the foundations of probability in terms of the amount of information which the members of these schools believe suitable for fruitful formalization. The bibliographies include articles by statisticians accessible to students of symbolic logic.

The Logical Structure of Science (Paperback): A. Cornelius Benjamin The Logical Structure of Science (Paperback)
A. Cornelius Benjamin
R1,181 Discovery Miles 11 810 Ships in 12 - 19 working days

This book addresses the argument in the history of the philosophy of science between the positivists and the anti-positivists. The author starts from a point of firm conviction that all science and philosophy must start with the given... But that the range of the given is not definite. He begins with an examination of science from the outside and then the inside, explaining his position on metaphysics and attempts to formulate the character of operational acts before a general theory of symbolism is explored. The last five chapters constitute a treatise to show that the development from one stage of symbolismto the next is inevitable, consequently that explanatory science represents the culmination of knowledge.

Quantification Theory (Paperback): J.A. Faris Quantification Theory (Paperback)
J.A. Faris
R1,084 Discovery Miles 10 840 Ships in 12 - 19 working days

Originally published in 1964. This book is concerned with general arguments, by which is meant broadly arguments that rely for their force on the ideas expressed by all, every, any, some, none and other kindred words or phrases. A main object of quantificational logic is to provide methods for evaluating general arguments. To evaluate a general argument by these methods we must first express it in a standard form. Quantificational form is dealt with in chapter one and in part of chapter three; in the remainder of the book an account is given of methods by which arguments when formulated quantificationally may be tested for validity or invalidity. Some attention is also paid to the logic of identity and of definite descriptions. Throughout the book an attempt has been made to give a clear explanation of the concepts involved and the symbols used; in particular a step-by-step and partly mechanical method is developed for translating complicated statements of ordinary discourse into the appropriate quantificational formulae. Some elementary knowledge of truth-functional logic is presupposed.

The Implications of Induction (Paperback): L. Jonathan Cohen The Implications of Induction (Paperback)
L. Jonathan Cohen
R1,096 Discovery Miles 10 960 Ships in 12 - 19 working days

Originally published in 1973. This book presents a valid mode of reasoning that is different to mathematical probability. This inductive logic is investigated in terms of scientific investigation. The author presents his criteria of adequacy for analysing inductive support for hypotheses and discusses each of these criteria in depth. The chapters cover philosophical problems and paradoxes about experimental support, probability and justifiability, ending with a system of logical syntax of induction. Each section begins with a summary of its contents and there is a glossary of technical terms to aid the reader.

The Incommensurability Thesis (Paperback): Howard Sankey The Incommensurability Thesis (Paperback)
Howard Sankey
R1,105 Discovery Miles 11 050 Ships in 12 - 19 working days

Originally published in 1994, The Incommensurability Thesis is a critical study of the Incommensurability Thesis of Thomas Kuhn and Paul Feyerabend. The book examines the theory that different scientific theories may be incommensurable because of conceptual variance. The book presents a critique of the thesis and examines and discusses the arguments for the theory, acknowledging and debating the opposing views of other theorists. The book provides a comprehensive and detailed discussion of the incommensurability thesis.

Modes of Truth - The Unified Approach to Truth, Modality, and Paradox (Hardcover): Carlo Nicolai, Johannes Stern Modes of Truth - The Unified Approach to Truth, Modality, and Paradox (Hardcover)
Carlo Nicolai, Johannes Stern
R4,490 Discovery Miles 44 900 Ships in 12 - 19 working days

The aim of this volume is to open up new perspectives and to raise new research questions about a unified approach to truth, modalities, and propositional attitudes. The volume's essays are grouped thematically around different research questions. The first theme concerns the tension between the theoretical role of the truth predicate in semantics and its expressive function in language. The second theme of the volume concerns the interaction of truth with modal and doxastic notions. The third theme covers higher-order solutions to the semantic and modal paradoxes, providing an alternative to first-order solutions embraced in the first two themes. This book will be of interest to researchers working in epistemology, logic, philosophy of logic, philosophy of language, philosophy of mathematics, and semantics. The Open Access version of this book, available at www.taylorfrancis.com, has been made available under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license.

Truth-Functional Logic (Paperback): J.A. Faris Truth-Functional Logic (Paperback)
J.A. Faris
R1,082 Discovery Miles 10 820 Ships in 12 - 19 working days

Originally published in 1962. This book gives an account of the concepts and methods of a basic part of logic. In chapter I elementary ideas, including those of truth-functional argument and truth-functional validity, are explained. Chapter II begins with a more comprehensive account of truth-functionality; the leading characteristics of the most important monadic and dyadic truth-functions are described, and the different notations in use are set forth. The main part of the book describes and explains three different methods of testing truth-functional aguments and agument forms for validity: the truthtable method, the deductive method and the method of normal forms; for the benefit mainly of readers who have not acquired in one way or another a general facility in the manipulation of symbols some of the procedures have been described in rather more detail than is common in texts of this kind. In the final chapter the author discusses and rejects the view, based largely on the so called paradoxes of material implication, that truth-functional logic is not applicable in any really important way to arguments of ordinary discourse.

The Logic of Choice - An Investigation of the Concepts of Rule and Rationality (Paperback): Gidon Gottlieb The Logic of Choice - An Investigation of the Concepts of Rule and Rationality (Paperback)
Gidon Gottlieb
R1,098 Discovery Miles 10 980 Ships in 12 - 19 working days

Originally published in 1968. This is a critical study of the concept of 'rule' featuring in law, ethics and much philosophical analysis which the author uses to investigate the concept of 'rationality'. The author indicates in what manner the modes of reasoning involved in reliance upon rules are unique and in what fashion they provide an alternative both to the modes of logico-mathematical reasoning and to the modes of scientific reasoning. This prepares the groundwork for a methodology meeting the requirements of the fields using rules such as law and ethics which could be significant for communications theory and the use of computers in normative fields. Other substantive issues related to the mainstream of legal philosophy are discussed - theories of interpretation, the notion of purpose and the requirements of principled decision-making. The book utilizes examples drawn from English and American legal decisions to suggest how the positions of legal positivism and of natural law are equally artificial and misleading.

Topics in Modern Logic (Paperback): D.C. Makinson Topics in Modern Logic (Paperback)
D.C. Makinson
R1,088 Discovery Miles 10 880 Ships in 12 - 19 working days

Originally published in 1973. This book is directed to the student of philosophy whose background in mathematics is very limited. The author strikes a balance between material of a philosophical and a formal kind, and does this in a way that will bring out the intricate connections between the two. On the formal side, he gives particular care to provide the basic tools from set theory and arithmetic that are needed to study systems of logic, setting out completeness results for two, three, and four valued logic, explaining concepts such as freedom and bondage in quantificational logic, describing the intuitionistic conception of the logical operators, and setting out Zermelo's axiom system for set theory. On the philosophical side, he gives particular attention to such topics as the problem of entailment, the import of the Loewenheim-Skolem theorem, the expressive powers of quantificational logic, the ideas underlying intuitionistic logic, the nature of set theory, and the relationship between logic and set theory. There are exercises within the text, set out alongside the theoretical ideas that they involve.

The Development of Mathematical Logic (Paperback): P.H. Nidditch The Development of Mathematical Logic (Paperback)
P.H. Nidditch
R1,085 Discovery Miles 10 850 Ships in 12 - 19 working days

Originally published in 1962. A clear and simple account of the growth and structure of Mathematical Logic, no earlier knowledge of logic being required. After outlining the four lines of thought that have been its roots - the logic of Aristotle, the idea of all the parts of mathematics as systems to be designed on the same sort of plan as that used by Euclid and his Elements, and the discoveries in algebra and geometry in 1800-1860 - the book goes on to give some of the main ideas and theories of the chief writers on Mathematical Logic: De Morgan, Boole, Jevons, Pierce, Frege, Peano, Whitehead, Russell, Post, Hilbert and Goebel. Written to assist readers who require a general picture of current logic, it will also be a guide for those who will later be going more deeply into the expert details of this field.

The Logic of Commands (Paperback): Nicholas Rescher The Logic of Commands (Paperback)
Nicholas Rescher
R1,126 Discovery Miles 11 260 Ships in 12 - 19 working days

Originally published in 1966. Professor Rescher's aim is to develop a "logic of commands" in exactly the same general way which standard logic has already developed a "logic of truth-functional statement compounds" or a "logic of quantifiers". The object is to present a tolerably accurate and precise account of the logically relevant facets of a command, to study the nature of "inference" in reasonings involving commands, and above all to establish a viable concept of validity in command inference, so that the logical relationships among commands can be studied with something of the rigour to which one is accustomed in other branches of logic.

The Province of Logic - An Interpretation of Certain Parts of Cook Wilson's "Statement and Inference" (Paperback): Richard... The Province of Logic - An Interpretation of Certain Parts of Cook Wilson's "Statement and Inference" (Paperback)
Richard Robinson
R1,159 Discovery Miles 11 590 Ships in 12 - 19 working days

Originally published in 1931. This inquiry investigates and develops John Cook Wilson's view of the province of logic. It bases the study on the posthumous collected papers Statement and Inference. The author seeks to answer questions on the nature of logic using Cook Wilson's thought. The chapters introduce and consider topics from metaphysics to grammar and from psychology to knowledge. An early conception of logic in the sciences and presenting the work of an important twentieth century philosopher, this is an engaging work.

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