Philosophy of mathematics Books
Princeton University Press The Language of Mathematics
Book Synopsis
£19.80
Princeton University Press Tales of Impossibility
Book SynopsisTrade Review"I greatly enjoyed Richeson's Tales of Impossibility. It deserves to become a classic and can be highly recommended."---Robin Wilson, Times Higher Education"Even if you never read a single proof through to its conclusion, you’ll enjoy the many entertaining side trips into a geometry far beyond what you learned in high school."---Jim Stein, New Books in Mathematics"The whole book, both informative and amusing, is a highly recommended read."---Adhemar Bulteel, European Mathematical Society"This book was a pleasure to read and I would recommend it for anybody who wants a lovely overview of many areas of the history of mathematics, with a focus on some very easy to understand problems."---Jonathan Shock, Mathemafrica"Richeson clearly explains what it means to be impossible to solve a problem, cites other impossibility results, goes into detail about geometric constructions with various instruments, and discusses the defective proofs and the cranks that have turned up along the way." * Mathematics Magazine *"This fascinating text will appeal to all those interested in the history of mathematics, not leasy because of its helpful notes on each chapter and its two dozen pages of references for further reading"---Laurence E. Nicholas CMath FIMA, Mathematics Today"A fact-filled, insightful, panoramic view of how mathematics developed to what it is today transformed by folks thinking both inside and outside of G so as to resolve the impossible."---Andrew J. Simoson, Mathematical Intelligencer
£21.25
Penguin Books Ltd The Ten Equations that Rule the World
Book SynopsisTHE INTERNATIONAL BESTSELLER''An entertaining tour that will change how you see the world'' Sean Carroll, author of Something Deeply HiddenIs there a secret formula for improving your life? For making something a viral hit? For deciding how long to stick with your current job, Netflix series, or even relationship?This book is all about the equations that make our world go round. Ten of them, in fact. They are integral to everything from investment banking to betting companies and social media giants. And they can help you to increase your chance of success, guard against financial loss, live more healthily and see through scaremongering. They are known only by mathematicians - until now.With wit and clarity, mathematician David Sumpter shows that it isn''t the technical details which make these formulas so successful. It is the way they allow mathematicians to view problems from a different angle - a way of seeing the world that anyone cTrade ReviewSometimes books about numbers come along and we're so ecstatic that we just pop with delight. One such book is The Ten Equations that Rule The World -- Tim Harford * More or Less BBC4 *Hugely entertaining, erudite and at times genuinely witty . . . it's nice to be spoken to in grown-up language by a genius. You will come away from Sumpter's book with a much clearer idea of why the world is less messy than it appears * E&T Magazine *These aren't the equations of Newton or Einstein -- crisp relations describing the evolution of a clockwork universe. These are the equations of randomness, expectation, and imperfect information. The equations, in other words, of the real world. David Sumpter provides an entertaining tour that will change how you see the world -- Sean Carroll author of Something Deeply HiddenSumpter writes fascinatingly about his experiences as a consulting mathematician. . . I will encourage my mathematics undergraduates to read this book since it will inspire them by showing the relevance of mathematics to today's world and make them think about the moral issues they will face as mathematicians * Times Higher Education *
£10.44
Penguin Putnam Inc A Beautiful Question
Book SynopsisDoes the universe embody beautiful ideas? Artists as well as scientists throughout human history have pondered this “beautiful question.” With Nobel laureate Frank Wilczek as your guide, embark on a voyage of related discoveries, from Plato and Pythagoras up to the present. Wilczek’s groundbreaking work in quantum physics was inspired by his intuition to look for a deeper order of beauty in nature. This is the deep logic of the universe—and it is no accident that it is also at the heart of what we find aesthetically pleasing and inspiring. Wilczek is hardly alone among great scientists in charting his course using beauty as his compass. As he reveals in A Beautiful Question, this has been the heart of scientific pursuit from Pythagoras and the ancient belief in the music of the spheres to Galileo, Newton, Maxwell, Einstein, and into the deep waters of twentieth-century physics. Wilczek brings us right to the edge of knowledge today, where the core insights of even the craziest quantum ideas apply principles we all understand. The equations for atoms and light are almost the same ones that govern musical instruments and sound; the subatomic particles that are responsible for most of our mass are determined by simple geometric symmetries. Gorgeously illustrated, A Beautiful Question is a mind-shifting book that braids the age-old quest for beauty and the age-old quest for truth into a thrilling synthesis. It is a dazzling and important work from one of our best thinkers, whose humor and infectious sense of wonder animate every page. Yes: The world is a work of art, and its deepest truths are ones we already feel, as if they were somehow written in our souls.
£15.00
Oxford University Press Gödels Theorem A Very Short Introduction Very
Book SynopsisWhen Kurt Gödel published his celebrated theorem, showing that no axiomatization can determine the whole truth and nothing but the truth concerning arithmetic, it had a profound impact on mathematical ideas and philosophical thought. Adrian Moore places the theorem in its intellectual and historical context, explaining the key concepts and misunderstandings.
£9.49
Oxford University Press Fundamentals of Bayesian Epistemology 2 Arguments
Book SynopsisBayesian ideas have recently been applied across such diverse fields as philosophy, statistics, economics, psychology, artificial intelligence, and legal theory. Fundamentals of Bayesian Epistemology examines epistemologists'' use of Bayesian probability mathematics to represent degrees of belief. Michael G. Titelbaum provides an accessible introduction to the key concepts and principles of the Bayesian formalism, enabling the reader both to follow epistemological debates and to see broader implicationsVolume 1 begins by motivating the use of degrees of belief in epistemology. It then introduces, explains, and applies the five core Bayesian normative rules: Kolmogorov''s three probability axioms, the Ratio Formula for conditional degrees of belief, and Conditionalization for updating attitudes over time. Finally, it discusses further normative rules (such as the Principal Principle, or indifference principles) that have been proposed to supplement or replace the core five.Volume 2 gives arguments for the five core rules introduced in Volume 1, then considers challenges to Bayesian epistemology. It begins by detailing Bayesianism''s successful applications to confirmation and decision theory. Then it describes three types of arguments for Bayesian rules, based on representation theorems, Dutch Books, and accuracy measures. Finally, it takes on objections to the Bayesian approach and alternative formalisms, including the statistical approaches of frequentism and likelihoodism.Trade ReviewMichael G. Titelbaum provides an accessible introduction to the key concepts and principles of the Bayesian formalism, enabling the reader both to follow epistemological debates and to see broader implications * MathSciNet *Table of ContentsIII Applications 6: Confirmation 7: Decision Theory IV Arguments for Bayesianism 8: Representation Theorems 9: Dutch Book Arguments 10: Accuracy Arguments Challenges and Objections 11: Memory Loss and Self-Location 12: Old Evidence, Logical Omniscience 13: Alternatives to Bayesianism 14: Comparisons, Ranges, Dempster-Shafer
£40.54
Oxford University Press Consequence Relations An Introduction to the
Book SynopsisAn in-depth study of the concept of a consequence relation, culminating in the concept of a Lindenbaum-Tarski algebra, intended for advanced undergraduate and graduate students in mathematics and philosophy, as well as researchers in the field of mathematical and philosophical logic.Table of Contents1: Introduction 2: Preliminaries 3: Sentential Formal Languages 4: Logical Consequences 5: Matrix Consequences 6: Unital Abstract Logics 7: Equational Consequence 8: Equational L-Consequence 9: Q-Consequence 10: Decidability Bibliography Index
£89.77
OUP USA The Mystery of Numbers
Book SynopsisWhy is the number seven lucky - even holy - in almost every culture? Why do we speak of the four corners of the earth? Why do cats have nine lives (except in Iran, where they have seven)? From literature to folklore to private superstitions, numbers play a conspicuous role in our daily lives. In The Mystery of Numbers Annemarie Schimmel conducts an illuminating tour of the mysteries attributed to numbers over the centuries. She covers the origins of numbers, the symbolism of numbers, the source of this symbolism, and examines individual numbers from one to ten thousand. Using examples ranging from the Bible to Shakespeare, this engaging account uncovers the roots of a phenomenon we all feel every Friday the thirteenth.Trade ReviewA delightful, cross-cultural romp, through the history of number mysticism... * The New York Times Book Review *Table of ContentsIntroduction; Number and number systems; The heritage of the Pythagoreans; Gnosis and Cabala; Islamic mysticism; Medieval and baroque number symbolism; Superstitions; Number games and magic squares; Little dictionary of numbers; Bibliography; Illustration credits.
£18.89
Oxford University Press Philosophy of Mathematics
Book SynopsisDo numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematicTrade ReviewExtremely interesting and deserves the attention of anyone with a serious interest in the field ... a careful study of the book will be enormously rewarding to anyone with some prior exposure to the field. * Philosophia Mathematica *
£30.17
Oxford University Press Mathematics and the Roots of Postmodern Thought
Book SynopsisThis is a charming and insightful contribution to an understanding of the Science Wars between postmodernist humanism and science, driving toward a resolution of the mutual misunderstanding that has driven the controversy. It traces the root of postmodern theory to a debate on the foundations of mathematics, early in the 20th century then compares developments in mathematics to what took place in the arts and humanities, discussing issues as diverse as literary theory, arts, and artificial intelligence. This is a straight forward, easily understood presentation of what can be difficult theoretical concepts and demonstrates that a pattern of misreading mathematics can be seen on both the part of science and on the part of postmodern thinking. This is a humorous, playful yet deeply serious look at the intellectual foundations of mathematics for those in the humanities and is the perfect critical introduction to the bases of modernism and postmodernism for those in the sciences.Trade ReviewThe book makes pleasant and interesting reading. * Mathematical Reviews *Table of Contents1: Introduction 2: Around the Cartesian Circuit 2.1: Imagination 2.2: Intuition 2.3: Counting to One 3: Space Oddity and Linguistic Turn 4: Wound of Language 4.1: Being and Time Continuum 4.2: Language and Will 5: Beyond the Code 5.1: Medium of Free Becoming 5.2: Nonpresence of Identity 6: The Expired Subject 6.1: Empire of Signs 6.2: Mechanical Bride 7: The Vanishing Author 8: Say Hello to the Structure Bubble 8.1: Algebra of Language 8.2: Functionalism Chic 9: Don't Think, Look 9.1: Interpolating the Self 9.2: Language Games 9.3: Thermostats "R" Us 10: Postmodern Enigmas 10.1: Unspeakable Diffd'erance 10.2: Dysfunctionalism Chic Notes Select Bibliography Index
£23.39
Oxford University Press Platonism and AntiPlatonism in Mathematics
Book SynopsisIn this deft and vigorous book, Mark Balaguer demonstrates that there are no good arguments for or against mathematical platonism (i.e., the view that abstract, or non-spatio-temporal, mathematical objects exist, and that mathematical theories are descriptions of such objects). Balaguer does this by establishing that both platonism and anti-platonism are defensible positions. In Part I, he shows that the former is defensible by introducing a novel version of platonism, which he calls full-blooded platonism, or FBP. He argues that if platonists endorse FBP, they can then solve all of the problems traditionally associated with their view, most notably the two Benacerrafian problems (that is, the epistemological problem and the non-uniqueness problem). In Part II, Balaguer defends anti-platonism (in particular, mathematical fictionalism) against various attacks, chief among them the Quine-Putnam indispensability argument. Balaguer''s version of fictionalism bears similarities to Hartry FiTrade Reviewexcellent book...exceptionally clear, insightful, and useful critical surve? * The Review of Modern Logic Platonism and anti-platonism in mathematics is an impressive work. Balaguer presents forceful arguments for the viability of both FBP and fictionalism, and against the feasibility of any substantially different Platonist or anti-Platonist position. ... an admirable achievement.The Bulletin of Symbolic Logic *excellent book...exceptionally clear, insightful, and useful critical survey. * The Review of Modern Logic *Platonism and anti-platonism in mathematics is an impressive work. Balaguer presents forceful arguments for the viability of both FBP and fictionalism, and against the feasibility of any substantially different Platonist or anti-Platonist position. ... an admirable achievement. * The Bulletin of Symbolic Logic *
£33.14
Oxford University Press Collected Works
Book SynopsisKurt Gödel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein''s equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought and accomplishment. The first two volumes were devoted to Gödel''s publications in full (both in original and translation), and the third volume featured a wide selection of unpublished articles and lecture texts found in Gödel''s Nachlass. These long-awaited final two volumes contain Gödel''s corTrade ReviewThe whole enterprise is superbly coordinated and assembled under the direction of Solomon Feferman ... The book is a tour de force and a labour of love. Superbly crafted and presented, what a bargain, given the many gems it contains! * The Mathematical Gazette *The books are carefully and beautifully produced and offer rich material, illuminating not only the outstanding work of Gödel, but also the whole mathematical logic of the twentieth century, including some philosophical and historical aspects. * EMS *Table of ContentsGödel's life and workSolomon Feferman: A Gödel chronologyJohn W. Dawson, Jr.: Gödel 1929: Introductory note to 1929, 1930 and 1930aBurton Dreben and Jean van Heijenoort: Über die Vollständigkeit des Logikkalküls On the completeness of the calculus of logic Gödel 1930: (See introductory note under Gödel 1929.) Die Vollständigkeit der Axiome des logischen Funktionenkalküls The completeness of the axioms of the functional calculus of logic Gödel 1930a: (See introductory note under Gödel 1929.) Über die Vollständigkeit des Logikkalküls On the completeness of the calculus of logic Gödel 1930b: Introductory note to 1930b, 1931 and 1932bStephen C. Kleene: Einige metamathematische Resultate über Entscheidungs-definitheit und Widerspruchsfreiheit Some metamathematical results on completeness and consistency Gödel 1931: (See introductory note under Gödel 1930b.) Über formal unentscheidbare Sätze der Principia mathematica und verwandter Systeme I On formally undecidable propositions of Principia mathematica and related systems I Gödel 1931a: Introductory note to 1931a, 1932e, f and gJohn W. Dawson, Jr.: Diskussion zur Grundlegung der Mathematik Discussion on providing a foundation for mathematics Gödel 1931b: Review of Neder 1931 Gödel 1931c: Introductory note to 1931cSolomon Feferman: Review of Hilbert 1931 Gödel 1931d: Review of Betsch 1926 Gödel 1931e: Review of Becker 1930 Gödel 1931f: Review of Hasse and Scholz 1928 Gödel 1931g: Review of von Juhos 1930 Gödel 1932: Introductory note to 1932A. S. Troelstra: Zum intuitionistischen aussagenkalkül On the intuitionistic propositional calculus Gödel 1932a: Introductory note to 1932a, 1933i and lWarren D. Goldfarb: Ein Spezialfall des Enscheidungsproblems der theoretischen Logik A special case of the decision problem for theoretical logic Gödel 1932b: (See introductory note under Gödel 1930b.) Über Vollständigkeit und Widerspruchsfreiheit On completeness and consistency Gödel 1932c: Introductory note to 1932cW. V. Quine: Eine Eigenschaft der Realisierungen des Aussagenkalküls A property of the realizations of the propositional calculus Gödel 1932d: Review of Skolem 1931 Gödel 1932e: (See introductory note under Gödel 1931a.) Review of Carnap 1931 Gödel 1932f: (See introductory note under Gödel 1931a.) Review of Heyting 1931 Gödel 1932g: (See introductory note under Gödel 1931a.) Review of von Neumann 1931 Gödel 1932h: Review of Klein 1931 Gödel 1932i: Review of Hoensbroech 1931 Gödel 1932j: Review of Klein 1932 Gödel 1932k: Introductory note to 1932k, 1934e and 1936bStephen C. Kleene: Review of Church 1932 Gödel 1932l: Review of Kalmár 1932 Gödel 1932m: Review of Huntington 1932 Gödel 1932n: Review of Skolem 1932 Gödel 1932o: Review of Dingler 1931 Gödel 1933: Introductory note to 1933W. V. Quine: [[Über die Parryschen Axiome]] [[On Parry's axioms]] Gödel 1933a: Introductory note to 1933aW. V. Quine: Über Unabhängigkeitsbeweise im Aussagenkalkül On independence proofs in the propositional calculus Gödel 1933b: Introductory note to 1933b, c, d, g and hJudson Webb: Über die metrische Einbettbarkeit der Quadrupel des R[3 in Kugelflächen On the isometric embeddability of quadruples of points of R[3 in the surface of a sphere Gödel 1933c: (See introductory note under Gödel 1933b.) Über die Waldsche Axiomatik des Zwichenbegriffes On Wald's axiomization of the notion of betweenness Gödel 1933d: (See introductory note under Gödel 1933b.) Zur Axiomatik der elementargeometrischen Verknüpfungs-relationen On the axiomatization of the relations of connection in elementary geometry Gödel 1933e: Introductory note to 1933eA. S. Troelstra: Zur institutionistischen Arithmetik und Zahlentheorie On intuitionistic arithmetic and number theory Gödel 1933f: Introductory note to 1933fA. S. Troelstra: Eine Interpretation des institutionistischen Aussagenkalküls An interpretation of the intuitionistic propositional calculus Gödel 1933g: (See introductory note under Gödel 1933b.) Bemerkung über projektive Abbildungen Remark concerning projective mappings Gödel 1933h: (See introductory note under Gödel 1933b.) Diskussion über koordinatenlose Differentialgeometrie Discussion concerning coordinate-free differential geometry Gödel 1933i: (See introductory note under Gödel 1932a.) Zum Enscheidungsproblem des logischen Funktionenkalküls On the decision probelm for the functional calculus of logic Gödel 1933j: Review of Kaczmarz 1932 Gödel 1933k: Review of Lewis 1932 Gödel 1933l: (See introductory note under Gödel 1932a.) Review of Kalmár 1933 Gödel 1933m: Review of Hahn 1932 Gödel 1934: Introductory note to 1934Stephen C. Kleene: On undecidable propositions of formal mathematical systems Gödel 1934a: Review of Skolem 1933 Gödel 1934b: Introductory note to 1934bW. V. Quine: Review of Quine 1933 Gödel 1934c: Introductory note to 1934c and 1935Robert L. Vaught: Review of Skolem 1933a Gödel 1934d: Review of Chen 1933 Gödel 1934e: (See introductory note under Gödel 1932k.) Review of Church 1933 Gödel 1934f: Review of Notcutt 1934 Gödel 1935: (See introductory note under Gödel 1934c.) Review of Skolem 1934 Gödel 1935a: Introductory note to 1935aW. V. Quine: Review of Huntington 1934 Gödel 1935b: Review of Carnap 1934 Gödel 1935c: Review of Kalmár 1934 Gödel 1936: Introductory note to 1936John W. Dawson, Jr.: Diskussionsbemerkung Discussion remark Gödel 1936a: Introductory note to 1936aRohit Parikh: Über die Länge von Beweisen On the length of proofs Gödel 1936b: (See introductory note under Gödel 1932k.) Review of Church 1935 Textual notes References Index
£60.80
Oxford University Press The Indispensability of Mathematics
Book SynopsisThe Quine-Putnam indispensability argument in the philosophy of mathematics urges us to place mathematical entities on the same ontological footing as other theoretical entities essential to our best scientific theories. Recently, the argument has come under serious scrutiny, with many influential philosophers unconvinced of its cogency. This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.Trade ReviewOverall, the book presents a clear picture of the Quinean world view. * Mathematical Reviews *
£37.39
Oxford University Press Bayess Theorem
Book SynopsisBayes''s theorem is a tool for assessing how probable evidence makes some hypothesis. The papers in this volume consider the worth and applicability of the theorem. Richard Swinburne sets out the philosophical issues. Elliott Sober argues that there are other criteria for assessing hypotheses. Colin Howson, Philip Dawid and John Earman consider how the theorem can be used in statistical science, in weighing evidence in criminal trials, and in assessing evidence for the occurrence of miracles. David Miller argues for the worth of the probability calculus as a tool for measuring propensities in nature rather than the strength of evidence. The volume ends with the original paper containing the theorem, presented to the Royal Society in 1763.Trade ReviewReview from previous edition This is a high quality, concise collection of articles on the foundations of probability and statistics. ... The volume closes with an Appendix containing a very polished reproduction of Bayes's classic 'An Essay Towards the Solving a Problem in the Doctrine of Chances'. The Essay still reads very well, and it should be on every probabilist's 'must read' list. I feel quite comfortable saying something almost as glowing about this entire volume. I found this book very edifying and clear, and the debates and issues it encompasses are of great importance for contemporary philosophy of probability, statistics, and decision-making. I highly recommend this book to anyone with interests in these areas, and I commend Swinburne for putting together this neat little book. * Notre Dame Philosophical Review *Table of ContentsIntroduction ; Bayesianism - its scopes and limits ; Bayesianism in Statistics ; Bayes's Theorem and Weighing Evidence by Juries ; Bayes, Hume, Price, and Miracles ; Propensities May Satisfy Bayes's Theorem ; 'An Essay Towards Solving a Problem in the Doctrine of Chances' by Thomas Bayes, presented to the Royal Society by Richard Price. Preceded by a historical introduction by G A Barnard.
£19.00
Oxford University Press Because Without Cause NonCasual Explanations In
Book SynopsisNot all scientific explanations work by describing causal connections between events or the world's overall causal structure. In addition, mathematicians regard some proofs as explaining why the theorems being proved do in fact hold. This book proposes new philosophical accounts of many kinds of non-causal explanations in science and mathematics.Trade ReviewThis is a tremendous book. It brings together and synthesizes Marc Lange's highly original work over the past decade on non-causal explanation in science and mathematics. Like much of Lange's oeuvre, it represents naturalistic metaphysics of science that draws inspiration and support from a wealth of detailed, carefully researched examples from the sciences, going back to the early nineteenth century and beyond. ... The way in which these examples are coupled with open-minded * dare I say adventurousmetaphysics of modality makes for an exciting and thought-provoking read.Juha Saatsi, Metasicence *[This book] exemplifies the methodology of integrating history and philosophy of science to full effect. Almost every example, of literally dozens, is new to the discussion and shows both careful attention to historical detail and impressive familiarity with the finer points of the relevant mathematics and physics. ... It is a fully prepared feast of new material for philosophers, especially but not only philosophers of science, to dive into, argue against, add to, refine, or apply to further discussions. * Holly Andersen, Mind *This is an original and thought-provoking contribution to the current debate on non-causal explanations in philosophy of science and philosophy of mathematics... Lange's book is an excellent, creative and thought-provoking scholarly contribution to the current debate on explanation. In particular, I believe it is likely the book will have a stimulating and fruitful effect on the literature. * Alexander Reutlinger, Notre Dame Philosophical Reviews *The book has plenty to recommend it: broadness of vision and ambition-he covers a lot of ground (both scientific and philosophical)-as well as a wealth of examples (several original, all worked out in detail)... My overall assessment is that this is a substantial book well worth studying. It will elicit interesting debates in the years to come. * Sorin Bangu, British Journal of Philosophy of Science *Table of Contents0. Preface 0.1 Welcome 0.2 What this book is not about 0.3 Coming attractions Part 1: Scientific Explanations by Constraint 1. What Makes a Scientific Explanation Distinctively Mathematical? 1.1 Distinctively mathematical explanations in science as non-causal scientific explanations 1.2 Are distinctively mathematical explanations set apart by their failure to cite causes? 1.3 Mathematical explanations do not exploit causal powers 1.4 How these distinctively mathematical explanations work 1.5 Elaborating my account of distinctively mathematical explanations 1.6 Conclusion 2. "There Sweep Great General Principles Which All The Laws Seem To Follow" 2.1 The task: to unpack the title of this chapter 2.2 Constraints versus coincidences 2.3 Hybrid explanations 2.4 Other possible kinds of constraints besides conservation laws 2.5 Constraints as modally more exalted than the force laws they constrain 2.6 My account of the difference between constraints and coincidences 2.7 Accounts that rule out explanations by constraint 3. The Lorentz Transformations and the Structure of Explanations by Constraint 3.1 Transformation laws as constraints or coincidences 3.2 The Lorentz transformations given an explanation by constraint 3.3 Principle versus constructive theories 3.4 How this non-causal explanation comes in handy 3.5 How explanations by constraint work 3.6 Supplying information about the source of a constraint's necessity 3.7 What makes a constraint Appendix: A purely kinematical derivation of the Lorentz transformations 4. The Parallelogram of Forces and the Autonomy of Statics 4.1 A forgotten controversy in the foundations of classical physics 4.2 The dynamical explanation of the parallelogram of forces 4.3 Duchayla's statical explanation 4.4 Poisson's statical explanation 4.5 Statical explanation under some familiar accounts of natural law 4.6 My account of what is at stake Part 2: Two Other Varieties of Non-Causal Explanation in Science 5. Really Statistical Explanations and Genetic Drift 5.1 Introduction to Part 2 5.2 RS (Really Statistical) explanations 5.3 Drift 6. Dimensional Explanations 6.1 A simple dimensional explanation 6.2 A more complicated dimensional explanation 6.3 Different features of a derivative law may receive different dimensional explanations 6.4 Dimensional homogeneity 6.5 Independence from some other quantities as part of a dimensional explanans Part 3. Explanation in Mathematics 7. Aspects of Mathematical Explanation: Symmetry, Salience, and Simplicity 7.1 Introduction to proofs that explain why mathematical theorems holds 7.2 Zeitz's biased coin: A suggestive example of mathematical explanation 7.3 Explanation by symmetry 7.4 A theorem explained by a symmetry in the unit imaginary number 7.5 Geometric explanations that exploit symmetry 7.6 Generalizing the proposal 7.7 Conclusion 8. Mathematical Coincidences and Mathematical Explanations That Unify 8.1 What is a mathematical coincidence? 8.2 Can mathematical coincidence be understood without appealing to mathematical explanation? 8.3 A mathematical coincidence's components have no common proof 8.4 A shift of context may change a proof's explanatory power 8.5 Comparison to other proposals 8.6 Conclusion 9 Desargues' Theorem as a Case Study of Mathematical Explanation, Existence, and Natural Properties 9.1 Introduction 9.2 Three proofs - but only one explanation - of Desargues' theorem in two-dimensional Euclidean geometry 9.3 Why Desargues' theorem in two-dimensional Euclidean geometry is explained by an exit to the third dimension 9.4 Desargues' theorem in projective geometry: unification and existence in mathematics 9.5 Desargues' theorem in projective geometry: explanation and natural properties in mathematics 9.6 Explanation by subsumption under a theorem 9.7 Conclusion Part 4: Explanations in Mathematics and Non-Causal Scientific Explanations -- Together 10 Mathematical Coincidence and Scientific Explanation 10.1 Physical coincidences that are no mathematical coincidence 10.2 Explanations from common mathematical form 10.3 Explanations from common dimensional architecture 10.4 Targeting new explananda 11 What Makes Some Reducible Physical Properties Explanatory? 11.1 Introduction 11.2 Centers of mass and reduced mass 11.3 Reducible properties on Strevens's account of scientific explanation 11.4 Dimensionless quantities as explanatorily powerful reducible properties 11.5 My proposal 11.6 Conclusion: all varieties of explanation as species of the same genus References Index
£53.54
Clarendon Press Realism in Mathematics
Book SynopsisWhen engaged in mathematics, most people tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Penelope Maddy delineates and defends a novel version of mathematical realism that answers the traditional questions and refocuses philosophical attention on the pressing foundational issues of contemporary mathematics.Trade ReviewShe has ... clearly marked out an original and interesting position. * Times Higher Education Supplement *the book is written in a lively, engaging style. We hope that it serves to stimulate others to think seriously about issues in philosophy of mathematics because, as Maddy claims, these issues bear directly on mainstream philosophy. * Philosophy of Science *Table of ContentsRealism: Pre-theoretic realism; Realism in philosophy; Realism and truth; Realism in mathematics; Perception and intuition: What is the question?; Perception; Intuition; Godelian Platonism; Numbers: What numbers could not be; Numbers as properties; Frege numbers; Axioms: Reals and sets of reals; Axiomization; Open problems; Competing theories; The challenge; Monism and beyond: Monism; Field's nominalism; Structuralism; Summary; References; Index.
£44.64
Oxford University Press Foundations without Foundationalism
Book SynopsisStewart Shapiro presents a distinctive and persuasive view of the foundations of mathematics, arguing controversially that second-order logic has a central role to play in laying these foundations. To support this contention, he first gives a detailed development of second-order and higher-order logic, in a way that will be accessible to graduate students. He then demonstrates that second-order notions are prevalent in mathematics as practised, and that higher-order logic is needed to codify many contemporary mathematical concepts. Throughout, he emphasizes philosophical and historical issues that the subject raises. Foundations without Foundationalism is a key contribution both to philosophy of mathematics and to mathematical logic. ''In this excellent treatise Shapiro defends the use of second-order languages and logic as framework for mathematics. His coverage of the wide range of logical and philosophical topics required for understanding the controversy over second-order logic is Trade ReviewContains more on second-order logic than is readily available in any other textbook or survey. Philosophically, the book also contains many words of wisdom. * Journal of Symbolic Logic *Table of ContentsPART I: ORIENTATION; 1. TERMS AND QUESTIONS; 2. FOUNDATIONALISM AND FOUNDATIONS OF MATHEMATICS; PART II: LOGIC AND MATHEMATICS; 3. THEORY; 4. METATHEORY; 5. SECOND-ORDER LOGIC AND MATHEMATICS; 6. ADVANCED METATHEORY; PART III: HISTORY AND PHILOSOPHY; 7. THE HISTORICAL 'TRIUMPH' OF FIRST-ORDER LANGUAGES; 8. SECOND-ORDER LOGIC AND RULE-FOLLOWING; 9. THE COMPETITION; REFERENCES; INDEX
£47.70
Oxford University Press The Adventure of Reason
Book SynopsisPaolo Mancosu presents a series of innovative studies in the history and the philosophy of logic and mathematics in the first half of the twentieth century. The Adventure of Reason is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert''s program, constructivity, Wittgenstein, Gödel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). Mancosu exploits extensive untapped archival sources to make available a wealth of new material that deepens in significant ways our understanding of these fascinating areas of modern intellectual history. At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exaTrade ReviewThis book contains an enormous amount of material that historians will wish to consult. Mancosu convincingly demonstrates that there is a great deal more that we can still learn about the origins of modern mathematical logic. * Michael Potter, Philosophia Mathematica *Table of ContentsPART 1: HISTORY OF LOGIC; OART 2: FOUNDATIONS OF MATHEMATICS; PART 3: PHENOMENOLOGY AND MATHEMATICS; PART 4: NOMINALISM; PART 5: THE EMERGENCE OF SEMANTICS: TRUTH AND LOGICAL CONSEQUENCE
£54.00
Oxford University Press Brief History of Numbers
Book SynopsisThis is the story behind the idea of number, from the Pythagoreans, up until the turn of the 20th century, through Greek, Islamic & European mathematics.Trade ReviewCorry has compiled a readable account of the history of mathematics focusing on numbers, although for most of the period in question, arithmetic and geometry are not easily separable. The required level of sophistication of the reader is not great, it is certainly at the level of a first-year undergraduate, or a keen sixth-former who is studying mathematics. Even as an experienced university mathematician, the reviewer learnt many interesting things, and has some misconceptions remedied, on reading Corry's Brief History. * Robin Chapman, LMS Newsletter *This fine book gives what its title promises ... a well-written treatment of the subject. * Underwood Dudley, MAA Reviews *It is a highly recommended and pleasant read, not pedantic, but not casual either ... The book is written with great care ... * Adhemar Bultheel, European Mathematical Society *A Brief History of Numbers is a meticulously researched and carefully crafted look at how mathematicians have explored the concept of number. Corry's prose is clear and engaging, and the mathematical content is uniformly accessible to his audience. ... I highly recommend A Brief History of Numbers to mathematics teachers who wish to know more about how our current edifice of natural, rational, real, complex, and infinite numbers came to be built. * James V. Rauff, Mathematics Teacher *Table of Contents1. The System of Numbers: An Overview ; 2. Writing Numbers: Now and Back Then ; 3. Numbers and Magnitudes in the Greek Mathematical Tradition ; 4. Construction Problems and Numerical Problems in the Greek Mathematical Tradition ; 5. Numbers in the Tradition of Medieval Islam ; 6. Numbers in Europe from the 12th to the 16th Centuries ; 7. Number and Equations at the Beginning of the Scientific Revolution ; 8. Number and Equations in theWorks of Descartes, Newton, and their Contemporaries ; 9. New Definitions of Complex Numbers in the Early 19th Century ; 10. "What are numbers and what should they be?" Understanding Numbers in the Late 19th Century ; 11. Exact Definitions for the Natural Numbers: Dedekind, Peano and Frege ; 12. Numbers, Sets and Infinity. A Conceptual Breakthrough at the Turn of the Twentieth Century ; 13. Epilogue: Numbers in Historical Perspective
£41.79
Oxford University Press Fundamentals of Bayesian Epistemology 1
Book SynopsisFundamentals of Bayesian Epistemology provides an accessible introduction to the key concepts and principles of the Bayesian formalism. This volume introduces degrees of belief as a concept in epistemology and the rules for updating degrees of belief derived from Bayesian principles.Table of ContentsQuick Reference Preface I Our Subject 1: Beliefs and Degrees of Belief II The Bayesian Formalism 2: Probability Distributions 3: Conditional Credences 4: Updating by Conditionalization 5: Further Rational Constraints
£89.51
Oxford University Press Fundamentals of Bayesian Epistemology 1
Book SynopsisBayesian ideas have recently been applied across such diverse fields as philosophy, statistics, economics, psychology, artificial intelligence, and legal theory. Fundamentals of Bayesian Epistemology examines epistemologists'' use of Bayesian probability mathematics to represent degrees of belief. Michael G. Titelbaum provides an accessible introduction to the key concepts and principles of the Bayesian formalism, enabling the reader both to follow epistemological debates and to see broader implicationsVolume 1 begins by motivating the use of degrees of belief in epistemology. It then introduces, explains, and applies the five core Bayesian normative rules: Kolmogorov''s three probability axioms, the Ratio Formula for conditional degrees of belief, and Conditionalization for updating attitudes over time. Finally, it discusses further normative rules (such as the Principal Principle, or indifference principles) that have been proposed to supplement or replace the core five.Volume 2 gives arguments for the five core rules introduced in Volume 1, then considers challenges to Bayesian epistemology. It begins by detailing Bayesianism''s successful applications to confirmation and decision theory. Then it describes three types of arguments for Bayesian rules, based on representation theorems, Dutch Books, and accuracy measures. Finally, it takes on objections to the Bayesian approach and alternative formalisms, including the statistical approaches of frequentism and likelihoodism.Table of ContentsQuick Reference Preface I Our Subject 1: Beliefs and Degrees of Belief II The Bayesian Formalism 2: Probability Distributions 3: Conditional Credences 4: Updating by Conditionalization 5: Further Rational Constraints
£28.37
Oxford University Press Leibniz
Book SynopsisGottfried Wilhelm Leibniz (1646-1716) was a man of extraordinary intellectual creativity who lived an exceptionally rich and varied intellectual life in troubled times. More than anything else, he was a man who wanted to improve the life of his fellow human beings through the advancement of all the sciences and the establishment of a stable and just political order. In this Very Short Introduction Maria Rosa Antognazza outlines the central features of Leibniz''s philosophy in the context of his overarching intellectual vision and aspirations. Against the backdrop of Leibniz''s encompassing scientific ambitions, she introduces the fundamental principles of Leibniz''s thought, as well as his theory of truth and theory of knowledge. Exploring Leibniz''s contributions to logic, mathematics, physics, and metaphysics, she considers how his theories sat alongside his concerns with politics, diplomacy, and a broad range of practical reforms: juridical, economic, administrative, technological, medical, and ecclesiastical. Discussing Leinbniz''s theories of possible worlds, she concludes by looking at what is ultimately real in this actual world that we experience, the good and evil there is in it, and Leibniz''s response to the problem of evil through his theodicy. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.Table of ContentsCONCLUSION; REFERENCES; FURTHER READING; INDEX
£9.49
Oxford University Press One True Logic
Book SynopsisLogical monism is the claim that there is a single correct logic, the ''one true logic'' of our title. The view has evident appeal, as it reflects assumptions made in ordinary reasoning as well as in mathematics, the sciences, and the law. In all these spheres, we tend to believe that there are determinate facts about the validity of arguments. Despite its evident appeal, however, logical monism must meet two challenges. The first is the challenge from logical pluralism, according to which there is more than one correct logic. The second challenge is to determine which form of logical monism is the correct one. One True Logic is the first monograph to explicitly articulate a version of logical monism and defend it against the first challenge. It provides a critical overview of the monism vs pluralism debate and argues for the former. It also responds to the second challenge by defending a particular monism, based on a highly infinitary logic. It breaks new ground on a number of fronts and unifies disparate discussions in the philosophical and logical literature. In particular, it generalises the Tarski-Sher criterion of logicality, provides a novel defence of this generalisation, offers a clear new argument for the logicality of infinitary logic and replies to recent pluralist arguments.Trade ReviewOne True Logic is the first monograph to explicitly articulate a version of logical monism and defend it against the first challenge. It provides a critical overview of the monism vs pluralism debate and argues for the former. It also responds to the second challenge by defending a particular monism, based on a highly infinitary logic. It breaks new ground on a number of fronts and unifies disparate discussions in the philosophical and logical literature. * MathSciNet *In One True Logic: A Monist Manifesto, Griffiths and Paseau set out to defend the doctrine known as logical monism. In short, the book is part of an ongoing debate between logical pluralists and logical monists...Their work is challenging yet worth the effort. It advances a strong defense of logical monism by offering just as strong objections to logical pluralism. Anyone interested in the philosophy of logic must read this book! * Choice *a bold and original book. Its discussion of foundational questions about logic is detailed and mathematically rigorous. At the same time, it is admirably clear and approachable. It is also fun to read. Its uncompromising style ...its precise argumentation, and its dialectical clarity make it an engaging and thought-provoking investigation into the nature of logical consequence... full of original arguments worthy of discussion... a fascinating and rich book. * Erik Stei, Notre Dame Philosophical Reviews *Table of ContentsIntroduction Prologue 1: Conceptions of Logical Consequence 2: What is Monism? 3: Against Pluralism 4: The LIFGIFS Hypothesis 5: Beyond the Finitary 6: Isomorphism Invariance 7: Towards the One True Logic 8: The Heterogeneity Objection 9: The Overgeneration Objection 10: The Absoluteness Objection 11: The Intensional Objection Conclusion
£80.00
Oxford University Press Martin Folkes 16901754 Newtonian Antiquary
Book SynopsisMartin Folkes (1690-1754): Newtonian, Antiquary, Connoisseur is a cultural and intellectual biography of the only President of both the Royal Society and the Society of Antiquaries.Trade ReviewRoos's book—generously illustrated with over seventy images of portraits, medals, engravings, archival documents and other objects—brings Folkes vividly to life. * LIAM SIMS, Cambridge, UK *[Anna Marie Roos's] depth and breadth of knowledge are awe inspiring . . . This is an all-round, first-class piece of scholarship that not only introduces the reader to the little known but important figure of Martin Folkes, but because of the extensive contextual embedding provides a solid introduction to the social and cultural context in which science was practiced not only in England but throughout Europe in the first half of the eighteenth century. Highly recommended and not just for historians of science * Thony Christie, The Renaissance Mathematicus Blog *Roos is to be commended for writing the initial monograph on an unjustly neglected figure, providing thoughtful accounts of Folkes's contributions to a multitude of disciplines. * William Eisler, The Medal *Table of Contents1: Introduction 2: Nascent Newtonian, 1690-1716 3: Lucretia Bradshaw: Recovering a Wife and a Life 4: Folkes and his Social Networks in 1720s London 5: Taking Newton on Tour 6: Martin Folkes, Antiquarian 7: Martin Folkes and the Royal Society Presidency: biological sciences and vitalism 8: Martin Folkes and the Royal Society Presidency: The Electric Imagination 9: Charting a Personal and Institutional Life
£100.67
Oxford University Press Journey to the Edge of Reason The Life of Kurt
Book SynopsisA remarkable account of Kurt Gödel, weaving together creative genius, mental illness, political corruption, and idealism in the face of the turmoil of war and upheaval.At age 24, a brilliant Austrian-born mathematician published a mathematical result that shook the world. Nearly a hundred years after Kurt Gödel''s famous 1931 paper On Formally Undecidable Propositions appeared, his proof that every mathematical system must contain propositions that are true - yet never provable within that system - continues to pose profound questions for mathematics, philosophy, computer science, and artificial intelligence. His close friend Albert Einstein, with whom he would walk home every day from Princeton''s famous Institute for Advanced Study, called him the greatest logician since Aristotle. He was also a man who felt profoundly out of place in his time, rejecting the entire current of 20th century philosophical thought in his belief that mathematical truths existed independent of the human miTrade ReviewBudiansky opens up the history of a time where great progress was achieved in foundations of mathematics against the backdrop of the Second World War. This is an easily accessible account for those who did not have the chance to meet Kurt Gödel in person...For the generations that possibly enjoy the t-shirt version of Gödel's work, I would hope that the variety of his work would spark more diversified Gödel merchandise * Annika Kanckos, Metascience *It would be easy to fall into the trap of repeating somewhat exaggerated anecdotes and to ridicule the leading character of this biography. Therefore, it is a pleasure to read a book on the life of Gödel that does all but that. The book offers a serious and unapologetic account of Gödel's life ... The new take on the topics is refreshing and brings the past to life through a coherent narrative. * Annika Kanckos, Metascience *Selected as a 2021 Book of the Year in the Times Literary Supplementwonderfully engrossing * Adam Gopnik, The New Yorker *Budiansky, for all his tremendous efforts and exhaustive interrogations of Gödel's times and places, acquaintances and offices, can only leave us, at the end, with an immeasurably enriched version of Gödel the wise child. It's an undeniably distracting and reductive picture. But - and this is the trouble - it's not wrong. * Simon Ings, Spectator *Journey to the Edge of Reason covers [Gödel's life and work] engagingly and clearly, which is quite a feat given the difficulty of the material. The author... also manages successfully to convey Gödel's naivety, eccentricity and paranoia as well as his genius. * Nick Spencer, Financial Times *In this excellent new biography, Stephen Budiansky introduces the reader to Gödel's stunning achievements in logic, illuminates his devastating mental illness and considers how the two might be related. * Cheryl Misak, Times Literary Supplement *An engaging read, both on a personal and professional level. * David Lorimer, Paradigm Explorer *One of the great geniuses of the 20th century, barely known outside the academy today, receives a much-needed expert biographical treatment ... An outstanding biography of a man of incomprehensible brilliance. * Kirkus reviews *Journey to the Edge of Reason is an intimate and haunting portrait of one of the most elusive gods on Princeton's Mt. Olympus. A triumph of research and a wonderful read. * Sylvia Nasar, author of A Beautiful Mind *Kurt Gödel's mathematical results on incompleteness and undecidable propositions leave it up to us, as individuals, to choose whether to mourn these limits to the power of formal systems, or celebrate his proof that even the most rigid numerical bureaucracy contains the tools by which higher truth will always be able to effect an escape. Stephen Budianksy's Journey to the Edge of Reason expertly and humanely frames these results between Gödel's childhood under the dark shadow of the Austrian and Nazi bureaucracies, his escape to America, his descent into physical and mental illness, and his achievement of a reconciliation between spiritual faith and scientific proof. * George Dyson, author of Analogia and Turing's Cathedral *A painstakingly researched and lucidly presented biography—a close-up of one of the most influential and enigmatic thinkers of the twentieth century—full of vivid detail and sharp historical insight. * Karl Sigmund, professor of mathematics, University of Vienna, and author of Exact Thinking in Demented Times *A brilliant biography of one of the most original thinkers of all time, Journey to the Edge of Reason is as deep and precise as the genius it describes. In a paradox befitting Gödel himself, it takes a tale of logic and its limits and finds, at its heart, something strangely soulful and sympathetic. * Steven Strogatz, professor of mathematics, Cornell University, and author ofInfinite Powers *Prepare yourself for a great adventure and fascinating book that can be picked up at ease and read at pace..Budiansky provides a gripping and interesting dialogue fitting the great story of this fascinating figure...an excellent book. * Kenny Green, Mathematics Today *Table of ContentsList of Maps and Illustrations Prologue 1: Dreams of an Empire 2: Alle echten Wiener sind aus Brünn 3: Vienna 1924 4: Floating in Midair 5: Undecidable Truths 6: The Scholar's Paradise 7: Fleeing the Reich 8: New Worlds 9: Plato's Shadow 10: "If the World is Constructed Rationally" Appendix: Gödel's Proof Notes Bibliography Acknowledgments Photo Credits Index
£20.69
Oxford University Press Journey to the Edge of Reason
Book Synopsis A remarkable account of Kurt Gödel, weaving together creative genius, mental illness, political corruption, and idealism in the face of the turmoil of war and upheaval. At age 24, a brilliant Austrian-born mathematician published a mathematical result that shook the world. Nearly a hundred years after Kurt Gödel''s famous 1931 paper On Formally Undecidable Propositions appeared, his proof that every mathematical system must contain propositions that are true - yet never provable within that system - continues to pose profound questions for mathematics, philosophy, computer science, and artificial intelligence. His close friend Albert Einstein, with whom he would walk home every day from Princeton''s famous Institute for Advanced Study, called him the greatest logician since Aristotle. He was also a man who felt profoundly out of place in his time, rejecting the entire current of 20th century philosophical thought in his belief that mathematical truths existed independent of theTrade ReviewBudiansky opens up the history of a time where great progress was achieved in foundations of mathematics against the backdrop of the Second World War. This is an easily accessible account for those who did not have the chance to meet Kurt Gödel in person...For the generations that possibly enjoy the t-shirt version of Gödel's work, I would hope that the variety of his work would spark more diversified Gödel merchandise * Annika Kanckos, Metascience *It would be easy to fall into the trap of repeating somewhat exaggerated anecdotes and to ridicule the leading character of this biography. Therefore, it is a pleasure to read a book on the life of Gödel that does all but that. The book offers a serious and unapologetic account of Gödel's life ... The new take on the topics is refreshing and brings the past to life through a coherent narrative. * Annika Kanckos, Metascience *Selected as a 2021 Book of the Year in the Times Literary Supplementwonderfully engrossing * Adam Gopnik, The New Yorker *Budiansky, for all his tremendous efforts and exhaustive interrogations of Gödel's times and places, acquaintances and offices, can only leave us, at the end, with an immeasurably enriched version of Gödel the wise child. It's an undeniably distracting and reductive picture. But - and this is the trouble - it's not wrong. * Simon Ings, Spectator *Journey to the Edge of Reason covers [Gödel's life and work] engagingly and clearly, which is quite a feat given the difficulty of the material. The author... also manages successfully to convey Gödel's naivety, eccentricity and paranoia as well as his genius. * Nick Spencer, Financial Times *In this excellent new biography, Stephen Budiansky introduces the reader to Gödel's stunning achievements in logic, illuminates his devastating mental illness and considers how the two might be related. * Cheryl Misak, Times Literary Supplement *An engaging read, both on a personal and professional level. * David Lorimer, Paradigm Explorer *One of the great geniuses of the 20th century, barely known outside the academy today, receives a much-needed expert biographical treatment ... An outstanding biography of a man of incomprehensible brilliance. * Kirkus reviews *Journey to the Edge of Reason is an intimate and haunting portrait of one of the most elusive gods on Princeton's Mt. Olympus. A triumph of research and a wonderful read. * Sylvia Nasar, author of A Beautiful Mind *Kurt Gödel's mathematical results on incompleteness and undecidable propositions leave it up to us, as individuals, to choose whether to mourn these limits to the power of formal systems, or celebrate his proof that even the most rigid numerical bureaucracy contains the tools by which higher truth will always be able to effect an escape. Stephen Budianksy's Journey to the Edge of Reason expertly and humanely frames these results between Gödel's childhood under the dark shadow of the Austrian and Nazi bureaucracies, his escape to America, his descent into physical and mental illness, and his achievement of a reconciliation between spiritual faith and scientific proof. * George Dyson, author of Analogia and Turing's Cathedral *A painstakingly researched and lucidly presented biography—a close-up of one of the most influential and enigmatic thinkers of the twentieth century—full of vivid detail and sharp historical insight. * Karl Sigmund, professor of mathematics, University of Vienna, and author of Exact Thinking in Demented Times *A brilliant biography of one of the most original thinkers of all time, Journey to the Edge of Reason is as deep and precise as the genius it describes. In a paradox befitting Gödel himself, it takes a tale of logic and its limits and finds, at its heart, something strangely soulful and sympathetic. * Steven Strogatz, professor of mathematics, Cornell University, and author ofInfinite Powers *Prepare yourself for a great adventure and fascinating book that can be picked up at ease and read at pace..Budiansky provides a gripping and interesting dialogue fitting the great story of this fascinating figure...an excellent book. * Kenny Green, Mathematics Today *
£19.99
Oxford University Press Syllogistic Logic and Mathematical Proof
Book SynopsisDoes syllogistic logic have the resources to capture mathematical proof? This volume provides the first unified account of the history of attempts to answer this question, the reasoning behind the different positions taken, and their far-reaching implications. Aristotle had claimed that scientific knowledge, which includes mathematics, is provided by syllogisms of a special sort: ''scientific'' (''demonstrative'') syllogisms. In ancient Greece and in the Middle Ages, the claim that Euclid''s theorems could be recast syllogistically was accepted without further scrutiny. Nevertheless, as early as Galen, the importance of relational reasoning for mathematics had already been recognized. Further critical voices emerged in the Renaissance and the question of whether mathematical proofs could be recast syllogistically attracted more sustained attention over the following three centuries. Supported by more detailed analyses of Euclidean theorems, this led to attempts to extend logical theory to include relational reasoning, and to arguments purporting to reduce relational reasoning to a syllogistic form. Philosophical proposals to the effect that mathematical reasoning is heterogenous with respect to logical proofs were famously defended by Kant, and the implications of the debate about the adequacy of syllogistic logic for mathematics are at the very core of Kant''s account of synthetic a priori judgments. While it is now widely accepted that syllogistic logic is not sufficient to account for the logic of mathematical proof, the history and the analysis of this debate, running from Aristotle to de Morgan and beyond, is a fascinating and crucial insight into the relationship between philosophy and mathematics.Table of ContentsIntroduction 1: Aristotelian Syllogism and Mathematics in Antiquity and the Medieval Period 2: Extensions of the Syllogism in Medieval Logic 3: Syllogistic and Mathematics: The Case of Piccolomini 4: Obliquities and Mathematics in the 17th and 18th Centuries: From Jungius to Wolff 5: The Extent of Syllogistic Reasoning: From Rüdiger to Wolff 6: Lambert and Kant 7: Bernard Bolzano on Non-Syllogistic Reasoning 8: Thomas Reid, William Hamilton and Augustus De Morgan Conclusion
£60.00
Oxford University Press Morality and Mathematics
Book SynopsisTo what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to being empirically justified than our moral beliefs. It is also incorrect that reflection on the genealogy of our moral beliefs establishes a lack of parity between the cases. In general, if one is a moral antirealist on the basis of epistemological considerations, then one ought to be a mathematical antirealist as well. And, yet, Clarke-Doane shows that moral realism and mathematical realism do not stand or fall together -- and for a surprising reason. Moral questions, insofar as they arTrade ReviewReview from previous edition Morality and Mathematics is an outstanding achievement and will be a standard point of reference for future work on the topics of which it treats. * Hallvard Lillehammer, International Journal for the Study of Skepticism *Clarke-Doane ... brings remarkable expertise and ... research to [this project]. The main argument [is] copiously defended in this lucid but highly technical treatise. ... Underlying [the argument] is the important distinction between realism and objectivity. * Sheila Mason, CHOICE *Clarke-Doane's book offers a coherent and plausible set of answers to the notorious epistemological questions provoked by morality, and to the analogous questions that are provoked by mathematics. It is striking for its creativity, its rigorous arguments, its many subtle but important distinctions, its unusual breadth of expertise (covering the philosophy of language, metaphysics, epistemology, philosophy of mathematics, and meta-ethics), and its rational control of a daunting battery of interacting considerations from these various branches of the subject. Exceptionally impressive philosophical talent and maturity are on display here. Needless to say, we probably haven't yet been given the final truth about these matters. But it's certain that anyone aiming to do better will have to grapple with Clarke-Doane's formidable arguments and conclusions. * Paul Horwich, New York University *Justin Clarke-Doane raises fascinating and important issues about evolutionary debunking arguments. He argues that insofar as our knowledge of the evolutionary origins of morality poses a challenge for moral realism, exactly similar difficulties will arise for mathematical realism. * Matthew Braddock, Andreas Mogensen, and Walter Sinnott-Armstrong, PEASoup *Clarke-Doane's overarching metaphilosophical conclusion ... is ... that across a large range of philosophical debates ... the real philosophical questions are not metaphysical ... but practical, about which concepts to use. ... [W]e are left with a purely practical question of which framework to pick, which cannot itself be justified by appeal to more normativity. ...[P]erhaps a monist response can be afforded via an adaptation of Quine's response to Carnap. ... But whether or not this response ... can be made to fly, Clarke-Doane's achievement ... is substantial. ... [I]ncreased specialization makes serious engagement across subfields of philosophy a challenge. Morality and Mathematics rises to this challenge, and will serve as a springboard to further serious engagement across the subdisciplines * Mary Leng, Mind *This excellent book ... compares morality and mathematics. Their similarities and differences are not what one might naively supposee, as the author demonstrates. The book is highly recommended to philosophers interested in both subjects, and to anyone who seeks a global understanding of how morality and mathematics fit into our belief system. ... The idea that practical questions alone resist deflation in the face of pluralist ... realism ... facilitated by the tension between realism and objectivity ... mak[es] ... for a rather striking metaphilosophical vision. * Michael Bevan & Alexander Paseau, Philosophia Mathematica *In this brilliantly original book, Justin Clarke-Doane ... has upended many long-held views on morality and mathematics. ... Accept it or reject it, it manifests Clarke-Doane's extraordinary combination of philosophical imagination and logical skill, and what I have discussed in this review is only a small sample of the philosophical gold to be found in his book. * David Gordon, Philosophical Quarterly *Table of ContentsIntroduction 1: Realism, Ontology, and Objectivity 2: Self-Evidence, Proof, and Disagreement 3: Observation and Indispensability 4: Genealogical Debunking Arguments 5: Explaining our Reliability 6: Realism, Objectivity, and Evaluation Conclusion
£19.99
Oxford University Press, USA Grounding Concepts
Book SynopsisGrounding Concepts tackles the issue of arithmetical knowledge, developing a new position which respects three intuitions which have appeared impossible to satisfy simultaneously: a priorism, mind-independence realism, and empiricism.Drawing on a wide range of philosophical influences, but avoiding unnecessary technicality, a view is developed whereby arithmetic can be known through the examination of empirically grounded concepts. These are concepts which, owing to their relationship to sensory input, are non-accidentally accurate representations of the mind-independent world. Examination of such concepts is an armchair activity, but enables us to recover information which has been encoded in the way our concepts represent. Emphasis on the key role of the senses in securing this coding relationship means that the view respects empiricism, but without undermining the mind-independence of arithmetic or the fact that it is knowable by means of a special armchair method called conceptual Trade ReviewAnyone with the slightest interest in the nature of mathematics should give [Jenkins] serious study. * James Robert Brown and James Davies. Philosophical Quarterly *offers and original treatment of arithmetic that is clearly articulated and carefully argued... It is a book that should be read by anyone with an interest in these topics, and will repay careful study. * Albert Casullo, Mind *I think highly of this book. Grounding Concepts adds a genuinely new option to the philosophical landscape. The central idea - that sense experience may be relevant to the epistemic status of concepts and thus play a non-evidential role in explaining knowledge - is both sensible and clever. The book is sophisticated and accessible, both extremely careful and extremely clear... Grounding Concepts is an excellent book. It provides a sophisticated and clear discussion of a difficult nest of issues in the philosophy of mathematics, epistemology, philosophy of mind, and metaphysics. By developing a new theoretical option, it makes a significant contribution to the literature on the epistemology of the a priori. Anyone interested in the epistemology of arithmetic or the nature of a priori knowledge would profit from reading it. * Joshua Schechter, Notre Dame Philosophical Reviews *Table of ContentsPART 1 - REALISM AND KNOWLEDGE; PART 2 - AN EPISTEMOLOGY FOR ARITHMETIC; PART 3 - OBJECTIONS
£71.10
Oxford University Press Category Theory
Book SynopsisCategory theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership. Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda''s lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists!This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.Trade ReviewThe book is well organised and very well written. The presentation of the material is from the concrete to the abstract, proofs are worked out in detail and the examples and the exercises spread throughout the text mark a pleasant rhythm for its reading. In all, Awodey's Category Theory is a very nice and recommendable introduction to the subject. * Pere Pascual, EMS Newsletter *Table of ContentsPreface ; 1. Categories ; 2. Abstract Structures ; 3. Duality ; 4. Groups and Categories ; 5. Limits and Colimits ; 6. Exponentials ; 7. Naturality ; 8. Categories of Diagrams ; 9. Adjoints ; 10. Monads and Algrebras ; References ; Solutions to Selected Exercises ; Index
£57.95
Clarendon Press Identity and Modality Mind Association Occasional Series
Book SynopsisAddresses fundamental and interrelated philosophical issues concerning modality and identity, issues that were pivotal to the development of analytic philosophy in the twentieth century. This work is intended for graduate students in the subject and professional philosophers.Trade ReviewThe essays make important contributions to contemporary debated concerning modality, individuation, mathmatical structuralism and personal identity. The collection is tus warmly recommended to anyone interested in these areas. * Oystein Linnebo MIND *the volume . . . is of high quality and contains important contributions to many areas of contemporary metaphysics * Matti Eklund, Notre Dame Philosophical Review *all in all, this is an impressive volume, of significant interest to anyone who wants to stay abreast of developments in contemporary metaphysics * Matti Eklund, Notre Dame Philosophical Review *Table of ContentsI. MODALITY ; II. IDENTITY AND INDIVIDUATION ; III. PERSONAL IDENTITY
£102.00
Oxford University Press Music and Mathematics
Book SynopsisFrom Ancient Greek times, music has been seen as a mathematical art, and this relationship has fascinated generations. This new in paperback edition of diverse, comprehensive and fully-illustrated papers, authored by leading scholars, links the two fields in a lucid manner that is suitable for students of each subject as well as the general reader.Trade ReviewAn attractive volume that covers almost al of the important aspects of the interplay between mathematics and music. * Ehrhard Behrends, The Mathematical Intelligencer, Vol 28, 3 *Table of ContentsPART I: MUSIC AND MATHEMATICS THROUGH HISTORY; PART II: THE MATHEMATICS OF MUSICAL SOUND; PART III: MATHEMATICAL STRUCTURE IN MUSIC; PART IV: THE COMPOSER SPEAKS
£39.89
Oxford University Press, USA Truth Through Proof A Formalist Foundation for Mathematics
Book SynopsisTruth Through Proof defends an anti-platonist philosophy of mathematics derived from game formalism. Classic formalists claimed implausibly that mathematical utterances are truth-valueless moves in a game. Alan Weir aims to develop a more satisfactory successor to game formalism utilising a widely accepted, broadly neo-Fregean framework, in which the proposition expressed by an utterance is a function of both sense and background circumstance. This framework allows for sentences whose truth-conditions are not representational, which are made true or false by conditions residing in the circumstances of utterances but not transparently in the sense. Applications to projectivism and fiction pave the way for the claim that mathematical utterances are made true or false by the existence of concrete proofs or refutations, though these truth-making conditions form no part of their sense or informational content. The position is compared with rivals, an account of the applicability of mathematics developed, and a new account of the nature of idealisation proffered in which it is argued that the finitistic limitations Gödel placed on proofs are without rational justification. Finally a non-classical logical system is provided in which excluded middle fails, yet enough logical power remains to recapture the results of standard mathematics.Trade ReviewIn this fascinating book, Weir defends a new account of what makes mathematical assertions objectively true or false. * Julian C. Cole, Philosophy in Review *Table of ContentsIntroduction ; 1. Metaphysics ; 2. Ontological Reduction ; 3. Neo-formalism ; 4. Objections and Comparisons ; 5. Applying Mathematics ; 6. Proof Set in Concrete ; 7. Idealisation Naturalised ; 8. Logic ; Conclusion ; Appendix
£80.10
OUP Oxford The Oxford Handbook of the History of Mathematics
Book SynopsisThis 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 practise 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, pTrade ReviewReview from previous edition "wonderful food for thought for any practitioner" * Times Higher Education Supplement *"a splendid, something-for-everybody treasure-trove of interesting, informative, challenging, well written testaments to the variety and vigor of history of mathematics in our time" * Historia Mathematica *"Well written, well edited and well rounded... a healthy contribution to a burgeoning field of newly self-aware research." * British Journal for the History of Science *Table of ContentsINTRODUCTION; GEOGRAPHIES AND CULTURES: GLOBAL; GEOGRAPHIES AND CULTURES: REGIONAL; GEOGRAPHIES AND CULTURES: LOCAL; PEOPLE AND PRACTICES: LIVES; PEOPLE AND PRACTICES: PRACTICES; PEOPLE AND PRACTICES: PRESENTATION; INTERACTIONS AND INTERPRETATIONS: INTELLECTUAL; INTERACTIONS AND INTERPRETATIONS: MATHEMATICAL; INTERACTIONS AND INTERPRETATIONS: HISTORICAL; ABOUT THE CONTRIBUTORS; INDEX
£40.84
Oxford University Press Mathematics and Reality
Book SynopsisMary Leng offers a defense of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at least approximately) true. But since claims whose truth would require the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematical theories utilized in empirical science are true. Previous responses to the indispensability argument have focussed on Trade ReviewMathematics and Reality is to be recommended highly ... it presents a distinctive new version of fictionalism to throw into the contemporary mix that will repay close attention by all philosophers of mathematics. * Alan Weir, British Journal for the Philosophy of Science *this book has the potential to serve as a source of productive disagreement that would significantly advance the realism-anti-realism debate in mathematics. * Jeffrey W. Rowland, Mind *Table of Contents1. Introduction ; 2. Naturalism and Ontology ; 3. The Indispensability of Mathematics ; 4. Naturalism and Mathematical Practice ; 5. Naturalism and Scientific Practice ; 6. Naturalized Ontology ; 7. Mathematics and Make-Believe ; 8. Mathematical Fictionalism and Constructive Empiricism ; 9. Explaining the Success of Mathematics ; 10. Conclusion
£29.59
Oxford University Press After Godel
Book SynopsisRichard Tieszen presents an analysis, development, and defense of a number of central ideas in Kurt Gödel''s writings on the philosophy and foundations of mathematics and logic. Tieszen structures the argument around Gödel''s three philosophical heroes - Plato, Leibniz, and Husserl - and his engagement with Kant, and supplements close readings of Gödel''s texts on foundations with materials from Gödel''s Nachlass and from Hao Wang''s discussions with Gödel. As well as providing discussions of Gödel''s views on the philosophical significance of his technical results on completeness, incompleteness, undecidability, consistency proofs, speed-up theorems, and independence proofs, Tieszen furnishes a detailed analysis of Gödel''s critique of Hilbert and Carnap, and of his subsequent turn to Husserl''s transcendental philosophy in 1959. On this basis, a new type of platonic rationalism that requires rational intuition, called ''constituted platonism'', is developed and defended. Tieszen showTrade ReviewTieszen has long been one of the bridge builders in contemporary philosophy, who is engaged by the philosophical issues and studies them with a broad background and an open mind. There is much to be learned by this, and I am eagerly looking forward to Tieszen's continuation of this interesting and very valuable work. * Dagfinn Follesda, Philosophia MathematicaJuliette Kennedy, Notre Dame Philosophical Reviews *Table of ContentsPreface ; 1. Setting the Stage ; 2. Consistency, and the Ascent to Platonic Rationalism ; 3. Godel's Path From Hilbert and Carnap to Husserl ; 4. A New Kind of Platonism ; 5. Consciousness, Reason, and Intentionality ; 6. Constituted Platonism, Reason, and Mathematical Knowledge ; 7. Minds and Machines ; 8. Reason, Science, and Evidence ; Bibliography ; Index
£35.69
Oxford University Press Inc Belief and Counterfactuals A Study in MeansEnd
Book SynopsisTrade ReviewThis brief work is dense with symbol-laden arguments...may advance the field of formal epistemology for specialists. * S. E. Forschler, CHOICE *Table of ContentsPreface 1. Introduction 2. Belief First 2.1 Ideal doxastic agents 2.2 Belief and ends 2.3 Conditional belief and belief revision 3. Belief Revision 3.1 The AGM theory of belief revision 3.2 Systems of spheres 3.3 Iterated belief revision 4. Conditional Belief 4.1 Ranking theory: static rules 4.2 Ranking theory: dynamic rules 4.3 Iterated belief revision revisited 5. Why Should I? 5.1 The consistency argument 5.2 The consistency argument continued 5.3 The consistency argument completed 5.4 Hypothetical imperatives 5.5 Conditional obligation and conditional belief 5.6 Appendix: Proofs 6. Applications in Epistemology 6.1 Conceptual belief change and logical learning 6.2 Learning indicative conditionals 6.3 In defense of rigidity References
£85.73
The University of Chicago Press Berkeleys Philosophy of Mathematics Science its
Book SynopsisIn this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work. Jesseph challenges the prevailing view that Berkeley's mathematical writings are peripheral to his philosophy and argues that mathematics is in fact central to his thought, developing out of his critique of abstraction. Jesseph's argument situates Berkeley's ideas within the larger historical and intellectual context of the Scientific Revolution. Jesseph begins with Berkeley's radical opposition to the received view of mathematics in the philosophy of the late seventeenth and early eighteenth centuries, when mathematics was considered a science of abstractions. Since this view seriously conflicted with Berkeley's critique of abstract ideas, Jesseph contends that he was forced to come up with a nonabstract philosophy of mathematics. Jesseph examines Berkeley's unique trea
£99.00
The University of Chicago Press Berkeleys Philosophy of Mathematics Science and
Book SynopsisIn this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work. Jesseph challenges the prevailing view that Berkeley's mathematical writings are peripheral to his philosophy and argues that mathematics is in fact central to his thought, developing out of his critique of abstraction. Jesseph's argument situates Berkeley's ideas within the larger historical and intellectual context of the Scientific Revolution. Jesseph begins with Berkeley's radical opposition to the received view of mathematics in the philosophy of the late seventeenth and early eighteenth centuries, when mathematics was considered a science of abstractions. Since this view seriously conflicted with Berkeley's critique of abstract ideas, Jesseph contends that he was forced to come up with a nonabstract philosophy of mathematics. Jesseph examines Berkeley's unique tr
£30.40
The University of Chicago Press Squaring the Circle The War between Hobbes and
Book SynopsisThis text presents an account of the argument between Thomas Hobbes and John Wallis, from the core mathematics to the broader issues. Their battle of the books illuminates the relationship between science and 17th-century debates over the limits of sovereign power and the existence of God.
£38.00
The University of Chicago Press Uncountable
Book SynopsisRanging from math to literature to philosophy, Uncountable explains how numbers triumphed as the basis of knowledge—and compromise our sense of humanity.Trade Review"Ricardo and David Nirenberg, father and son scholars of mathematics and history, have teamed up in a breathtaking voyage examining the foundations and limits of knowledge in western thought. Not content with secondary sources, they have translated from the literature in their original languages: Arabic, French, German, Greek, Hebrew, Italian, Latin, and Spanish. In particular, they target mathematics and the natural sciences, and the way the concepts of sameness and differences affect our understanding of the natural world. But in the process, the authors touch upon many other facets of human endeavor, all named after their Greek roots: poetry, philosophy, psychology, economy. Along this wildly entertaining journey, we meet dozens of erudite thinkers, scientists, and writers such as Anaximander, Al-Farabi, Fyodor Dostoevsky, Ludwig Wittgenstein, Werner Heisenberg, and Reiner Maria Rilke. The book arrives just in time to give us ammunition as attempts are being made to put truth itself into the supercollider. It is a source of inspiration and comfort to learn how the far-flung ideas about numbers, our existence, and the world we live in have been debated in the past."--Joachim Frank, Columbia University, Nobel Prize in ChemistryTable of ContentsIntroduction: Playing with Pebbles 1 World War Crisis 2 The Greeks: A Protohistory of Theory 3 Plato, Aristotle, and the Future of Western Thought 4 Monotheism’s Math Problem 5 From Descartes to Kant: An Outrageously Succinct History of Philosophy 6 What Numbers Need: Or, When Does 2 + 2 = 4? 7 Physics (and Poetry): Willing Sameness and Difference 8 Axioms of Desire: Economics and the Social Sciences 9 Killing Time 10 Ethical Conclusions Acknowledgments Notes Bibliography Index of Names
£25.65
The University of Chicago Press Reactionary Mathematics
Book SynopsisTrade Review“The complex relationship between tradition and modernization is the pulsing heart of this engaging book. Beside a valuable historical analysis, Reactionary Mathematics offers an interesting and useful synthesis vision to help us understand, in these times of rapid and convulsive transformation, the mathematics of the present and, most importantly, the reasons for the mathematics that will come.” * Nature *“Reactionary Mathematics is an ambitious book that is more than just a history of mathematics but an episode in the history of reason, furnished with a delightful display of different kinds of evidence, from archival documents to political satires to theological treatises to paintings to mathematics textbooks. . . . [It] is a deftly written and timely book brimming with empirical, conceptual and historiographical insights.” * British Journal for the History of Science *"For anyone interested in the "politics of mathematical modernity," this book shows how allegiances to particular types or styles of mathematics may indeed be related to Neapolitan academicians' personal responses to the urgent political pressures of their day." * Choice *“One notable strength of Mazzotti’s book is its ability to transition seamlessly between different levels of analysis. It connects an in-depth historical exploration of a specific local context, such as Naples, with the social and political constraints unique to that site. Simultaneously, it addresses major upheavals and broad conceptual changes such as the evolution of purity, rigor, and abstraction and the very definition of 'modernity' in mathematics. In doing so, the book tackles a critical methodological challenge in the social history of mathematics, bridging the gap between the claim of universality associated with mathematical knowledge and the intricate study of the local contexts and social practices that underpin the production of such knowledge. Mazzotti’s thought-provoking narrative not only demonstrates . . . that mathematics is intimately connected to its cultural, social and political context, but it also prompts readers to consider new avenues of research.” * Historia Mathematica *“Mazzotti offers us a superbly crafted historical study of the interweaving of mathematics, politics, religion, social order, and even olive oil presses in the Kingdom of Naples around 1800. This gives him a distinctive, striking platform from which to address big questions: the relationship between science and politics, the connections between mathematics and modernity, and how we should understand mathematics’ past.” -- Donald MacKenzie, University of Edinburgh“Mazzotti has written a fascinating case study of ‘mathematical resistance’ in late eighteenth- and nineteenth-century Naples. On the most fundamental level, the book’s exploration of ‘mathematics as politics’ observes the reciprocal interactions between the mathematical imagination of historical actors and their sociopolitical circumstances. Mazzotti’s keen attention to the political actors themselves tells a very human story of mathematics, and of the events and changes that led to the development of this seemingly quixotic Neapolitan resistance to mathematical modernity.” -- Sean Cocco, Trinity College“A landmark account of Neapolitan reactionary mathematics in context that contributes insightfully to the histories of Naples, reaction, and mathematics in their separate and interacting respects.” -- Michael Barany, University of EdinburghTable of ContentsIntroduction: Mathematics as Social Order 1 Adventures of the Analytic Reason 2 Mathematics at the Barricades 3 Empire of Analysis 4 The Shape of the Kingdom Intermezzo: Algorithm or Intuition? 5 The Geometry of Reaction 6 A Scientific Counterrevolution 7 A Reactionary Reason 8 Mathematical Purity as Return to Order Notes Bibliography Index
£85.50
The University of Chicago Press Reactionary Mathematics A Genealogy of Purity
Book SynopsisTrade Review“The complex relationship between tradition and modernization is the pulsing heart of this engaging book. Beside a valuable historical analysis, Reactionary Mathematics offers an interesting and useful synthesis vision to help us understand, in these times of rapid and convulsive transformation, the mathematics of the present and, most importantly, the reasons for the mathematics that will come.” * Nature *“Reactionary Mathematics is an ambitious book that is more than just a history of mathematics but an episode in the history of reason, furnished with a delightful display of different kinds of evidence, from archival documents to political satires to theological treatises to paintings to mathematics textbooks. . . . [It] is a deftly written and timely book brimming with empirical, conceptual and historiographical insights.” * British Journal for the History of Science *"For anyone interested in the "politics of mathematical modernity," this book shows how allegiances to particular types or styles of mathematics may indeed be related to Neapolitan academicians' personal responses to the urgent political pressures of their day." * Choice *“One notable strength of Mazzotti’s book is its ability to transition seamlessly between different levels of analysis. It connects an in-depth historical exploration of a specific local context, such as Naples, with the social and political constraints unique to that site. Simultaneously, it addresses major upheavals and broad conceptual changes such as the evolution of purity, rigor, and abstraction and the very definition of 'modernity' in mathematics. In doing so, the book tackles a critical methodological challenge in the social history of mathematics, bridging the gap between the claim of universality associated with mathematical knowledge and the intricate study of the local contexts and social practices that underpin the production of such knowledge. Mazzotti’s thought-provoking narrative not only demonstrates . . . that mathematics is intimately connected to its cultural, social and political context, but it also prompts readers to consider new avenues of research.” * Historia Mathematica *“Mazzotti offers us a superbly crafted historical study of the interweaving of mathematics, politics, religion, social order, and even olive oil presses in the Kingdom of Naples around 1800. This gives him a distinctive, striking platform from which to address big questions: the relationship between science and politics, the connections between mathematics and modernity, and how we should understand mathematics’ past.” -- Donald MacKenzie, University of Edinburgh“Mazzotti has written a fascinating case study of ‘mathematical resistance’ in late eighteenth- and nineteenth-century Naples. On the most fundamental level, the book’s exploration of ‘mathematics as politics’ observes the reciprocal interactions between the mathematical imagination of historical actors and their sociopolitical circumstances. Mazzotti’s keen attention to the political actors themselves tells a very human story of mathematics, and of the events and changes that led to the development of this seemingly quixotic Neapolitan resistance to mathematical modernity.” -- Sean Cocco, Trinity College“A landmark account of Neapolitan reactionary mathematics in context that contributes insightfully to the histories of Naples, reaction, and mathematics in their separate and interacting respects.” -- Michael Barany, University of EdinburghTable of ContentsIntroduction: Mathematics as Social Order 1 Adventures of the Analytic Reason 2 Mathematics at the Barricades 3 Empire of Analysis 4 The Shape of the Kingdom Intermezzo: Algorithm or Intuition? 5 The Geometry of Reaction 6 A Scientific Counterrevolution 7 A Reactionary Reason 8 Mathematical Purity as Return to Order Notes Bibliography Index
£28.50
The University of Chicago Press Science and an African Logic
Book SynopsisDoes two and two equal four? Ask someone and they should answer yes. An equation such as this seems the very definition of certainty, but is it? Helen Verran describes how she went from the conclusion that logic and maths are culturally relative, to a new understanding of all generalizing logic.
£80.00
The University of Chicago Press Science and an African Logic
Book SynopsisDoes two and two equal four? Ask someone and they should answer yes. An equation such as this seems the very definition of certainty, but is it? Helen Verran describes how she went from the conclusion that logic and maths are culturally relative, to a new understanding of all generalizing logic.
£26.60
Palgrave MacMillan UK G.F. Stout and the Psychological Origins of Analytic Philosophy History of Analytic Philosophy
Book SynopsisSeries Editor's Foreword Preface Introduction 1. Judgement and the Emergence of Logical Realism in Britain 2. From Descriptive Psychology to Analytic Philosophy (1888-1899) 3. Psychologism and the Problem of Error (1899-1907) 4. Judgement, Propositional Attitudes and the Proposition (1908-1944) 5. Tropes and Predication Conclusion Bibliography IndexTrade Review“This book is one recent product of her work on this subject, which first saw light as a dissertation, then in a series of papers, and now appears in a revised and expanded version of her early work for the History of Analytic Philosophy series … . The perspective van der Schaar brings here is … a valuable addition to the detailed account of the early development of analytic philosophy at Cambridge.” (Consuelo Preti, Journal of the History of Analytical Philosophy, Vol. 4 (3), 2016)Table of ContentsSeries Editor's Foreword Preface Introduction 1. Judgement and the Emergence of Logical Realism in Britain 2. From Descriptive Psychology to Analytic Philosophy (1888-1899) 3. Psychologism and the Problem of Error (1899-1907) 4. Judgement, Propositional Attitudes and the Proposition (1908-1944) 5. Tropes and Predication Conclusion Bibliography Index
£42.74
Indiana University Press Women in Mathematics The Addition of Difference
Book SynopsisThe role of gender in making and shaping mathematicians.Trade Review'Mathematicians do their best work in their youth'; 'mathematicians work in complete isolation'; 'mathematics and politics don't mix.'These and other myths are discussed and debunked—in both theoretical and concrete terms—in the particular context of the role of women in mathematics. Henrion studies the nature of the participation of women in mathematical research and surrounding issues of gender and race by weaving her narrative around detailed profiles of nine respected women mathematicians (including two African American women). The individual biographies themselves make for enthralling, often inspiring, reading; combined with Henrion's careful, generally evenhanded, and tightly conceived commentary, this volume should be compelling reading for women mathematics students and professionals. A fine addition to the literature on women in science and, as it is written by a mathematical 'insider,' it is all the more likely to receive attention by the mathematics community. Highly recommended. Undergraduates through faculty. -- S. J. Colley * Choice *
£16.14
MIT Press Leibniz on Binary
Book Synopsis
£29.70
