Humanizing Mathematics and its Philosophy
Humanizing Mathematics and its Philosophy

Author: Bharath Sriraman

Publisher: Birkhäuser

Published: 2017-11-07

Total Pages: 357

ISBN-13: 331961231X

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This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume: Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians? Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data processing and scientific computing? The essays also offer glimpses into Reuben’s fertile mind and his lasting influence on the mathematical community, as well as revealing the diverse roots, obstacles and philosophical dispositions that characterize the working lives of mathematicians. With contributions from a veritable “who’s who” list of 20th century luminaries from mathematics and philosophy, as well as from Reuben himself, this volume will appeal to a wide variety of readers from curious undergraduates to prominent mathematicians.

What Is Mathematics, Really?
What Is Mathematics, Really?

Author: Reuben Hersh

Publisher: Oxford University Press

Published: 1997-08-21

Total Pages: 369

ISBN-13: 0199839395

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Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

The Making of Mathematics
The Making of Mathematics

Author: Carlo Cellucci

Publisher: Springer Nature

Published: 2022-03-07

Total Pages: 457

ISBN-13: 3030897311

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This book offers an alternative to current philosophy of mathematics: heuristic philosophy of mathematics. In accordance with the heuristic approach, the philosophy of mathematics must concern itself with the making of mathematics and in particular with mathematical discovery. In the past century, mainstream philosophy of mathematics has claimed that the philosophy of mathematics cannot concern itself with the making of mathematics but only with finished mathematics, namely mathematics as presented in published works. On this basis, mainstream philosophy of mathematics has maintained that mathematics is theorem proving by the axiomatic method. This view has turned out to be untenable because of Gödel’s incompleteness theorems, which have shown that the view that mathematics is theorem proving by the axiomatic method does not account for a large number of basic features of mathematics. By using the heuristic approach, this book argues that mathematics is not theorem proving by the axiomatic method, but is rather problem solving by the analytic method. The author argues that this view can account for the main items of the mathematical process, those being: mathematical objects, demonstrations, definitions, diagrams, notations, explanations, applicability, beauty, and the role of mathematical knowledge.

The Best Writing on Mathematics 2019
The Best Writing on Mathematics 2019

Author: Mircea Pitici

Publisher: Princeton University Press

Published: 2019-11-05

Total Pages: 288

ISBN-13: 0691198357

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An anthology of the year's finest writing on mathematics from around the world, featuring promising new voices as well as some of the foremost names in mathematics.

Imagination and Art: Explorations in Contemporary Theory
Imagination and Art: Explorations in Contemporary Theory

Author: Keith Moser

Publisher: BRILL

Published: 2020-07-27

Total Pages: 810

ISBN-13: 9004436359

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This transdisciplinary project represents the most comprehensive study of imagination to date. The eclectic group of international scholars who comprise Imagination and Art propose bold and innovative theoretical frameworks for (re-) conceptualizing imagination in all of its divergent forms.

Rethinking Knowledge
Rethinking Knowledge

Author: Carlo Cellucci

Publisher: Springer

Published: 2017-03-29

Total Pages: 432

ISBN-13: 3319532375

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This monograph addresses the question of the increasing irrelevance of philosophy, which has seen scientists as well as philosophers concluding that philosophy is dead and has dissolved into the sciences. It seeks to answer the question of whether or not philosophy can still be fruitful and what kind of philosophy can be such. The author argues that from its very beginning philosophy has focused on knowledge and methods for acquiring knowledge. This view, however, has generally been abandoned in the last century with the belief that, unlike the sciences, philosophy makes no observations or experiments and requires only thought. Thus, in order for philosophy to once again be relevant, it needs to return to its roots and focus on knowledge as well as methods for acquiring knowledge. Accordingly, this book deals with several questions about knowledge that are essential to this view of philosophy, including mathematical knowledge. Coverage examines such issues as the nature of knowledge; plausibility and common sense; knowledge as problem solving; modeling scientific knowledge; mathematical objects, definitions, diagrams; mathematics and reality; and more. This monograph presents a new approach to philosophy, epistemology, and the philosophy of mathematics. It will appeal to graduate students and researchers with interests in the role of knowledge, the analytic method, models of science, and mathematics and reality.

Attributing Knowledge
Attributing Knowledge

Author: Jody Azzouni

Publisher: Oxford University Press

Published: 2020-09-21

Total Pages: 481

ISBN-13: 0197508820

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In Attributing Knowledge, Jody Azzouni challenges philosophical conventions about what it means to know something. He argues that the restrictive conditions philosophers place on knowers only hold in special cases; knowledge can be attributed to babies, sophisticated animals (great apes, orcas), unsophisticated animals (bees), and machinery (drones, driverless cars). Azzouni also gives a fresh defense of fallibilism. Relying on lexical semantics and ordinary usage, he shows that there are no knowledge norms for assertion or action. He examines everyday cases of knowledge challenge and attribution to show many recent and popular epistemological positions are wrong. By providing a long-sought intelligible characterization of knowledge attribution, Azzouni explains why the concept has puzzled philosophers so long, and he solves longstanding and recent puzzles that have perplexed epistemologists--including the dogmatism paradox, Gettier puzzles, and the surprise-exam paradox. "This is a terrific book, full of surprises. For instance, Chapter 9 is full of points that are original, insightful, and useful in helping to resolve stale debates. I especially liked the points that we don't ordinarily describe someone as losing knowledge by gaining defeating evidence, that "knows" is vague and tri-scoped, that vagueness needn't be explained by appeal to precise metasemantic machinery, and that Williamson's anti-luminosity argument founders on the fact that knowledge doesn't require confidence. Bravo!" --Ram Neta, University of North Carolina, Chapel Hill Praise for Jody Azzouni's Ontology without Borders: "Azzouni offers a very strong drink, proposing that we do without central elements of what almost anyone would call logic or ontology. His arguments are serious and wide-ranging. If he's right, the reader will have learned something very important. If he's wrong, then the reader who figures out how he went wrong will also have learned something very important. Not every book has this feature." --Michael Gorman, The Catholic University of America

Handbook of Abductive Cognition
Handbook of Abductive Cognition

Author: Lorenzo Magnani

Publisher: Springer Nature

Published: 2023-03-31

Total Pages: 1921

ISBN-13: 3031101359

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This Handbook offers the first comprehensive reference guide to the interdisciplinary field of abductive cognition, providing readers with extensive information on the process of reasoning to hypotheses in humans, animals, and in computational machines. It highlights the role of abduction in both theory practice: in generating and testing hypotheses and explanatory functions for various purposes and as an educational device. It merges logical, cognitive, epistemological and philosophical perspectives with more practical needs relating to the application of abduction across various disciplines and practices, such as in diagnosis, creative reasoning, scientific discovery, diagrammatic and ignorance-based cognition, and adversarial strategies. It also discusses the inferential role of models in hypothetical reasoning, abduction and creativity, including the process of development, implementation and manipulation for different scientific and technological purposes. Written by a group of internationally renowned experts in philosophy, logic, general epistemology, mathematics, cognitive, and computer science, as well as life sciences, engineering, architecture, and economics, the Handbook of Abductive Cognition offers a unique reference guide for readers approaching the process of reasoning to hypotheses from different perspectives and for various theoretical and practical purposes. Numerous diagrams, schemes and other visual representations are included to promote a better understanding of the relevant concepts and to make concepts highly accessible to an audience of scholars and students with different scientific backgrounds.

Great Circles
Great Circles

Author: Emily Rolfe Grosholz

Publisher: Springer

Published: 2018-11-13

Total Pages: 275

ISBN-13: 3319982311

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This volume explores the interaction of poetry and mathematics by looking at analogies that link them. The form that distinguishes poetry from prose has mathematical structure (lifting language above the flow of time), as do the thoughtful ways in which poets bring the infinite into relation with the finite. The history of mathematics exhibits a dramatic narrative inspired by a kind of troping, as metaphor opens, metonymy and synecdoche elaborate, and irony closes off or shifts the growth of mathematical knowledge. The first part of the book is autobiographical, following the author through her discovery of these analogies, revealed by music, architecture, science fiction, philosophy, and the study of mathematics and poetry. The second part focuses on geometry, the circle and square, launching us from Shakespeare to Housman, from Euclid to Leibniz. The third part explores the study of dynamics, inertial motion and transcendental functions, from Descartes to Newton, and in 20th c. poetry. The final part contemplates infinity, as it emerges in modern set theory and topology, and in contemporary poems, including narrative poems about modern cosmology.