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Frege Dedekind And Peano On The Foundations Of Arithmetic Routledge Revivals
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Book Synopsis Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals) by : Donald Gillies
Download or read book Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals) written by Donald Gillies and published by Routledge. This book was released on 2013-01-11 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This historical-critical study provides an excellent introduction to the problems of the philosophy of mathematics - problems which have wide implications for philosophy as a whole. This reissue will appeal to students of both mathematics and philosophy who wish to improve their knowledge of logic.
Book Synopsis Frege, Dedekind, and Peano on the Foundations of Arithmetic by : Donald Gillies
Download or read book Frege, Dedekind, and Peano on the Foundations of Arithmetic written by Donald Gillies and published by . This book was released on 2011 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This historical-critical study provides an excellent introduction to the problems of the philosophy of mathematics - problems which have wide implications for philosophy as a whole. This reissue will appeal to students of both mathematics and philosophy who wish to improve their knowledge of logic.
Book Synopsis The Foundations of Arithmetic by : Gottlob Frege
Download or read book The Foundations of Arithmetic written by Gottlob Frege and published by Northwestern University Press. This book was released on 1980-12 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Foundations of Arithmetic is undoubtedly the best introduction to Frege's thought; it is here that Frege expounds the central notions of his philosophy, subjecting the views of his predecessors and contemporaries to devastating analysis. The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly influenced developments in the philosophy of mathematics and in general ontology.
Book Synopsis From Mathematics to Philosophy (Routledge Revivals) by : Hao Wang
Download or read book From Mathematics to Philosophy (Routledge Revivals) written by Hao Wang and published by Routledge. This book was released on 2016-06-10 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more general method of approach called substantial factualism which the author asserts allows for the development of a more comprehensive philosophical position by not trivialising or distorting substantial facts of human knowledge.
Download or read book Gottlob Frege written by Gottlob Frege and published by Routledge. This book was released on 2017-09 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of the �Longman Library of Primary Sources in Philosophy,� this edition of Frege's Foundations of Arithmetic is framed by a pedagogical structure designed to make this important work of philosophy more accessible and meaningful for undergraduates.
Book Synopsis Bertrand Russell's Dialogue with His Contemporaries (Routledge Revivals) by : Elizabeth Ramsden Eames
Download or read book Bertrand Russell's Dialogue with His Contemporaries (Routledge Revivals) written by Elizabeth Ramsden Eames and published by Routledge. This book was released on 2013-10-08 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1989, this book considers Bertrand Russell’s philosophy through his correspondence with others. Indeed, his exchanges with his elders in philosophy, with his contemporaries, and with one of his most outstanding pupils are brought to life in this judicious exposition: meticulously documented before being judged with insight and sympathy, as well as impartiality. Elizabeth Ramsden Eames here explores the issues that emerged from Russell’s exchanges with certain other philosophers, and interprets the resulting reciprocal influences and reactions. The conversations presented cover subjects such as: the nature of relations; pluralism versus monism; the relation of the subject and object in knowledge; the analysis of experience; the definition of truth; the analysis of belief; and the theory of meaning. These have been in the forefront of philosophical discussion in our time, and Russell’s dialogue with his contemporaries promises to illumine them.
Book Synopsis Grundlagen der Arithmetik by : Gottlob Frege
Download or read book Grundlagen der Arithmetik written by Gottlob Frege and published by . This book was released on 1950 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Foundations of Arithmetic written by and published by . This book was released on 1980 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Theory of Logical Types (Routledge Revivals) by : Irving M. Copi
Download or read book The Theory of Logical Types (Routledge Revivals) written by Irving M. Copi and published by Routledge. This book was released on 2011-02-28 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reissue, first published in 1971, provides a brief historical account of the Theory of Logical Types; and describes the problems that gave rise to it, its various different formulations (Simple and Ramified), the difficulties connected with each, and the criticisms that have been directed against it. Professor Copi seeks to make the subject accessible to the non-specialist and yet provide a sufficiently rigorous exposition for the serious student to see exactly what the theory is and how it works.
Book Synopsis The Foundations of Arithmetic by : Gottlob Frege
Download or read book The Foundations of Arithmetic written by Gottlob Frege and published by . This book was released on 1958 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Essays on Frege's by : Philip A. Ebert
Download or read book Essays on Frege's written by Philip A. Ebert and published by . This book was released on 2019 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first collective study of a foundational text in modern philosophy and logic, Gottlob Frege's Basic Laws of Arithmetic which appeared in two volumes in 1893 and 1903. Twenty-two Frege scholars discuss a wide range of philosophical and logical topics arising from Basic Laws of Arithmetic, and demonstrate the technical and philosophical richness of the work. Their original contributions make vivid the importance of this magnum opus not just for Frege scholars but for the study of the history of logic, mathematics, and philosophy.
Book Synopsis The Concise Encyclopedia of Western Philosophy and Philosophers by : J. O. Urmson
Download or read book The Concise Encyclopedia of Western Philosophy and Philosophers written by J. O. Urmson and published by Psychology Press. This book was released on 1991 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fully revised third edition of this Concise Encyclopedia brings it completely up-to-date. Featuring lively and engaging entries by some of the leading philosophers of our age, it is a readable reference work and engaging introduction.
Book Synopsis Axiomatic Method and Category Theory by : Andrei Rodin
Download or read book Axiomatic Method and Category Theory written by Andrei Rodin and published by Springer Science & Business Media. This book was released on 2013-10-14 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.
Book Synopsis The Philosophers and Mathematics by : Hassan Tahiri
Download or read book The Philosophers and Mathematics written by Hassan Tahiri and published by Springer. This book was released on 2018-08-14 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the unique relationship between two different approaches to understand the nature of knowledge, reality, and existence. It collects essays that examine the distinctive historical relationship between mathematics and philosophy. Readers learn what key philosophers throughout the ages thought about mathematics. This includes both thinkers who recognized the relevance of mathematics to their own work as well as those who chose to completely ignore its many achievements. The essays offer insight into the role that mathematics played in the formation of each included philosopher’s doctrine as well as the impact its remarkable expansion had on the philosophical systems each erected. Conversely, the authors also highlight the ways that philosophy contributed to the growth and transformation of mathematics. Throughout, significant historical examples help to illustrate these points in a vivid way. Mathematics has often been a favored interlocutor of philosophers and a major source of inspiration. This book is the outcome of an international conference held in honor of Roshdi Rashed, a renowned historian of mathematics. It provides researchers, students, and interested readers with remarkable insights into the history of an important relationship throughout the ages.
Book Synopsis Proof and Proving in Mathematics Education by : Gila Hanna
Download or read book Proof and Proving in Mathematics Education written by Gila Hanna and published by Springer Science & Business Media. This book was released on 2012-06-14 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: *THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.
Book Synopsis Autonomy Platonism and the Indispensability Argument by : Russell Marcus
Download or read book Autonomy Platonism and the Indispensability Argument written by Russell Marcus and published by Lexington Books. This book was released on 2015-06-11 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical platonism is the view that mathematical statements are true of real mathematical objects like numbers, shapes, and sets. One central problem with platonism is that numbers, shapes, sets, and the like are not perceivable by our senses. In contemporary philosophy, the most common defense of platonism uses what is known as the indispensability argument. According to the indispensabilist, we can know about mathematics because mathematics is essential to science. Platonism is among the most persistent philosophical views. Our mathematical beliefs are among our most entrenched. They have survived the demise of millennia of failed scientific theories. Once established, mathematical theories are rarely rejected, and never for reasons of their inapplicability to empirical science. Autonomy Platonism and the Indispensability Argument is a defense of an alternative to indispensability platonism. The autonomy platonist believes that mathematics is independent of empirical science: there is purely mathematical evidence for purely mathematical theories which are even more compelling to believe than empirical science. Russell Marcus begins by contrasting autonomy platonism and indispensability platonism. He then argues against a variety of indispensability arguments in the first half of the book. In the latter half, he defends a new approach to a traditional platonistic view, one which includes appeals to a priori but fallible methods of belief acquisition, including mathematical intuition, and a natural adoption of ordinary mathematical methods. In the end, Marcus defends his intuition-based autonomy platonism against charges that the autonomy of mathematics is viciously circular. This book will be useful to researchers, graduate students, and advanced undergraduates with interests in the philosophy of mathematics or in the connection between science and mathematics.
Book Synopsis Social Constructivism as a Philosophy of Mathematics by : Paul Ernest
Download or read book Social Constructivism as a Philosophy of Mathematics written by Paul Ernest and published by SUNY Press. This book was released on 1998-01-01 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.
