Download or read book Philosophy s Loss of Logic to Mathematics written by Woosuk Park and published by Springer. This book was released on 2018-07-12 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand Tarski’s and Gödel’s work, explaining why the problems they discussed are still unsolved. Finally, the book reports on some of the most influential positions in contemporary philosophy of mathematics, i.e., Maddy’s mathematical naturalism and Shapiro’s mathematical structuralism. Last but not least, the book introduces Biancani’s Aristotelian philosophy of mathematics as this is considered important to understand current philosophical issue in the applications of mathematics. One of the main purposes of the book is to stimulate readers to reconsider the Aristotelian position, which disappeared almost completely from the scene in logic and mathematics in the early twentieth century.
Download or read book Mathematical Thought written by E.W. Beth and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: In contributing a foreword to this book I am complying with a wish my husband expressed a few days before his death. He had completed the manuscript of this work, which may be considered a companion volume to his book Formal Methods. The task of seeing it through the press was undertaken by Mr. J. J. A. Mooij, acting director of the Institute for Research in Foundations and the Philosophy of Science (Instituut voor Grondslagenonderzoek en Filoso:fie der Exacte Wetenschappen) of the University of Amsterdam, with the help of Mrs. E. M. Barth, lecturer at the Institute. I wish to thank Mr. Mooij and Mrs. Barth most cordially for the care with which they have acquitted themselves of this delicate task and for the speed with which they have brought it to completion. I also wish to express my gratitude to Miss L. E. Minning, M. A. , for the helpful advice she has so kindly given to Mr. Mooij and Mrs. Barth during the proof reading. C. P. C. BETH-PASTOOR VII PREFACE A few years ago Mr. Horace S.
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 445 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 New Directions in the Philosophy of Mathematics written by Thomas Tymoczko and published by Princeton University Press. This book was released on 1998-02 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form. This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.
Download or read book Russell s Unknown Logicism written by S. Gandon and published by Springer. This book was released on 2012-08-30 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics , meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.
Download or read book Philosophy of Mathematics written by Stewart Shapiro and published by Oxford University Press. This book was released on 1997-08-07 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Do 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 mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians.
Download or read book From Logic to Practice written by Gabriele Lolli and published by . This book was released on 2014-12-31 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Search for Certainty A Philosophical Account of Foundations of Mathematics written by Marcus Giaquinto and published by Clarendon Press. This book was released on 2002-06-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nineteenth century saw a movement to make higher mathematics rigorous. This seemed to be on the brink of success when it was thrown into confusion by the discovery of the class paradoxes. That initiated a period of intense research into the foundations of mathematics, and with it the birth of mathematical logic and a new, sharper debate in the philosophy of mathematics. The Search for Certainty examines this foundational endeavour from the discovery of the paradoxes to the present. Focusing on Russell's logicist programme and Hilbert's finitist programme, Giaquinto investigates how successful they were and how successful they could be. These questions are set in the context of a clear, non-technical exposition and assessment of the most important discoveries in mathematical logic, above all G--ouml--;del's underivability theorems. More than six decades after those discoveries, Giaquinto asks what our present perspective should be on the question of certainty in mathematics. Taking recent developments into account, he gives reasons for a surprisingly positive response.
Download or read book Introduction to Mathematical Philosophy written by Bertrand Russell and published by . This book was released on 1920 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
Download or read book More Precisely The Math You Need to Do Philosophy Second Edition written by Eric Steinhart and published by Broadview Press. This book was released on 2017-11-21 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: More Precisely is a rigorous and engaging introduction to the mathematics necessary to do philosophy. Eric Steinhart provides lucid explanations of many basic mathematical concepts and sets out the most commonly used notational conventions. He also demonstrates how mathematics applies to fundamental issues in various branches of philosophy, including metaphysics, philosophy of language, epistemology, and ethics. This second edition adds a substantial section on decision and game theory, as well as a chapter on information theory and the efficient coding of information.
Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by National Geographic Books. This book was released on 2021-03-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Collected Papers on Mathematics Logic and Philosophy written by Gottlob Frege and published by . This book was released on 1984 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Mathematical Philosophy written by Bertrand Russell and published by Forgotten Books. This book was released on 2015-06-16 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groundbreaking in its day the aim of this fantastic, if dated book by renowned philosopher Bertrand Russell is nothing less than to demonstrate that all of mathematics is describable by a single system of logic. It does so in a way which, while not simplistic, is still accessible to anyone willing to put in some thought. A foundation in logic and philosophy would certainly be a help when reading this book however. This approach was later demonstrated to be impossible, with Kurt Godel's incompleteness theorems proving that for any consistent logical system there are some problems which cannot be solved within that system. Godel's work would not have been the same without these earlier attempts however, so they provide an essential context for understanding these later developments. This does not mean that Russell's work is devoid of insight or use for its own sake however, as most of the individual sections as well as the history of mathematical philosophy are very valuable. Those whose interest is piqued by this book may wish to move on to Russell and Whitehead's Principia Mathematica for a more difficult and in depth work. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book Objects Structures and Logics written by Gianluigi Oliveri and published by Springer Nature. This book was released on 2022-03-08 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited collection casts light on central issues within contemporary philosophy of mathematics such as the realism/anti-realism dispute; the relationship between logic and metaphysics; and the question of whether mathematics is a science of objects or structures. The discussions offered in the papers involve an in-depth investigation of, among other things, the notions of mathematical truth, proof, and grounding; and, often, a special emphasis is placed on considerations relating to mathematical practice. A distinguishing feature of the book is the multicultural nature of the community that has produced it. Philosophers, logicians, and mathematicians have all contributed high-quality articles which will prove valuable to researchers and students alike.
Download or read book Philosophy of Mathematics written by Charles S. Peirce and published by Indiana University Press. This book was released on 2010-08-19 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The philosophy of mathematics plays a vital role in the mature philosophy of Charles S. Peirce. Peirce received rigorous mathematical training from his father and his philosophy carries on in decidedly mathematical and symbolic veins. For Peirce, math was a philosophical tool and many of his most productive ideas rest firmly on the foundation of mathematical principles. This volume collects Peirce's most important writings on the subject, many appearing in print for the first time. Peirce's determination to understand matter, the cosmos, and "the grand design" of the universe remain relevant for contemporary students of science, technology, and symbolic logic.
