Philosophy S Loss Of Logic To Mathematics

Philosophy S Loss Of Logic To Mathematics Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Philosophy S Loss Of Logic To Mathematics book. This book definitely worth reading, it is an incredibly well-written.

Philosophy's Loss of Logic to Mathematics

Woosuk Park
Philosophy s Loss of Logic to Mathematics Book PDF

Author : Woosuk Park
Publisher : Springer
Page : 230 pages
File Size : 50,9 Mb
Release : 2018-07-12
Category : Philosophy
ISBN : 9783319951478

Get Book

Philosophy's Loss of Logic to Mathematics by Woosuk Park Pdf

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.

Mathematical Thought

E.W. Beth
Mathematical Thought Book PDF

Author : E.W. Beth
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 53,6 Mb
Release : 2013-06-29
Category : Science
ISBN : 9789401722070

Get Book

Mathematical Thought by E.W. Beth Pdf

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.

Philosophical and Mathematical Logic

Harrie de Swart
Philosophical and Mathematical Logic Book PDF

Author : Harrie de Swart
Publisher : Springer
Page : 539 pages
File Size : 40,6 Mb
Release : 2018-11-28
Category : Philosophy
ISBN : 9783030032555

Get Book

Philosophical and Mathematical Logic by Harrie de Swart Pdf

This book was written to serve as an introduction to logic, with in each chapter – if applicable – special emphasis on the interplay between logic and philosophy, mathematics, language and (theoretical) computer science. The reader will not only be provided with an introduction to classical logic, but to philosophical (modal, epistemic, deontic, temporal) and intuitionistic logic as well. The first chapter is an easy to read non-technical Introduction to the topics in the book. The next chapters are consecutively about Propositional Logic, Sets (finite and infinite), Predicate Logic, Arithmetic and Gödel’s Incompleteness Theorems, Modal Logic, Philosophy of Language, Intuitionism and Intuitionistic Logic, Applications (Prolog; Relational Databases and SQL; Social Choice Theory, in particular Majority Judgment) and finally, Fallacies and Unfair Discussion Methods. Throughout the text, the author provides some impressions of the historical development of logic: Stoic and Aristotelian logic, logic in the Middle Ages and Frege's Begriffsschrift, together with the works of George Boole (1815-1864) and August De Morgan (1806-1871), the origin of modern logic. Since "if ..., then ..." can be considered to be the heart of logic, throughout this book much attention is paid to conditionals: material, strict and relevant implication, entailment, counterfactuals and conversational implicature are treated and many references for further reading are given. Each chapter is concluded with answers to the exercises. Philosophical and Mathematical Logic is a very recent book (2018), but with every aspect of a classic. What a wonderful book! Work written with all the necessary rigor, with immense depth, but without giving up clarity and good taste. Philosophy and mathematics go hand in hand with the most diverse themes of logic. An introductory text, but not only that. It goes much further. It's worth diving into the pages of this book, dear reader! Paulo Sérgio Argolo

Lectures on the Philosophy of Mathematics

Joel David Hamkins
Lectures on the Philosophy of Mathematics Book PDF

Author : Joel David Hamkins
Publisher : MIT Press
Page : 350 pages
File Size : 55,9 Mb
Release : 2021-03-09
Category : Mathematics
ISBN : 9780262542234

Get Book

Lectures on the Philosophy of Mathematics by Joel David Hamkins Pdf

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.

Philosophy of Science, Logic and Mathematics in the 20th Century

Stuart G. Shanker
Philosophy of Science Logic and Mathematics in the 20th Century Book PDF

Author : Stuart G. Shanker
Publisher : Taylor & Francis
Page : 508 pages
File Size : 42,5 Mb
Release : 2023-05-09
Category : Philosophy
ISBN : 9781000949698

Get Book

Philosophy of Science, Logic and Mathematics in the 20th Century by Stuart G. Shanker Pdf

The twentieth century witnessed the birth of analytic philosophy. This volume covers some of its key movements and philosophers, including Frege and Wittgenstein's Tractatus.

From Mathematics to Philosophy (Routledge Revivals)

Hao Wang
From Mathematics to Philosophy Routledge Revivals Book PDF

Author : Hao Wang
Publisher : Routledge
Page : 445 pages
File Size : 44,5 Mb
Release : 2016-06-10
Category : Philosophy
ISBN : 9781134884339

Get Book

From Mathematics to Philosophy (Routledge Revivals) by Hao Wang Pdf

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.

Frege

Michael Dummett
Frege Book PDF

Author : Michael Dummett
Publisher : Harvard University Press
Page : 364 pages
File Size : 54,7 Mb
Release : 1991
Category : Mathematics
ISBN : 0674319354

Get Book

Frege by Michael Dummett Pdf

No one has figured more prominently in the study of the German philosopher Gottlob Frege than Michael Dummett. His magisterial Frege: Philosophy of Language is a sustained, systematic analysis of Frege's thought, omitting only the issues in philosophy of mathematics. In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume of Basic Laws of Arithmetic, establishing what parts of the philosopher's views can be salvaged and employed in new theorizing, and what must be abandoned, either as incorrectly argued or as untenable in the light of technical developments. Gottlob Frege (1848-1925) was a logician, mathematician, and philosopher whose work had enormous impact on Bertrand Russell and later on the young Ludwig Wittgenstein, making Frege one of the central influences on twentieth-century Anglo-American philosophy; he is considered the founder of analytic philosophy. His philosophy of mathematics contains deep insights and remains a useful and necessary point of departure for anyone seriously studying or working in the field.

Essays in the Philosophy and History of Logic and Mathematics

Roman Murawski
Essays in the Philosophy and History of Logic and Mathematics Book PDF

Author : Roman Murawski
Publisher : BRILL
Page : 327 pages
File Size : 54,8 Mb
Release : 2015-06-29
Category : Philosophy
ISBN : 9789042030916

Get Book

Essays in the Philosophy and History of Logic and Mathematics by Roman Murawski Pdf

The book is a collection of the author’s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered. This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields.

The Evolution of Logic

W. D. Hart
The Evolution of Logic Book PDF

Author : W. D. Hart
Publisher : Cambridge University Press
Page : 128 pages
File Size : 53,5 Mb
Release : 2010-08-23
Category : Philosophy
ISBN : 9781139491204

Get Book

The Evolution of Logic by W. D. Hart Pdf

Examines the relations between logic and philosophy over the last 150 years. Logic underwent a major renaissance beginning in the nineteenth century. Cantor almost tamed the infinite, and Frege aimed to undercut Kant by reducing mathematics to logic. These achievements were threatened by the paradoxes, like Russell's. This ferment generated excellent philosophy (and mathematics) by excellent philosophers (and mathematicians) up to World War II. This book provides a selective, critical history of the collaboration between logic and philosophy during this period. After World War II, mathematical logic became a recognized subdiscipline in mathematics departments, and consequently but unfortunately philosophers have lost touch with its monuments. This book aims to make four of them (consistency and independence of the continuum hypothesis, Post's problem, and Morley's theorem) more accessible to philosophers, making available the tools necessary for modern scholars of philosophy to renew a productive dialogue between logic and philosophy.

Russell's Unknown Logicism

S. Gandon
Russell s Unknown Logicism Book PDF

Author : S. Gandon
Publisher : Springer
Page : 263 pages
File Size : 48,7 Mb
Release : 2012-08-30
Category : Mathematics
ISBN : 9781137024657

Get Book

Russell's Unknown Logicism by S. Gandon Pdf

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.

Philosophy of Logic (Routledge Revivals)

Hilary Putnam
Philosophy of Logic Routledge Revivals Book PDF

Author : Hilary Putnam
Publisher : Routledge
Page : 86 pages
File Size : 42,8 Mb
Release : 2014-04-04
Category : Philosophy
ISBN : 9781317832584

Get Book

Philosophy of Logic (Routledge Revivals) by Hilary Putnam Pdf

First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.

Philosophy of Mathematics

Ahmet Cevik
Philosophy of Mathematics Book PDF

Author : Ahmet Cevik
Publisher : CRC Press
Page : 352 pages
File Size : 47,8 Mb
Release : 2021-11-09
Category : Mathematics
ISBN : 9781000468809

Get Book

Philosophy of Mathematics by Ahmet Cevik Pdf

The philosophy of mathematics is an exciting subject. Philosophy of Mathematics: Classic and Contemporary Studies explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians to think about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge. With this new approach, the author rekindles an interest in philosophical subjects surrounding the foundations of mathematics. He offers the mathematical motivations behind the topics under debate. He introduces various philosophical positions ranging from the classic views to more contemporary ones, including subjects which are more engaged with mathematical logic. Most books on philosophy of mathematics have little to no focus on the effects of philosophical views on mathematical practice, and no concern on giving crucial mathematical results and their philosophical relevance, consequences, reasons, etc. This book fills this gap. The book can be used as a textbook for a one-semester or even one-year course on philosophy of mathematics. "Other textbooks on the philosophy of mathematics are aimed at philosophers. This book is aimed at mathematicians. Since the author is a mathematician, it is a valuable addition to the literature." - Mark Balaguer, California State University, Los Angeles "There are not many such texts available for mathematics students. I applaud efforts to foster the dialogue between mathematics and philosophy." - Michele Friend, George Washington University and CNRS, Lille, France

Philosophy of Mathematics

Thomas Bedürftig,Roman Murawski
Philosophy of Mathematics Book PDF

Author : Thomas Bedürftig,Roman Murawski
Publisher : Walter de Gruyter GmbH & Co KG
Page : 474 pages
File Size : 45,9 Mb
Release : 2018-10-26
Category : Mathematics
ISBN : 9783110468335

Get Book

Philosophy of Mathematics by Thomas Bedürftig,Roman Murawski Pdf

The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection

Introduction to Mathematical Philosophy

Bertrand Russell
Introduction to Mathematical Philosophy Book PDF

Author : Bertrand Russell
Publisher : Psychology Press
Page : 228 pages
File Size : 47,7 Mb
Release : 1993
Category : Mathematics
ISBN : 0415096049

Get Book

Introduction to Mathematical Philosophy by Bertrand Russell Pdf

Bertrand Russell is the most important philosopher of mathematics of the twentieth century. The author of The Principles of Mathematicsand, with Alfred Whitehead, the massive Principia Mathematica, Russell brought together his skills as a gifted communicator to provide a classic introduction to the philosophy of mathematics. Introduction to Mathematical Philosophysets out in a lucid and non-technical way the main ideas of Principia Mathematica. It is as inspiring and useful to the beginner now as it was when it was first published in 1919.

S. Leśniewski’s Lecture Notes in Logic

Jan J.T. Srzednicki,Z. Stachniak
S Le niewski s Lecture Notes in Logic Book PDF

Author : Jan J.T. Srzednicki,Z. Stachniak
Publisher : Springer Science & Business Media
Page : 191 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Philosophy
ISBN : 9789400927414

Get Book

S. Leśniewski’s Lecture Notes in Logic by Jan J.T. Srzednicki,Z. Stachniak Pdf

Stanislaw Lesniewski (1886-1939) was one of the leading Polish logicians and founders of the Warsaw School of Logic whose membership included, beside himself, Jan Lukasiewicz, Tadeusz Kotarbinski, Alfred Tarski, and many others. In his lifetime LeSniewski published only a few hundred pages. He produced many important results in many areas of mathematics; these stood in various relations to each other, and to materials produced by others, and, in time, created more and more editorial problems. Very many were left unpublished at the time of his death. Then in 1944 in the fire of Warsaw the whole of this material was burned and lost -a considerable loss since a great deal of what is important could have been reconstructed from these notes. The present publication aims at presenting unique Lesniewski's materials from alternative sources comprising lecture notes taken during some of Lesniewski's lectures and seminars delivered at the University of Warsaw be tween the two world wars. The editors are aware of the limitations of student notes which cannot compensate for the loss of the original materials. However, they are unique in reflecting Lesniewski's ideas as he himself presented them. Already at the time of his death it was realized that these notes would provide a unique access to Lesniewski's own thought as well as a valuable record of some of the activities of the Warsaw School of Logic.