Mathematics Logic And Their Philosophies

Mathematics Logic And Their Philosophies 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 Mathematics Logic And Their Philosophies book. This book definitely worth reading, it is an incredibly well-written.

Mathematics, Logic, and their Philosophies

Mojtaba Mojtahedi,Shahid Rahman,Mohammad Saleh Zarepour
Mathematics Logic and their Philosophies Book PDF

Author : Mojtaba Mojtahedi,Shahid Rahman,Mohammad Saleh Zarepour
Publisher : Springer Nature
Page : 493 pages
File Size : 55,9 Mb
Release : 2021-02-09
Category : Philosophy
ISBN : 9783030536541

Get Book

Mathematics, Logic, and their Philosophies by Mojtaba Mojtahedi,Shahid Rahman,Mohammad Saleh Zarepour Pdf

This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. The third category contains papers on Avicenna’s logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community.

Philosophical and Mathematical Logic

Harrie de Swart
Philosophical and Mathematical Logic Book PDF

Author : Harrie de Swart
Publisher : Springer
Page : 539 pages
File Size : 40,5 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

The Oxford Handbook of Philosophy of Mathematics and Logic

Stewart Shapiro
The Oxford Handbook of Philosophy of Mathematics and Logic Book PDF

Author : Stewart Shapiro
Publisher : Oxford University Press
Page : 856 pages
File Size : 42,9 Mb
Release : 2005-02-10
Category : Mathematics
ISBN : 9780190287535

Get Book

The Oxford Handbook of Philosophy of Mathematics and Logic by Stewart Shapiro Pdf

Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.

Mathematics and Mind

Alexander George
Mathematics and Mind Book PDF

Author : Alexander George
Publisher : Oxford University Press, USA
Page : 218 pages
File Size : 54,9 Mb
Release : 1994
Category : Mathematics
ISBN : 9780195079296

Get Book

Mathematics and Mind by Alexander George Pdf

The essays in this volume investigate the conceptual foundations of mathematics illuminating the powers of the mind. Contributors include Alexander George, Michael Dummett, George Boolos, W.W. Tait, Wilfried Sieg, Daniel Isaacson, Charles Parsons, and Michael Hallett.

Logic, Epistemology, and the Unity of Science

Shahid Rahman,John Symons,Dov M. Gabbay,jean paul van bendegem
Logic Epistemology and the Unity of Science Book PDF

Author : Shahid Rahman,John Symons,Dov M. Gabbay,jean paul van bendegem
Publisher : Springer Science & Business Media
Page : 618 pages
File Size : 51,6 Mb
Release : 2009-03-15
Category : Philosophy
ISBN : 9781402028083

Get Book

Logic, Epistemology, and the Unity of Science by Shahid Rahman,John Symons,Dov M. Gabbay,jean paul van bendegem Pdf

The first volume in this new series explores, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The book offers essays from important and influential philosophers in contemporary philosophy, discussing a range of topics from philosophy of science to epistemology, philosophy of logic and game theoretical approaches. It will be of interest to philosophers, computer scientists and all others interested in the scientific rationality.

Three Views of Logic

Donald W. Loveland,Richard E. Hodel,S. G. Sterrett
Three Views of Logic Book PDF

Author : Donald W. Loveland,Richard E. Hodel,S. G. Sterrett
Publisher : Princeton University Press
Page : 344 pages
File Size : 45,7 Mb
Release : 2014-01-26
Category : Mathematics
ISBN : 9781400848751

Get Book

Three Views of Logic by Donald W. Loveland,Richard E. Hodel,S. G. Sterrett Pdf

Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses

LOGIC: Lecture Notes for Philosophy, Mathematics, and Computer Science

Andrea Iacona
LOGIC Lecture Notes for Philosophy Mathematics and Computer Science Book PDF

Author : Andrea Iacona
Publisher : Springer Nature
Page : 228 pages
File Size : 40,6 Mb
Release : 2021-05-10
Category : Philosophy
ISBN : 9783030648114

Get Book

LOGIC: Lecture Notes for Philosophy, Mathematics, and Computer Science by Andrea Iacona Pdf

This textbook is a logic manual which includes an elementary course and an advanced course. It covers more than most introductory logic textbooks, while maintaining a comfortable pace that students can follow. The technical exposition is clear, precise and follows a paced increase in complexity, allowing the reader to get comfortable with previous definitions and procedures before facing more difficult material. The book also presents an interesting overall balance between formal and philosophical discussion, making it suitable for both philosophy and more formal/science oriented students. This textbook is of great use to undergraduate philosophy students, graduate philosophy students, logic teachers, undergraduates and graduates in mathematics, computer science or related fields in which logic is required.

Mathematical Logic

Roman Kossak
Mathematical Logic Book PDF

Author : Roman Kossak
Publisher : Springer
Page : 186 pages
File Size : 45,7 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9783319972985

Get Book

Mathematical Logic by Roman Kossak Pdf

This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. The exposition does not assume any prerequisites; it is rigorous, but as informal as possible. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. Although more advanced, this second part is accessible to the reader who is either already familiar with basic mathematical logic, or has carefully read the first part of the book. Classical developments in model theory, including the Compactness Theorem and its uses, are discussed. Other topics include tameness, minimality, and order minimality of structures. The book can be used as an introduction to model theory, but unlike standard texts, it does not require familiarity with abstract algebra. This book will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.

Logic, Mathematics, Philosophy, Vintage Enthusiasms

David DeVidi,Michael Hallett,Peter Clark
Logic Mathematics Philosophy Vintage Enthusiasms Book PDF

Author : David DeVidi,Michael Hallett,Peter Clark
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 49,9 Mb
Release : 2011-03-23
Category : Philosophy
ISBN : 9789400702141

Get Book

Logic, Mathematics, Philosophy, Vintage Enthusiasms by David DeVidi,Michael Hallett,Peter Clark Pdf

The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic (William Lawvere, Peter Aczel, Graham Priest, Giovanni Sambin); analytical philosophy (Michael Dummett, William Demopoulos), philosophy of science (Michael Redhead, Frank Arntzenius), philosophy of mathematics (Michael Hallett, John Mayberry, Daniel Isaacson) and decision theory and foundations of economics (Ken Bimore). Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic.

Introduction to Mathematical Philosophy

Bertrand Russell
Introduction to Mathematical Philosophy Book PDF

Author : Bertrand Russell
Publisher : Courier Corporation
Page : 230 pages
File Size : 41,9 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 0486277240

Get Book

Introduction to Mathematical Philosophy by Bertrand Russell Pdf

In the words of Bertrand Russell, "Because language is misleading, as well as because it is diffuse and inexact when applied to logic (for which it was never intended), logical symbolism is absolutely necessary to any exact or thorough treatment of mathematical philosophy." That assertion underlies this book, a seminal work in the field for more than 70 years. In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy. In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.

A Profile of Mathematical Logic

Howard DeLong
A Profile of Mathematical Logic Book PDF

Author : Howard DeLong
Publisher : Courier Corporation
Page : 322 pages
File Size : 46,9 Mb
Release : 2012-09-26
Category : Mathematics
ISBN : 9780486139159

Get Book

A Profile of Mathematical Logic by Howard DeLong Pdf

This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.

Logic, Philosophy of Mathematics, and Their History

Erich H Reck
Logic Philosophy of Mathematics and Their History Book PDF

Author : Erich H Reck
Publisher : Unknown
Page : 326 pages
File Size : 45,7 Mb
Release : 2018-11-16
Category : Mathematics
ISBN : 1848902875

Get Book

Logic, Philosophy of Mathematics, and Their History by Erich H Reck Pdf

In a career that spans 60 years so far, W.W. Tait has made many highly influential contributions to logic, the philosophy of mathematics, and their history. The present collection of new essays - contributed by former students, colleagues, and friends - is a Festschrift, i.e., a celebration of his life and work. The essays address a variety of themes prominent in his work or related to it. The collection starts with an introduction in which Tait's contributions are sketched and put into context. The eleven essays that follow are arranged in three parts: Part I. Proof Theory and its History; Part II. Logic and Philosophy of Mathematics; and Part III. History of Logic and Philosophy of Mathematics. Each of the essays contributes substantially to one or several of these areas. The authors included are: Steve Awodey, Solomon Feferman, Michael Friedman, Warren Goldfarb, Geoffrey Hellman, William Howard, Stephen Menn, Rebecca Morris, Charles Parsons, Erich Reck, Thomas Ricketts, and Wilfried Sieg. The editor, Erich H. Reck is Professor of Philosophy at the University of California at Riverside.

Logic for Philosophy

Theodore Sider
Logic for Philosophy Book PDF

Author : Theodore Sider
Publisher : Oxford University Press
Page : 305 pages
File Size : 53,7 Mb
Release : 2010-01-07
Category : Philosophy
ISBN : 9780192658814

Get Book

Logic for Philosophy by Theodore Sider Pdf

Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii) extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for predicate logic (completeness, undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to do philosophy.

Philosophy of Mathematics

Ahmet Cevik
Philosophy of Mathematics Book PDF

Author : Ahmet Cevik
Publisher : CRC Press
Page : 352 pages
File Size : 41,6 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

Mathematical Logic

George Tourlakis
Mathematical Logic Book PDF

Author : George Tourlakis
Publisher : John Wiley & Sons
Page : 314 pages
File Size : 48,7 Mb
Release : 2011-03-01
Category : Mathematics
ISBN : 9781118030691

Get Book

Mathematical Logic by George Tourlakis Pdf

A comprehensive and user-friendly guide to the use of logic in mathematical reasoning Mathematical Logic presents a comprehensive introduction to formal methods of logic and their use as a reliable tool for deductive reasoning. With its user-friendly approach, this book successfully equips readers with the key concepts and methods for formulating valid mathematical arguments that can be used to uncover truths across diverse areas of study such as mathematics, computer science, and philosophy. The book develops the logical tools for writing proofs by guiding readers through both the established "Hilbert" style of proof writing, as well as the "equational" style that is emerging in computer science and engineering applications. Chapters have been organized into the two topical areas of Boolean logic and predicate logic. Techniques situated outside formal logic are applied to illustrate and demonstrate significant facts regarding the power and limitations of logic, such as: Logic can certify truths and only truths. Logic can certify all absolute truths (completeness theorems of Post and Gödel). Logic cannot certify all "conditional" truths, such as those that are specific to the Peano arithmetic. Therefore, logic has some serious limitations, as shown through Gödel's incompleteness theorem. Numerous examples and problem sets are provided throughout the text, further facilitating readers' understanding of the capabilities of logic to discover mathematical truths. In addition, an extensive appendix introduces Tarski semantics and proceeds with detailed proofs of completeness and first incompleteness theorems, while also providing a self-contained introduction to the theory of computability. With its thorough scope of coverage and accessible style, Mathematical Logic is an ideal book for courses in mathematics, computer science, and philosophy at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who wish to learn how to use logic in their everyday work.