The Principles Of Mathematics Revisited

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The Principles of Mathematics Revisited

Author : Jaakko Hintikka
Publisher : Cambridge University Press
ISBN 13 : 9780521624985
Total Pages : 308 pages
Book Rating : 4.6/5 (249 download)

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Book Synopsis The Principles of Mathematics Revisited by : Jaakko Hintikka

Download or read book The Principles of Mathematics Revisited written by Jaakko Hintikka and published by Cambridge University Press. This book was released on 1998-04-28 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous impossibility results by Gödel and Tarski that have dominated the field for the last sixty years turn out to be much less significant than has been thought. All of ordinary mathematics can in principle be done on this first-order level, thus dispensing with the existence of sets and other higher-order entities.

The Principles of Mathematics Revisited

Author : Hintikka Jaakko
Publisher :
ISBN 13 :
Total Pages : 288 pages
Book Rating : 4.:/5 (668 download)

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Book Synopsis The Principles of Mathematics Revisited by : Hintikka Jaakko

Download or read book The Principles of Mathematics Revisited written by Hintikka Jaakko and published by . This book was released on 1996 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Principles of Mathematics

Author : Vladimir Lepetic
Publisher : John Wiley & Sons
ISBN 13 : 1119131650
Total Pages : 672 pages
Book Rating : 4.1/5 (191 download)

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Book Synopsis Principles of Mathematics by : Vladimir Lepetic

Download or read book Principles of Mathematics written by Vladimir Lepetic and published by John Wiley & Sons. This book was released on 2015-11-30 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a uniquely balanced approach that bridges introductory and advanced topics in modern mathematics An accessible treatment of the fundamentals of modern mathematics, Principles of Mathematics: A Primer provides a unique approach to introductory andadvanced mathematical topics. The book features six main subjects, whichcan be studied independently or in conjunction with each other including: settheory; mathematical logic; proof theory; group theory; theory of functions; andlinear algebra. The author begins with comprehensive coverage of the necessary building blocks in mathematics and emphasizes the need to think abstractly and develop an appreciation for mathematical thinking. Maintaining a useful balance of introductory coverage and mathematical rigor, Principles of Mathematics: A Primer features: Detailed explanations of important theorems and their applications Hundreds of completely solved problems throughout each chapter Numerous exercises at the end of each chapter to encourage further exploration Discussions of interesting and provocative issues that spark readers’ curiosity and facilitate a better understanding and appreciation of the field of mathematics Principles of Mathematics: A Primer is an ideal textbook for upper-undergraduate courses in the foundations of mathematics and mathematical logic as well as for graduate-level courses related to physics, engineering, and computer science. The book is also a useful reference for readers interested in pursuing careers in mathematics and the sciences.

Lingua Universalis vs. Calculus Ratiocinator:

Author : Jaakko Hintikka
Publisher : Springer Science & Business Media
ISBN 13 : 9401586012
Total Pages : 290 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Lingua Universalis vs. Calculus Ratiocinator: by : Jaakko Hintikka

Download or read book Lingua Universalis vs. Calculus Ratiocinator: written by Jaakko Hintikka and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: R. G. Collingwood saw one of the main tasks of philosophers and of historians of human thought in uncovering what he called the ultimate presuppositions of different thinkers, of different philosophical movements and of entire eras of intellectual history. He also noted that such ultimate presuppositions usually remain tacit at first, and are discovered only by subsequent reflection. Collingwood would have been delighted by the contrast that constitutes the overall theme of the essays collected in this volume. Not only has this dichotomy ofviews been one ofthe mostcrucial watersheds in the entire twentieth-century philosophical thought. Not only has it remained largely implicit in the writings of the philosophers for whom it mattered most. It is a truly Collingwoodian presupposition also in that it is not apremise assumed by different thinkers in their argumentation. It is the presupposition of a question, an assumption to the effect that a certain general question can be raised and answered. Its role is not belied by the fact that several philosophers who answered it one way or the other seem to be largely unaware that the other answer also makes sense - if it does. This Collingwoodian question can be formulated in a first rough approximation by asking whether language - our actual working language, Tarski's "colloquiallanguage" - is universal in the sense of being inescapable. This formulation needs all sorts of explanations, however.

Language, Truth and Logic in Mathematics

Author : Jaakko Hintikka
Publisher : Springer Science & Business Media
ISBN 13 : 9401720452
Total Pages : 339 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Language, Truth and Logic in Mathematics by : Jaakko Hintikka

Download or read book Language, Truth and Logic in Mathematics written by Jaakko Hintikka and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: One can distinguish, roughly speaking, two different approaches to the philosophy of mathematics. On the one hand, some philosophers (and some mathematicians) take the nature and the results of mathematicians' activities as given, and go on to ask what philosophical morals one might perhaps find in their story. On the other hand, some philosophers, logicians and mathematicians have tried or are trying to subject the very concepts which mathematicians are using in their work to critical scrutiny. In practice this usually means scrutinizing the logical and linguistic tools mathematicians wield. Such scrutiny can scarcely help relying on philosophical ideas and principles. In other words it can scarcely help being literally a study of language, truth and logic in mathematics, albeit not necessarily in the spirit of AJ. Ayer. As its title indicates, the essays included in the present volume represent the latter approach. In most of them one of the fundamental concepts in the foundations of mathematics and logic is subjected to a scrutiny from a largely novel point of view. Typically, it turns out that the concept in question is in need of a revision or reconsideration or at least can be given a new twist. The results of such a re-examination are not primarily critical, however, but typically open up new constructive possibilities. The consequences of such deconstructions and reconstructions are often quite sweeping, and are explored in the same paper or in others.

The Arché Papers on the Mathematics of Abstraction

Author : Roy T. Cook
Publisher : Springer Science & Business Media
ISBN 13 : 1402042655
Total Pages : 480 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis The Arché Papers on the Mathematics of Abstraction by : Roy T. Cook

Download or read book The Arché Papers on the Mathematics of Abstraction written by Roy T. Cook and published by Springer Science & Business Media. This book was released on 2007-11-27 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines. Attention is focused on extending the Neo-Fregean treatment to all of mathematics, with the reconstruction of real analysis from various cut- or cauchy-sequence-related abstraction principles and the reconstruction of set theory from various restricted versions of Basic Law V as case studies.

Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method

Author : Carlo Cellucci
Publisher : Springer Science & Business Media
ISBN 13 : 9400760914
Total Pages : 391 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method by : Carlo Cellucci

Download or read book Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method written by Carlo Cellucci and published by Springer Science & Business Media. This book was released on 2013-10-09 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. trigger

All the Math You Missed

Author : Thomas A. Garrity
Publisher : Cambridge University Press
ISBN 13 : 1009006207
Total Pages : 417 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis All the Math You Missed by : Thomas A. Garrity

Download or read book All the Math You Missed written by Thomas A. Garrity and published by Cambridge University Press. This book was released on 2021-07-01 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beginning graduate students in mathematical sciences and related areas in physical and computer sciences and engineering are expected to be familiar with a daunting breadth of mathematics, but few have such a background. This bestselling book helps students fill in the gaps in their knowledge. Thomas A. Garrity explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The explanations are accompanied by numerous examples, exercises and suggestions for further reading that allow the reader to test and develop their understanding of these core topics. Featuring four new chapters and many other improvements, this second edition of All the Math You Missed is an essential resource for advanced undergraduates and beginning graduate students who need to learn some serious mathematics quickly.

The Structure of Thinking

Author : Laura E. Wood
Publisher : Andrews UK Limited
ISBN 13 : 1845405862
Total Pages : 297 pages
Book Rating : 4.8/5 (454 download)

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Book Synopsis The Structure of Thinking by : Laura E. Wood

Download or read book The Structure of Thinking written by Laura E. Wood and published by Andrews UK Limited. This book was released on 2013-06-17 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic philosophers and cognitive scientists have long argued that the mind is a computer-like syntactical engine, and that all human mental capacities can be described as digital computational processes. This book presents an alternative, naturalistic view of human thinking, arguing that computers are merely sophisticated machines. Computers are only simulating thought when they crunch symbols, not thinking. Human cognition - semantics, de re reference, indexicals, meaning and causation - are all rooted in human experience and life. Without life and experience, these elements of discourse and knowledge refer to nothing. And without these elements of discourse and knowledge, syntax is vacant structure, not thinking.

Reduction - Abstraction - Analysis

Author : Alexander Hieke
Publisher : Walter de Gruyter
ISBN 13 : 3110328879
Total Pages : 432 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Reduction - Abstraction - Analysis by : Alexander Hieke

Download or read book Reduction - Abstraction - Analysis written by Alexander Hieke and published by Walter de Gruyter. This book was released on 2013-05-02 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Philosophers often have tried to either reduce "disagreeable" objects or concepts to (more) acceptable objects or concepts. Reduction is regarded attractive by those who subscribe to an ideal of ontological parsimony. But the topic is not just restricted to traditional metaphysics or ontology. In the philosophy of mathematics, abstraction principles, such as Hume's principle, have been suggested to support a reconstruction of mathematics by logical means only. In the philosophy of language and the philosophy of science, the logical analysis of language has long been regarded to be the dominating paradigm, and liberalized projects of logical reconstruction remain to be driving forces of modern philosophy. This volume collects contributions comprising all those topics, including articles by Alexander Bird, Jaakko Hintikka, James Ladyman, Rohit Parikh, Gerhard Schurz, Peter Simons, Crispin Wright and Edward N. Zalta.

The Making of Mathematics

Author : Carlo Cellucci
Publisher : Springer Nature
ISBN 13 : 3030897311
Total Pages : 457 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis The Making of Mathematics by : Carlo Cellucci

Download or read book The Making of Mathematics written by Carlo Cellucci and published by Springer Nature. This book was released on 2022-03-07 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Philosophy and Model Theory

Author : Tim Button
Publisher : Oxford University Press
ISBN 13 : 0198790392
Total Pages : 534 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Philosophy and Model Theory by : Tim Button

Download or read book Philosophy and Model Theory written by Tim Button and published by Oxford University Press. This book was released on 2018 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging uses of model theory have created a highly fragmented literature. On the one hand, many philosophically significant results are found only in mathematics textbooks: these are aimed squarely at mathematicians; they typically presuppose that the reader has a serious background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are scattered across disconnected pockets of papers. The first aim of this book, then, is to explore the philosophical uses of model theory, focusing on the central topics of reference, realism, and doxology. Its second aim is to address important questions in the philosophy of model theory, such as: sameness of theories and structure, the boundaries of logic, and the classification of mathematical structures. Philosophy and Model Theory will be accessible to anyone who has completed an introductory logic course. It does not assume that readers have encountered model theory before, but starts right at the beginning, discussing philosophical issues that arise even with conceptually basic model theory. Moreover, the book is largely self-contained: model-theoretic notions are defined as and when they are needed for the philosophical discussion, and many of the most philosophically significant results are given accessible proofs.

Mathematical Methods in Interdisciplinary Sciences

Author : Snehashish Chakraverty
Publisher : John Wiley & Sons
ISBN 13 : 1119585503
Total Pages : 464 pages
Book Rating : 4.1/5 (195 download)

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Book Synopsis Mathematical Methods in Interdisciplinary Sciences by : Snehashish Chakraverty

Download or read book Mathematical Methods in Interdisciplinary Sciences written by Snehashish Chakraverty and published by John Wiley & Sons. This book was released on 2020-07-15 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brings mathematics to bear on your real-world, scientific problems Mathematical Methods in Interdisciplinary Sciences provides a practical and usable framework for bringing a mathematical approach to modelling real-life scientific and technological problems. The collection of chapters Dr. Snehashish Chakraverty has provided describe in detail how to bring mathematics, statistics, and computational methods to the fore to solve even the most stubborn problems involving the intersection of multiple fields of study. Graduate students, postgraduate students, researchers, and professors will all benefit significantly from the author's clear approach to applied mathematics. The book covers a wide range of interdisciplinary topics in which mathematics can be brought to bear on challenging problems requiring creative solutions. Subjects include: Structural static and vibration problems Heat conduction and diffusion problems Fluid dynamics problems The book also covers topics as diverse as soft computing and machine intelligence. It concludes with examinations of various fields of application, like infectious diseases, autonomous car and monotone inclusion problems.

Logic and Discrete Mathematics

Author : Willem Conradie
Publisher : John Wiley & Sons
ISBN 13 : 1119000092
Total Pages : 456 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Logic and Discrete Mathematics by : Willem Conradie

Download or read book Logic and Discrete Mathematics written by Willem Conradie and published by John Wiley & Sons. This book was released on 2015-04-16 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise yet rigorous introduction to logic and discrete mathematics. This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. The chapters on logic - propositional and first-order - provide a robust toolkit for logical reasoning, emphasizing the conceptual understanding of the language and the semantics of classical logic as well as practical applications through the easy to understand and use deductive systems of Semantic Tableaux and Resolution. The chapters on set theory, number theory, combinatorics and graph theory combine the necessary minimum of theory with numerous examples and selected applications. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in the accompanying solutions manual. Key Features: Suitable for a variety of courses for students in both Mathematics and Computer Science. Extensive, in-depth coverage of classical logic, combined with a solid exposition of a selection of the most important fields of discrete mathematics Concise, clear and uncluttered presentation with numerous examples. Covers some applications including cryptographic systems, discrete probability and network algorithms. Logic and Discrete Mathematics: A Concise Introduction is aimed mainly at undergraduate courses for students in mathematics and computer science, but the book will also be a valuable resource for graduate modules and for self-study.

Semantics and Truth

Author : Jan Woleński
Publisher : Springer Nature
ISBN 13 : 3030245365
Total Pages : 392 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Semantics and Truth by : Jan Woleński

Download or read book Semantics and Truth written by Jan Woleński and published by Springer Nature. This book was released on 2020-01-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a historical (with an outline of the history of the concept of truth from antiquity to our time) and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s. This theory became famous very soon and inspired logicians and philosophers. It has two different, but interconnected aspects: formal-logical and philosophical. The book deals with both, but it is intended mostly as a philosophical monograph. It explains Tarski’s motivation and presents discussions about his ideas (pro and contra) as well as points out various applications of the semantic theory of truth to philosophical problems (truth-criteria, realism and anti-realism, future contingents or the concept of correspondence between language and reality).

All the Mathematics You Missed

Author : Thomas A. Garrity
Publisher : 清华大学出版社有限公司
ISBN 13 : 9787302090854
Total Pages : 380 pages
Book Rating : 4.0/5 (98 download)

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Book Synopsis All the Mathematics You Missed by : Thomas A. Garrity

Download or read book All the Mathematics You Missed written by Thomas A. Garrity and published by 清华大学出版社有限公司. This book was released on 2004 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Compendium for Early Career Researchers in Mathematics Education

Author : Gabriele Kaiser
Publisher : Springer
ISBN 13 : 3030156362
Total Pages : 528 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Compendium for Early Career Researchers in Mathematics Education by : Gabriele Kaiser

Download or read book Compendium for Early Career Researchers in Mathematics Education written by Gabriele Kaiser and published by Springer. This book was released on 2019-04-26 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this Open Access compendium, written by experienced researchers in mathematics education, is to serve as a resource for early career researchers in furthering their knowledge of the state of the field and disseminating their research through publishing. To accomplish this, the book is split into four sections: Empirical Methods, Important Mathematics Education Themes, Academic Writing and Academic Publishing, and a section Looking Ahead. The chapters are based on workshops that were presented in the Early Career Researcher Day at the 13th International Congress on Mathematical Education (ICME-13). The combination of presentations on methodological approaches and theoretical perspectives shaping the field in mathematics education research, as well as the strong emphasis on academic writing and publishing, offered strong insight into the theoretical and empirical bases of research in mathematics education for early career researchers in this field. Based on these presentations, the book provides a state-of-the-art overview of important theories from mathematics education and the broad variety of empirical approaches currently widely used in mathematics education research. This compendium supports early career researchers in selecting adequate theoretical approaches and adopting the most appropriate methodological approaches for their own research. Furthermore, it helps early career researchers in mathematics education to avoid common pitfalls and problems while writing up their research and it provides them with an overview of the most important journals for research in mathematics education, helping them to select the right venue for publishing and disseminating their work.