Mathematics and Logic

Author: Mark Kac,Stanislaw M. Ulam

Publisher: Courier Corporation

ISBN: 0486670856

Category: Philosophy

Page: 170

View: 2367

Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."

The Philosophy of Mathematics and Logic in the 1920s and 1930s in Poland

Author: Roman Murawski

Publisher: Springer

ISBN: 3034808313

Category: Mathematics

Page: 228

View: 9089

The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s. It was a remarkable period in the history of Polish science, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent the development of logic and mathematics was accompanied by a philosophical reflection. We try to answer those questions by analyzing both works of Polish logicians and mathematicians who have a philosophical temperament as well as their research practice. Works and philosophical views of the following Polish scientists will be analyzed: Wacław Sierpiński, Zygmunt Janiszewski, Stefan Mazurkiewicz, Stefan Banach Hugo Steinhaus, Eustachy Żylińsk and Leon Chwistek, Jan Łukasiewicz, Zygmunt Zawirski, Stanisław Leśniewski, Tadeusz Kotarbiński, Kazimierz Ajdukiewicz, Alfred Tarski, Andrzej Mostowski and Henryk Mehlberg, Jan Sleszyński, Stanisław Zaremba and Witold Wilkosz. To indicate the background of scientists being active in the 1920s and 1930s we consider in Chapter 1 some predecessors, in particular: Jan Śniadecki, Józef Maria Hoene-Wroński, Samuel Dickstein and Edward Stamm.

Mathematics and Logic in History and in Contemporary Thought

Author: Ettore Carruccio,Isabel Quigly

Publisher: Routledge

ISBN: 1351506617

Category: Mathematics

Page: 400

View: 6723

This book is not a conventional history of mathematics as such, a museum of documents and scientific curiosities. Instead, it identifies this vital science with the thought of those who constructed it and in its relation to the changing cultural context in which it evolved. Particular emphasis is placed on the philosophic and logical systems, from Aristotle onward, that provide the basis for the fusion of mathematics and logic in contemporary thought.

Giuseppe Peano between Mathematics and Logic

Proceeding of the International Conference in honour of Giuseppe Peano on the 150th anniversary of his birth and the centennial of the Formulario Mathematico Torino (Italy) October 2-3, 2008

Author: Fulvia Skof

Publisher: Springer Science & Business Media

ISBN: 9788847018365

Category: Mathematics

Page: 190

View: 9608

This book contains the papers developing out the presentations given at the International Conference organized by the Torino Academy of Sciences and the Department of Mathematics Giuseppe Peano of the Torino University to celebrate the 150th anniversary of G. Peano's birth - one of the greatest figures in modern mathematics and logic and the most important mathematical logician in Italy - a century after the publication of Formulario Mathematico, a great attempt to systematise Mathematics in symbolic form.

The Oxford Handbook of Philosophy of Mathematics and Logic

Author: Stewart Shapiro

Publisher: Oxford University Press

ISBN: 0190287535

Category: Mathematics

Page: 856

View: 4172

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.

Basic Concepts of Mathematics and Logic

Author: Michael C. Gemignani

Publisher: Courier Corporation

ISBN: 0486435067

Category: Mathematics

Page: 280

View: 5444

This text emphasizes logic and the theory of sets. Students who take no further courses in the field will find it an excellent resource for developing an appreciation for the nature of mathematics. Others will discover the foundations for future studies — set theory, logic, counting, numbers, functions, and more. 1968 edition. 43 figures. 25 tables.

Cultures of Mathematics and Logic

Selected Papers from the Conference in Guangzhou, China, November 9-12, 2012

Author: Shier Ju,Benedikt Löwe,Thomas Müller,Yun Xie

Publisher: Birkhäuser

ISBN: 3319315021

Category: Mathematics

Page: 123

View: 5475

This book gathers the proceedings of the conference "Cultures of Mathematics and Logic," held in Guangzhou, China. The event was the third in a series of interdisciplinary, international conferences emphasizing the cultural components of philosophy of mathematics and logic. It brought together researchers from many disciplines whose work sheds new light on the diversity of mathematical and logical cultures and practices. In this context, the cultural diversity can be diachronical (different cultures in different historical periods), geographical (different cultures in different regions), or sociological in nature.

My Best Mathematical and Logic Puzzles

Author: Martin Gardner

Publisher: Courier Corporation

ISBN: 0486320324

Category: Games & Activities

Page: 96

View: 2660

The noted expert selects 70 of his favorite "short" puzzles, including such mind-bogglers as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, and dozens more involving logic and basic math. Solutions.

Math and logic games

Author: Franco Agostini

Publisher: Harper Perennial

ISBN: 9780060970215

Category: Games

Page: 181

View: 7319

Discusses games with numbers, geometrical figures, logic, probability, and paradoxes, and looks at their mathematical basis

After Gödel

Platonism and Rationalism in Mathematics and Logic

Author: Richard L. Tieszen

Publisher: Oxford University Press

ISBN: 019960620X

Category: Mathematics

Page: 245

View: 3263

Richard Tieszen analyzes, develops, and defends the writings of Kurt Gödel (1906-1978) on the philosophy and foundations of mathematics and logic. Gödel's relation to the work of Plato, Leibniz, Husserl, and Kant is examined, and a new type of platonic rationalism that requires rational intuition, called 'constituted platonism', is proposed.

Mensa Challenge Your Brain Math & Logic Puzzles

Author: Dave Tuller,Michael Rios

Publisher: Sterling Publishing Company, Inc.

ISBN: 9781402714498

Category: Games

Page: 96

View: 6462

Looking for a brain workout? Well look no further with a collection of Mensa-level conundrums. Puzzles range from classics like Battleships to "Hex Loops" - locate a path that travels through the adjacent hexagons: the trick is it has to end where it started, and the lines can't touch or cross.

Topics in Logic, Philosophy and Foundations of Mathematics, and Computer Science

In Recognition of Professor Andrzej Grzegorczyk

Author: Stanisław Krajewski

Publisher: IOS Press

ISBN: 9781586038144

Category: Computers

Page: 365

View: 3852

Professor Andrzej Grzegorczyk has made fundamental contributions to logic and to philosophy. This volume honors Professor Grzegorczyk, the nestor of Polish logicians, on his 85th anniversary. It presents the work and life of Professor Grzegorczyk.

Puzzles in Math and Logic

100 New Recreations

Author: Aaron J. Friedland

Publisher: Courier Corporation

ISBN: 9780486222561

Category: Games

Page: 66

View: 4708

Selected brain teasers requiring geometric, algebraic, and logical solutions

David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933

Author: William Ewald,Wilfried Sieg

Publisher: Springer-Verlag

ISBN: 3540694447

Category: Mathematics

Page: 1062

View: 5284

The core of Volume 3 consists of lecture notes for seven sets of lectures Hilbert gave (often in collaboration with Bernays) on the foundations of mathematics between 1917 and 1926. These texts make possible for the first time a detailed reconstruction of the rapid development of Hilbert’s foundational thought during this period, and show the increasing dominance of the metamathematical perspective in his logical work: the emergence of modern mathematical logic; the explicit raising of questions of completeness, consistency and decidability for logical systems; the investigation of the relative strengths of various logical calculi; the birth and evolution of proof theory, and the parallel emergence of Hilbert’s finitist standpoint. The lecture notes are accompanied by numerous supplementary documents, both published and unpublished, including a complete version of Bernays’s Habilitationschrift of 1918, the text of the first edition of Hilbert and Ackermann’s Grundzüge der theoretischen Logik (1928), and several shorter lectures by Hilbert from the later 1920s. These documents, which provide the background to Hilbert and Bernays’s monumental Grundlagen der Mathematik (1934, 1938), are essential for understanding the development of modern mathematical logic, and for reconstructing the interactions between Hilbert, Bernays, Brouwer, and Weyl in the philosophy of mathematics.

Alfred Tarski

Life and Logic

Author: Anita Burdman Feferman,Solomon Feferman

Publisher: Cambridge University Press

ISBN: 9780521802406

Category: Biography & Autobiography

Page: 425

View: 957

Alfred Tarski, one of the greatest logicians of all time, is widely thought of as 'the man who defined truth'. His mathematical work on the concepts of truth and logical consequence are cornerstones of modern logic, influencing developments in philosophy, linguistics and computer science. Tarski was a charismatic teacher and zealous promoter of his view of logic as the foundation of all rational thought, a bon-vivant and a womanizer, who played the 'great man' to the hilt. Born in Warsaw in 1901 to Jewish parents, he changed his name and converted to Catholicism, but was never able to obtain a professorship in his home country. A fortuitous trip to the United States at the outbreak of war saved his life and turned his career around, even while it separated him from his family for years. By the war's end he was established as a professor of mathematics at the University of California, Berkeley. There Tarski built an empire in logic and methodology that attracted students and distinguished researchers from all over the world. From the cafes of Warsaw and Vienna to the mountains and deserts of California, this first full length biography places Tarski in the social, intellectual and historical context of his times and presents a frank, vivid picture of a personally and professionally passionate man, interlaced with an account of his major scientific achievements.