Download or read book Axiomatics written by Alma Steingart and published by University of Chicago Press. This book was released on 2023-01-10 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first history of postwar mathematics, offering a new interpretation of the rise of abstraction and axiomatics in the twentieth century. Why did abstraction dominate American art, social science, and natural science in the mid-twentieth century? Why, despite opposition, did abstraction and theoretical knowledge flourish across a diverse set of intellectual pursuits during the Cold War? In recovering the centrality of abstraction across a range of modernist projects in the United States, Alma Steingart brings mathematics back into the conversation about midcentury American intellectual thought. The expansion of mathematics in the aftermath of World War II, she demonstrates, was characterized by two opposing tendencies: research in pure mathematics became increasingly abstract and rarified, while research in applied mathematics and mathematical applications grew in prominence as new fields like operations research and game theory brought mathematical knowledge to bear on more domains of knowledge. Both were predicated on the same abstractionist conception of mathematics and were rooted in the same approach: modern axiomatics. For American mathematicians, the humanities and the sciences did not compete with one another, but instead were two complementary sides of the same epistemological commitment. Steingart further reveals how this mathematical epistemology influenced the sciences and humanities, particularly the postwar social sciences. As mathematics changed, so did the meaning of mathematization. Axiomatics focuses on American mathematicians during a transformative time, following a series of controversies among mathematicians about the nature of mathematics as a field of study and as a body of knowledge. The ensuing debates offer a window onto the postwar development of mathematics band Cold War epistemology writ large. As Steingart’s history ably demonstrates, mathematics is the social activity in which styles of truth—here, abstraction—become synonymous with ways of knowing.

Download or read book Theory Change Ancient Axiomatics and Galileo s Methodology written by Jaakko Hintikka and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the 1978 Pisa, Italy, September 4-8, 1978 Conference on the History and Philosophy of Science

Download or read book Probing The Structure Of Quantum Mechanics Nonlinearity Nonlocality Computation And Axiomatics written by Diederik Aerts and published by World Scientific. This book was released on 2002-06-11 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last decade, scientists working in quantum theory have been engaging in promising new fields such as quantum computation and quantum information processing, and have also been reflecting on the possibilities of nonlinear behavior on the quantum level. These are challenging undertakings because (1) they will result in new solutions to important technical and practical problems that were unsolvable by the classical approaches (for example, quantum computers can calculate problems that are intractable if one uses classical computers); and (2) they open up new 'hard' problems of a fundamental nature that touch the foundation of quantum theory itself (for example, the contradiction between locality and nonlinearity and the interpretation of quantum computing as a universal process).In this book, one can distinguish two main streams of research to approach the just-mentioned problem field: (1) a theoretical structural part, which concentrates on the elaboration of a nonlinear quantum mechanics and the fundamentals of quantum computation; and (2) a theoretical experimental part, which focuses on the theoretical aspects of applications that arise from new technology and novel research perspectives such as quantum optics and quantum cryptography. Particular attention is also paid to the measurement problem, the classical limit and alternative interpretations (such as the hidden measurement approach).

Download or read book The Axiomatics of Economic Design Vol 1 written by William Thomson and published by Springer Nature. This book was released on with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Axiomatics written by Robert Blanché and published by . This book was released on 1962 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Foundations and Fundamental Concepts of Mathematics written by Howard Eves and published by Courier Corporation. This book was released on 2012-04-10 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.

Download or read book Axiomatics and Dogmatics written by John Robb Carnes and published by . This book was released on 1982 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Modern Physics and its Philosophy written by M. Strauss and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: In selecting the papers for this volume I have excluded all physics papers proper. I have further omitted all book rev.iews. Instead, I have included two papers not published previously; they are marked by an asterisk (*) in the table of contents. Since many of the papers were occasioned by Symposia or similar gatherings their chronological order is rather accidental. Hence I have tried to group the papers thematically into four parts. Within each part the order of sequence is from the more general to the more special, or from a more popular to a more technical treatment. The same principle has been applied to the sequential order of the parts. The foundational papers on quantum mechanics have been arranged in a somewhat dif ferent manner. Chapters XVI-XIX are concerned with the logic of complementarity while in Chapters XX-XXII a more radical recon ceptualization is carried out. Two of the older papers (Chapters VI and VIII) have been revised to bring them more into line with present terminology. Other papers have been corrected by additions and omissions. Additions are marked by square brackets [ ], while double square brackets [[ II signify omis sions or parts to be omitted. Hence [[A]] [B] means that 'A' should be replaced by 'B'. The heading of one paper (Chapter XX) has been changed to make it more descriptive.

Download or read book Induction Physics and Ethics written by P. Weingartner and published by Springer Science & Business Media. This book was released on 1970-07-31 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings and Discussion of the 1968 Salzburg Colloquium in the Philosophy of Science.

Download or read book Hajnal Andr ka and Istv n N meti on Unity of Science written by Judit Madarász and published by Springer Nature. This book was released on 2021-05-31 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features more than 20 papers that celebrate the work of Hajnal Andréka and István Németi. It illustrates an interaction between developing and applying mathematical logic. The papers offer new results as well as surveys in areas influenced by these two outstanding researchers. They also provide details on the after-life of some of their initiatives. Computer science connects the papers in the first part of the book. The second part concentrates on algebraic logic. It features a range of papers that hint at the intricate many-way connections between logic, algebra, and geometry. The third part explores novel applications of logic in relativity theory, philosophy of logic, philosophy of physics and spacetime, and methodology of science. They include such exciting subjects as time travelling in emergent spacetime. The short autobiographies of Hajnal Andréka and István Németi at the end of the book describe an adventurous journey from electric engineering and Maxwell’s equations to a complex system of computer programs for designing Hungary’s electric power system, to exploring and contributing deep results to Tarskian algebraic logic as the deepest core theory of such questions, then on to applications of the results in such exciting new areas as relativity theory in order to rejuvenate logic itself.

Download or read book The Methodology of Economic Model Building Routledge Revivals written by Lawrence A. Boland and published by Routledge. This book was released on 2014-05-01 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: The major methodological task for modern economists has been to establish the testability of models. Too often, however, methodological assumptions can make a model virtually impossible to test even under ideal conditions, yet few theorists have examined the requirements and problems of assuring testability in economics. In The Methodology of Economic Model Building, first published in 1989, Lawrence Boland presents the results of a research project that spanned more than twenty years. He examines how economists have applied the philosophy of Karl Popper, relating methodological debates about falsifiability to wider discussions about the truth status of models in natural and social sciences. He concludes that model building in economics reflects more the methodological prescriptions of the economist Paul Samuelson than Popper’s ‘falsificationism’. This title will prove invaluable to both students and researchers, and represents a substantial contribution to debates about the scientific status of economics.

Download or read book The Teaching of Geometry at the Pre College Level written by Hans-Georg Steiner and published by Springer. This book was released on 2013-11-11 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Prehistory of Mathematical Structuralism written by Erich H. Reck and published by Oxford University Press. This book was released on 2020 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.

Download or read book Philosophy of Physics written by M. Bunge and published by Springer Science & Business Media. This book was released on 1972-12-31 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with some of the current issues in the philosophy, methodology and foundations of physics. Some such problems are: - Do mathematical formalisms interpret themselves or is it necessary to adjoin them interpretation assumptions, and if so how are these as sumptions to be framed? - What are physical theories about: physical systems or laboratory operations or both or neither? - How are the basic concepts of a theory to be introduced: by ref erence to measurements or by explicit definition or axiomatically? - What is the use ofaxiomatics in physics? - How are the various physical theories inter-related: like Chinese boxes or in more complex ways? - What is the role of analogy in the construction and in the inter pretation of physical theories? In particular, are classical analogues like those of particle and wave indispensable in quantum theories? - What is the role of the apparatus in quantum phenomena and what is the place of measurement theory in quantum mechanics? - How does a theory face experiment: single-handed or with the help of further theories? These and several other questions of the kind are met with by the research physicist, the physics teacher and the physics student in their everyday work. If dodged they will recur. And a wrong answer to them may obscure the understanding of what has been achieved and may even hamper further advancement. Philosophy, methodology and foundations, like rose bushes, are enjoyable when cultivated but become ugly and thorny when neglected.

Download or read book Philosophy of Mathematics written by Ahmet Cevik and published by CRC Press. This book was released on 2021-11-09 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book The Infinite in Mathematics written by Felix Kaufmann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main item in the present volume was published in 1930 under the title Das Unendliche in der Mathematik und seine Ausschaltung. It was at that time the fullest systematic account from the standpoint of Husserl's phenomenology of what is known as 'finitism' (also as 'intuitionism' and 'constructivism') in mathematics. Since then, important changes have been required in philosophies of mathematics, in part because of Kurt Godel's epoch-making paper of 1931 which established the essential in completeness of arithmetic. In the light of that finding, a number of the claims made in the book (and in the accompanying articles) are demon strably mistaken. Nevertheless, as a whole it retains much of its original interest and value. It presents the issues in the foundations of mathematics that were under debate when it was written (and in some cases still are); , and it offers one alternative to the currently dominant set-theoretical definitions of the cardinal numbers and other arithmetical concepts. While still a student at the University of Vienna, Felix Kaufmann was greatly impressed by the early philosophical writings (especially by the Logische Untersuchungen) of Edmund Husser!' He was never an uncritical disciple of Husserl, and he integrated into his mature philosophy ideas from a wide assortment of intellectual sources. But he thought of himself as a phenomenologist, and made frequent use in all his major publications of many of Husserl's logical and epistemological theses.

Download or read book Landmark Writings in Western Mathematics 1640 1940 written by Ivor Grattan-Guinness and published by Elsevier. This book was released on 2005-02-11 with total page 1042 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. - First book of its kind - Covers the period 1640-1940 of massive development in mathematics - Describes many of the main writings of mathematics - Articles written by specialists in their field