Axiomatics

Author : Alma Steingart
Publisher : University of Chicago Press
Page : 300 pages
File Size : 52,8 Mb
Release : 2023-01-17
Category : Mathematics
ISBN : 9780226824192

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Axiomatics by Alma Steingart Pdf

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.

Author : Jaakko Hintikka,D. Gruender,E. Agazzi
Publisher : Springer Science & Business Media
Page : 359 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400990456

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Theory Change, Ancient Axiomatics, and Galileo’s Methodology by Jaakko Hintikka,D. Gruender,E. Agazzi Pdf

Proceedings of the 1978 Pisa, Italy, September 4-8, 1978 Conference on the History and Philosophy of Science

Author : Diederik Aerts,Thomas Durt,Marek Czachor
Publisher : World Scientific
Page : 400 pages
File Size : 51,7 Mb
Release : 2002-06-11
Category : Science
ISBN : 9789814489409

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Probing the Structure of Quantum Mechanics by Diederik Aerts,Thomas Durt,Marek Czachor Pdf

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). Contents:Probing the Structure of Quantum Mechanics (D Aerts et al.)The Linearity of Quantum Mechanics at Stake: The Description of Separated Quantum Entities (D Aerts & F Valckenborgh)Linearity and Compound Physical Systems: The Case of Two Separated Spin 1/2 Entities (D Aerts & F Valckenborgh)Being and Change: Foundations of a Realistic Operational Formalism (D Aerts)The Classical Limit of the Lattice-Theoretical Orthocomplementation in the Framework of the Hidden-Measurement Approach (T Durt & B D'Hooghe)State Property Systems and Closure Spaces: Extracting the Classical en Non-Classical Parts (D Aerts & D Deses)Hidden Measurements from Contextual Axiomatics (S Aerts)High Energy Approaches to Low Energy Phenomena in Astrophysics (S M Austin)Memory Effects in Atomic Interferometry: A Negative Result (T Durt et al.)Reality and Probability: Introducing a New Type of Probability Calculus (D Aerts)Quantum Computation: Towards the Construction of a ‘Between Quantum and Classical Computer’ (D Aerts & B D'Hooghe)Buckley-Siler Connectives for Quantum Logics of Fuzzy Sets (J Pykacz & B D'Hooghe)Some Notes on Aerts' Interpretation of the EPR-Paradox and the Violation of Bell-Inequalities (W Christiaens)Quantum Cryptographic Encryption in Three Complementary Bases Through a Mach-Zehnder Set Up (T Durt & B Nagler)Quantum Cryptography Without Quantum Uncertainties (T Durt)How to Construct Darboux-Invariant Equations of von Neumann Type (J L Cie(li(ski)Darboux-Integrable Equations with Non-Abelian Nonlinearities (N V Ustinov & M Czachor)Dressing Chain Equations Associated with Difference Soliton Systems (S Leble)Covariance Approach to the Free Photon Field (M Kuna & J Naudts) Readership: Graduate students, researchers and academics in quantum physics. Keywords:Quantum Mechanics;Quantum Computation;Quantum Information Processing

Author : William Thomson
Publisher : Springer Nature
Page : 314 pages
File Size : 46,9 Mb
Release : 2024-06-01
Category : Electronic
ISBN : 9783031293986

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The Axiomatics of Economic Design, Vol. 1 by William Thomson Pdf

Author : Robert Blanché
Publisher : Unknown
Page : 82 pages
File Size : 53,5 Mb
Release : 1965
Category : Axioms
ISBN : UOM:39076005517318

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Axiomatics by Robert Blanché Pdf

Author : Howard Eves
Publisher : Courier Corporation
Page : 370 pages
File Size : 42,5 Mb
Release : 2012-04-10
Category : Mathematics
ISBN : 9780486132204

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Foundations and Fundamental Concepts of Mathematics by Howard Eves Pdf

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.

Author : John Robb Carnes
Publisher : Unknown
Page : 156 pages
File Size : 46,6 Mb
Release : 1982
Category : Axiomatic set theory
ISBN : UOM:39015001722126

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Axiomatics and Dogmatics by John Robb Carnes Pdf

Author : M. Strauss
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401028936

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Modern Physics and its Philosophy by M. Strauss Pdf

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.

Author : P. Weingartner,G. Zecha
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 44,5 Mb
Release : 1970-07-31
Category : Science
ISBN : 902770158X

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Induction, Physics and Ethics by P. Weingartner,G. Zecha Pdf

Proceedings and Discussion of the 1968 Salzburg Colloquium in the Philosophy of Science.

Author : Judit Madarász,Gergely Székely
Publisher : Springer Nature
Page : 517 pages
File Size : 51,8 Mb
Release : 2021-05-31
Category : Philosophy
ISBN : 9783030641870

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Hajnal Andréka and István Németi on Unity of Science by Judit Madarász,Gergely Székely Pdf

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.

Author : Lawrence A. Boland
Publisher : Routledge
Page : 209 pages
File Size : 40,6 Mb
Release : 2014-05-01
Category : Business & Economics
ISBN : 9781317680963

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The Methodology of Economic Model Building (Routledge Revivals) by Lawrence A. Boland Pdf

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.

Author : Hans-Georg Steiner,NA Central Midwestern Regional Educational Laboratory,NA Comprehensive School Mathematics Programme,NA Southern Illinois University (System)
Publisher : Springer
Page : 395 pages
File Size : 43,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9789401758963

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The Teaching of Geometry at the Pre-College Level by Hans-Georg Steiner,NA Central Midwestern Regional Educational Laboratory,NA Comprehensive School Mathematics Programme,NA Southern Illinois University (System) Pdf

Author : Erich H. Reck,Georg Schiemer
Publisher : Oxford University Press
Page : 469 pages
File Size : 45,8 Mb
Release : 2020
Category : Mathematics
ISBN : 9780190641221

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The Prehistory of Mathematical Structuralism by Erich H. Reck,Georg Schiemer Pdf

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.

Author : M. Bunge
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 54,6 Mb
Release : 1972-12-31
Category : Philosophy
ISBN : 9027702535

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Philosophy of Physics by M. Bunge Pdf

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.

Author : Ahmet Cevik
Publisher : CRC Press
Page : 352 pages
File Size : 52,6 Mb
Release : 2021-11-09
Category : Mathematics
ISBN : 9781000468809

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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