Axiomatic

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Axiomatic

Maria Tumarkin
Axiomatic Book PDF

Author : Maria Tumarkin
Publisher : Random House Australia
Page : 226 pages
File Size : 54,7 Mb
Release : 2021-05-04
Category : Culture
ISBN : 9781761043581

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Axiomatic by Maria Tumarkin Pdf

Stories are not enough, even though they are essential. And books about history, books of psychology--the best of them take us closer, but still not close enough. Maria Tumarkin's Axiomatic is a boundary-shifting fusion of thinking, storytelling, reportage and meditation. It takes as its starting point five axioms: 'Time Heals All Wounds'; 'History Repeats Itself'; 'Those Who Forget the Past are Condemned to Repeat It'; 'Give Me a Child Before the Age of Seven and I Will Show You the Woman'; and 'You Can't Enter The Same River Twice.' These beliefs--or intuitions--about the role the past plays in our present are often evoked as if they are timeless and self-evident truths. It is precisely because they are neither, yet still we are persuaded by them, that they tell us a great deal about the forces that shape our culture and the way we live.

Axiomatic Set Theory

Patrick Suppes
Axiomatic Set Theory Book PDF

Author : Patrick Suppes
Publisher : Courier Corporation
Page : 265 pages
File Size : 43,7 Mb
Release : 2012-05-04
Category : Mathematics
ISBN : 9780486136875

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Axiomatic Set Theory by Patrick Suppes Pdf

Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.

Axiomatic Quality

Basem El-Haik
Axiomatic Quality Book PDF

Author : Basem El-Haik
Publisher : John Wiley & Sons
Page : 370 pages
File Size : 45,9 Mb
Release : 2005-05-06
Category : Technology & Engineering
ISBN : 9780471714675

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Axiomatic Quality by Basem El-Haik Pdf

The first book to integrate axiomatic design and robust design fora comprehensive quality approach As the adoption of quality methods grows across various industries,its implementation is challenged by situations where statisticaltools are inadequate, yet the earlier a proactive quality system isintroduced into a given process, the greater the payback thesemethods will yield. Axiomatic Quality brings together two well-established theories,axiomatic design and robust design, to eliminate or reduce bothconceptual and operational weaknesses. Providing a completeframework for immediate implementation, this book guides designteams in producing systems that operate at high-quality levels foreach of their design requirements. And it shows the way towardsachieving the Six-Sigma target--six times the standard deviationcontained between the target and each side of the specificationlimits--for each requirement. This book develops an aggressive axiomatic quality approachthat: * Provides the tools to reduce conceptual weaknesses of systemsusing a framework called the conceptual design for capability * Reduces operational weaknesses of systems in terms of qualitylosses and control costs * Uses mathematical relationships to bridge the gap betweenscience-based engineering and quality methods Acclaro DFSS Light, a Java-based software package that implementsaxiomatic design processes, is available for download from a Wileyftp site. Acclaro DFSS Light is a software product of AxiomaticDesign Solutions, Inc. Laying out a comprehensive approach while working through eachaspect of its implementation, Axiomatic Quality is an essentialresource for managers, engineers, and other professionals who wantto successfully deploy the most advanced methodology to tacklesystem weaknesses and improve quality.

Axiomatic

Greg Egan
Axiomatic Book PDF

Author : Greg Egan
Publisher : Gollancz
Page : 352 pages
File Size : 54,5 Mb
Release : 2010-12-30
Category : Fiction
ISBN : 9780575105409

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Axiomatic by Greg Egan Pdf

THE HUNDRED LIGHT YEAR DIARY - Scientists can bounce messages from the future back to the present, but there's no guarantee they'll tell the truth ... LEARNING TO BE ME - Crystalline minds may take the place of human brains, but where does the self really lie? CLOSER - Lovers exchange bodies and minds, but their experiments go just that little bit too far, proving that you can have too much of a good thing

Axiomatic Projective Geometry

A. Heyting
Axiomatic Projective Geometry Book PDF

Author : A. Heyting
Publisher : Elsevier
Page : 160 pages
File Size : 46,9 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483259314

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Axiomatic Projective Geometry by A. Heyting Pdf

Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume V: Axiomatic Projective Geometry, Second Edition focuses on the principles, operations, and theorems in axiomatic projective geometry, including set theory, incidence propositions, collineations, axioms, and coordinates. The publication first elaborates on the axiomatic method, notions from set theory and algebra, analytic projective geometry, and incidence propositions and coordinates in the plane. Discussions focus on ternary fields attached to a given projective plane, homogeneous coordinates, ternary field and axiom system, projectivities between lines, Desargues' proposition, and collineations. The book takes a look at incidence propositions and coordinates in space. Topics include coordinates of a point, equation of a plane, geometry over a given division ring, trivial axioms and propositions, sixteen points proposition, and homogeneous coordinates. The text examines the fundamental proposition of projective geometry and order, including cyclic order of the projective line, order and coordinates, geometry over an ordered ternary field, cyclically ordered sets, and fundamental proposition. The manuscript is a valuable source of data for mathematicians and researchers interested in axiomatic projective geometry.

Intuition and the Axiomatic Method

Emily Carson,Renate Huber
Intuition and the Axiomatic Method Book PDF

Author : Emily Carson,Renate Huber
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 40,7 Mb
Release : 2006-01-24
Category : Mathematics
ISBN : 1402040393

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Intuition and the Axiomatic Method by Emily Carson,Renate Huber Pdf

Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant’s theory of intuition to be obsolete. But this only represents one side of the story concerning Kant, intuition and twentieth century science. Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. All of Hilbert, Gödel, Poincaré, Weyl and Bohr thought that intuition was an indispensable element in describing the foundations of science. They had very different reasons for thinking this, and they had very different accounts of what they called intuition. But they had in common that their views of mathematics and physics were significantly influenced by their readings of Kant. In the present volume, various views of intuition and the axiomatic method are explored, beginning with Kant’s own approach. By way of these investigations, we hope to understand better the rationale behind Kant’s theory of intuition, as well as to grasp many facets of the relations between theories of intuition and the axiomatic method, dealing with both their strengths and limitations; in short, the volume covers logical and non-logical, historical and systematic issues in both mathematics and physics.

Axiomatic choice models and duality

H.N. Weddepohl
Axiomatic choice models and duality Book PDF

Author : H.N. Weddepohl
Publisher : Springer Science & Business Media
Page : 183 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9789401198318

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Axiomatic choice models and duality by H.N. Weddepohl Pdf

Every day people frequently have to make a choice. For practical and scientific reasons therefore it is interesting to know what choices they make and how they arrive at them. An approach to this question can be made via psychology. However, it is also possible to approach it on a more formal basis. In this book Dr. Wedde pohl describes the logical structure of an individual's rational choice. It is this formal, logical approach to the decision problem that makes the book interesting reading matter for all those who are engaged in the study of individual choice. The introduction apart this study may be divided into two parts. The first part, consisting of chapters II and III, deals with choice theory on a very abstract level. In chapter II some mathematical concepts are presented and in chapter III two related choice models are treated, the first one based on preferences, the second one on choice functions. The second part consists of chapters IV, V and VI and covers consumer choice theory. After the pre sentation of the mathematical tools, two models that are extensions of the models of chapter III are dealt with. In the discussion of consumer choice theory the concept of duality plays an important role and it is found that duality is closely related to the notion of favourability introduced in chap ter II I. Mr. Weddepohl's study forms an introduction to a larger research project to develop the theory of collective choice.

Axiomatic Fuzzy Set Theory and Its Applications

Xiaodong Liu,Witold Pedrycz
Axiomatic Fuzzy Set Theory and Its Applications Book PDF

Author : Xiaodong Liu,Witold Pedrycz
Publisher : Springer Science & Business Media
Page : 522 pages
File Size : 48,8 Mb
Release : 2009-04-07
Category : Mathematics
ISBN : 9783642004018

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Axiomatic Fuzzy Set Theory and Its Applications by Xiaodong Liu,Witold Pedrycz Pdf

It is well known that “fuzziness”—informationgranulesand fuzzy sets as one of its formal manifestations— is one of important characteristics of human cognitionandcomprehensionofreality. Fuzzy phenomena existinnature and are encountered quite vividly within human society. The notion of a fuzzy set has been introduced by L. A. , Zadeh in 1965 in order to formalize human concepts, in connection with the representation of human natural language and computing with words. Fuzzy sets and fuzzy logic are used for mod- ing imprecise modes of reasoning that play a pivotal role in the remarkable human abilities to make rational decisions in an environment a?ected by - certainty and imprecision. A growing number of applications of fuzzy sets originated from the “empirical-semantic” approach. From this perspective, we were focused on some practical interpretations of fuzzy sets rather than being oriented towards investigations of the underlying mathematical str- tures of fuzzy sets themselves. For instance, in the context of control theory where fuzzy sets have played an interesting and practically relevant function, the practical facet of fuzzy sets has been stressed quite signi?cantly. However, fuzzy sets can be sought as an abstract concept with all formal underpinnings stemming from this more formal perspective. In the context of applications, it is worth underlying that membership functions do not convey the same meaning at the operational level when being cast in various contexts.

Sets: Naïve, Axiomatic and Applied

D. Van Dalen,H. C. Doets,H. De Swart
Sets Na ve Axiomatic and Applied Book PDF

Author : D. Van Dalen,H. C. Doets,H. De Swart
Publisher : Elsevier
Page : 360 pages
File Size : 43,7 Mb
Release : 2014-05-09
Category : Mathematics
ISBN : 9781483150390

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Sets: Naïve, Axiomatic and Applied by D. Van Dalen,H. C. Doets,H. De Swart Pdf

Sets: Naïve, Axiomatic and Applied is a basic compendium on naïve, axiomatic, and applied set theory and covers topics ranging from Boolean operations to union, intersection, and relative complement as well as the reflection principle, measurable cardinals, and models of set theory. Applications of the axiom of choice are also discussed, along with infinite games and the axiom of determinateness. Comprised of three chapters, this volume begins with an overview of naïve set theory and some important sets and notations. The equality of sets, subsets, and ordered pairs are considered, together with equivalence relations and real numbers. The next chapter is devoted to axiomatic set theory and discusses the axiom of regularity, induction and recursion, and ordinal and cardinal numbers. In the final chapter, applications of set theory are reviewed, paying particular attention to filters, Boolean algebra, and inductive definitions together with trees and the Borel hierarchy. This book is intended for non-logicians, students, and working and teaching mathematicians.

Axiomatic Consensus Theory in Group Choice and Biomathematics

William H. E. Day,F. R. McMorris
Axiomatic Consensus Theory in Group Choice and Biomathematics Book PDF

Author : William H. E. Day,F. R. McMorris
Publisher : SIAM
Page : 171 pages
File Size : 46,9 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0898717507

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Axiomatic Consensus Theory in Group Choice and Biomathematics by William H. E. Day,F. R. McMorris Pdf

Provides a unique comprehensive review of axiomatic consensus theory in biomathematics as it has developed over the past 30 years.

Axiomatic Method and Category Theory

Andrei Rodin
Axiomatic Method and Category Theory Book PDF

Author : Andrei Rodin
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 44,8 Mb
Release : 2013-10-14
Category : Philosophy
ISBN : 9783319004044

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Axiomatic Method and Category Theory by Andrei Rodin Pdf

This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.

Axiomatic Geometry

John M. Lee
Axiomatic Geometry Book PDF

Author : John M. Lee
Publisher : American Mathematical Soc.
Page : 490 pages
File Size : 52,7 Mb
Release : 2013-04-10
Category : Mathematics
ISBN : 9780821884782

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Axiomatic Geometry by John M. Lee Pdf

The story of geometry is the story of mathematics itself: Euclidean geometry was the first branch of mathematics to be systematically studied and placed on a firm logical foundation, and it is the prototype for the axiomatic method that lies at the foundation of modern mathematics. It has been taught to students for more than two millennia as a mode of logical thought. This book tells the story of how the axiomatic method has progressed from Euclid's time to ours, as a way of understanding what mathematics is, how we read and evaluate mathematical arguments, and why mathematics has achieved the level of certainty it has. It is designed primarily for advanced undergraduates who plan to teach secondary school geometry, but it should also provide something of interest to anyone who wishes to understand geometry and the axiomatic method better. It introduces a modern, rigorous, axiomatic treatment of Euclidean and (to a lesser extent) non-Euclidean geometries, offering students ample opportunities to practice reading and writing proofs while at the same time developing most of the concrete geometric relationships that secondary teachers will need to know in the classroom. -- P. [4] of cover.

Entropy and Diversity

Tom Leinster
Entropy and Diversity Book PDF

Author : Tom Leinster
Publisher : Cambridge University Press
Page : 457 pages
File Size : 55,7 Mb
Release : 2021-04-22
Category : Language Arts & Disciplines
ISBN : 9781108832700

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Entropy and Diversity by Tom Leinster Pdf

Discover the mathematical riches of 'what is diversity?' in a book that adds mathematical rigour to a vital ecological debate.

Axiomatics

Alma Steingart
Axiomatics Book PDF

Author : Alma Steingart
Publisher : University of Chicago Press
Page : 300 pages
File Size : 42,5 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.

Axiomatic Theories of Truth

Volker Halbach
Axiomatic Theories of Truth Book PDF

Author : Volker Halbach
Publisher : Cambridge University Press
Page : 128 pages
File Size : 47,5 Mb
Release : 2014-02-27
Category : Philosophy
ISBN : 9781316584231

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Axiomatic Theories of Truth by Volker Halbach Pdf

At the centre of the traditional discussion of truth is the question of how truth is defined. Recent research, especially with the development of deflationist accounts of truth, has tended to take truth as an undefined primitive notion governed by axioms, while the liar paradox and cognate paradoxes pose problems for certain seemingly natural axioms for truth. In this book, Volker Halbach examines the most important axiomatizations of truth, explores their properties and shows how the logical results impinge on the philosophical topics related to truth. In particular, he shows that the discussion on topics such as deflationism about truth depends on the solution of the paradoxes. His book is an invaluable survey of the logical background to the philosophical discussion of truth, and will be indispensable reading for any graduate or professional philosopher in theories of truth.