Axiomatic Thinking I
DOWNLOAD
READ ONLINE
Download Axiomatic Thinking I PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Axiomatic Thinking I book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Axiomatic Thinking I
DOWNLOAD
READ ONLINE
Author : Fernando Ferreira
language : en
Publisher: Springer Nature
Release Date : 2022-10-13
Axiomatic Thinking I written by Fernando Ferreira and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-13 with Mathematics categories.
In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere. The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Göttingen as his main collaborator in foundational studies in the years to come. The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations. Chapter 8 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Axiomatic Thinking Ii
DOWNLOAD
READ ONLINE
Author : Fernando Ferreira
language : en
Publisher: Springer Nature
Release Date : 2022-09-17
Axiomatic Thinking Ii written by Fernando Ferreira and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-17 with Mathematics categories.
In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere. The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Göttingen as his main collaborator in foundational studies in the years to come. The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations.
Axiomatic Thinking
DOWNLOAD
READ ONLINE
Author : Fernando Ferreira
language : en
Publisher:
Release Date : 2022
Axiomatic Thinking written by Fernando Ferreira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Axioms categories.
In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere. The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Gottingen as his main collaborator in foundational studies in the years to come. The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations.
Intuition And The Axiomatic Method
DOWNLOAD
READ ONLINE
Author : Emily Carson
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-02
Intuition And The Axiomatic Method written by Emily Carson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-02 with Philosophy categories.
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.
Axiomatics
DOWNLOAD
READ ONLINE
Author : Alma Steingart
language : en
Publisher: University of Chicago Press
Release Date : 2023-01-17
Axiomatics written by Alma Steingart and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-17 with Mathematics categories.
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 Method And Category Theory
DOWNLOAD
READ ONLINE
Author : Andrei Rodin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-14
Axiomatic Method And Category Theory written by Andrei Rodin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-14 with Philosophy categories.
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
DOWNLOAD
READ ONLINE
Author : Maria Tumarkin
language : en
Publisher: Penguin Group Australia
Release Date : 2021-05-04
Axiomatic written by Maria Tumarkin and has been published by Penguin Group Australia this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-04 with Literary Collections categories.
The past shapes the present—they teach us that in schools and universities. (Shapes? Infiltrates, more like; imbues, infuses.) This past cannot be visited like an ageing aunt. It doesn’t live in little zoo enclosures. Half the time, this past is nothing less than the beating heart of the present. So, how to speak of the searing, unpindownable power that the past—ours, our family’s, our culture’s—wields in the present? 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.
Principles Of Innovative Design Thinking
DOWNLOAD
READ ONLINE
Author : Wenjuan Li
language : en
Publisher: Springer Nature
Release Date : 2022-06-20
Principles Of Innovative Design Thinking written by Wenjuan Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-20 with Technology & Engineering categories.
The book presents a comprehensive treatment on a novel design theory that fosters innovative thinking and creativity essential for addressing wicked problems. Wicked problems are ill-defined, ambiguous in both aims and solutions, and complex with interconnected and intertwined (coupled) factors. While being ubiquitous and difficult, however, wicked problems share characteristics common to science and design in three regards, namely agent finitude, system complexity, and problem normativity. These fundamental attributes allow a core cognitive process common to design and science to be identified and a strategic problem-solving conception of methodology be formulated as a result. The theory facilitates new opportunities for synergetic cross-disciplinary research and practice by incorporating the essences of Extenics to axiomatic design. Innovative thinking is enabled by exploring Extenics for problem reframing, paradigm shift, and abductive reasoning and by engaging axiomatic design in the co-evolution (iteration) of the need and viable design concept. The theory is unique in that it is a framework for quantifying imprecise and vague design information available during the conceptual design stage as mathematical expression and algorithm early in the design effort and enables the objective evaluation and emergence of an optimal design concept from among multitude of viable ones. The book is conceived for students and real-world practitioners in engineering, natural and social sciences, business, and fine arts who seek to develop powerful design thinking for solving problems in a creative and innovative way.
Cromby S Axiom
DOWNLOAD
READ ONLINE
Author : Gary J. Kirchner
language : en
Publisher: FriesenPress
Release Date : 2021-03-16
Cromby S Axiom written by Gary J. Kirchner and has been published by FriesenPress this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-16 with Fiction categories.
Before we were all connected, before we were The Hive, there was individualism, privacy, ‘personal space’ . . . so quaint, so unnecessary . . . so dangerous . . . TOMMY PIERRE ANTIKAGAMAC, a star quarterback, is the most followed player in the world’s most popular sport: American football. While off-season training in the unpopulated European Fallowlands, he abruptly finds himself detached from the Hive. Agonizingly alone in his head for the first time in his life, he panics, becomes hopelessly lost, and then is captured by a fringe group of anti-Hive saboteurs. The Freemen, as they call themselves, have concocted an audacious plan to "cataclysmically disrupt the brain of the Hive," and Tommy may just be the key they need to make it successful. But Tommy’s arrival among the Freemen is not as serendipitous as it may appear. Neither he nor his captors suspect that it is not the terrorists, but Tommy, who is the threat to the Hive. And the Hive has ways of protecting itself.
Gentzen S Centenary
DOWNLOAD
READ ONLINE
Author : Reinhard Kahle
language : en
Publisher: Springer
Release Date : 2015-11-02
Gentzen S Centenary written by Reinhard Kahle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-02 with Mathematics categories.
Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzen’s original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. They underlie modern developments in computer science such as automated theorem proving and type theory.