Axiomatic Thinking I
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| Author | : Andrei Rodin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 285 |
| Release | : 2013-10-14 |
| Genre | : Philosophy |
| ISBN | : 3319004042 |
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.
| Author | : Fernando Ferreira |
| Publisher | : Springer Nature |
| Total Pages | : 209 |
| Release | : 2022-10-13 |
| Genre | : Mathematics |
| ISBN | : 3030776573 |
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.
| Author | : Fernando Ferreira |
| Publisher | : Springer Nature |
| Total Pages | : 293 |
| Release | : 2022-09-17 |
| Genre | : Mathematics |
| ISBN | : 3030777995 |
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.
| Author | : Fernando Ferreira |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2022 |
| Genre | : Axioms |
| ISBN | : 9788303077790 |
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.
| Author | : Maria Tumarkin |
| Publisher | : Random House Australia |
| Total Pages | : 226 |
| Release | : 2021-05-04 |
| Genre | : Culture |
| ISBN | : 1761043587 |
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.
| Author | : Lindsay Ellis |
| Publisher | : St. Martin's Press |
| Total Pages | : 397 |
| Release | : 2020-07-21 |
| Genre | : Fiction |
| ISBN | : 1250256747 |
THE INSTANT NEW YORK TIMES BESTSELLER The alternate history first contact adventure Axiom's End is an extraordinary debut from Hugo finalist and video essayist Lindsay Ellis. Truth is a human right. It’s fall 2007. A well-timed leak has revealed that the US government might have engaged in first contact. Cora Sabino is doing everything she can to avoid the whole mess, since the force driving the controversy is her whistleblower father. Even though Cora hasn’t spoken to him in years, his celebrity has caught the attention of the press, the Internet, the paparazzi, and the government—and with him in hiding, that attention is on her. She neither knows nor cares whether her father’s leaks are a hoax, and wants nothing to do with him—until she learns just how deeply entrenched her family is in the cover-up, and that an extraterrestrial presence has been on Earth for decades. Realizing the extent to which both she and the public have been lied to, she sets out to gather as much information as she can, and finds that the best way for her to uncover the truth is not as a whistleblower, but as an intermediary. The alien presence has been completely uncommunicative until she convinces one of them that she can act as their interpreter, becoming the first and only human vessel of communication. Their otherworldly connection will change everything she thought she knew about being human—and could unleash a force more sinister than she ever imagined.
| Author | : Penelope Maddy |
| Publisher | : Oxford University Press |
| Total Pages | : 161 |
| Release | : 2011-01-27 |
| Genre | : Mathematics |
| ISBN | : 0199596182 |
Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. The axioms of set theory have long played this role, so the question of how they are properly judged is of central importance. Maddy discusses the appropriate methods for such evaluations and the philosophical backdrop that makes them appropriate.
| Author | : Pei Wang |
| Publisher | : World Scientific |
| Total Pages | : 275 |
| Release | : 2013 |
| Genre | : Computers |
| ISBN | : 9814440280 |
This book provides a systematic and comprehensive description of Non-Axiomatic Logic, which is the result of the author''s research for about three decades.Non-Axiomatic Logic is designed to provide a uniform logical foundation for Artificial Intelligence, as well as an abstract description of the OC laws of thoughtOCO followed by the human mind. Different from OC mathematicalOCO logic, where the focus is the regularity required when demonstrating mathematical conclusions, Non-Axiomatic Logic is an attempt to return to the original aim of logic, that is, to formulate the regularity in actual human thinking. To achieve this goal, the logic is designed under the assumption that the system has insufficient knowledge and resources with respect to the problems to be solved, so that the OC logical conclusionsOCO are only valid with respect to the available knowledge and resources. Reasoning processes according to this logic covers cognitive functions like learning, planning, decision making, problem solving, This book is written for researchers and students in Artificial Intelligence and Cognitive Science, and can be used as a textbook for courses at graduate level, or upper-level undergraduate, on Non-Axiomatic Logic."
| Author | : Thomas J. Jech |
| Publisher | : Courier Corporation |
| Total Pages | : 226 |
| Release | : 2008-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486466248 |
Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.
| Author | : Michael Potter |
| Publisher | : Clarendon Press |
| Total Pages | : 362 |
| Release | : 2004-01-15 |
| Genre | : Philosophy |
| ISBN | : 0191556432 |
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
