Download or read book Memoirs of a Proof Theorist written by Gaisi Takeuti and published by World Scientific. This book was released on 2003 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a translation of the book Gvdel, written in Japanese by Gaisi Takeuti, a distinguished proof theorist. The core of the book comprises a memoir of K Gvdel, Takeuti's personal recollections, and his interpretation of Gvdel's attitudes towards mathematical logic. It also contains Takeuti's recollection of association with some other famous logicians. Everything in the book is original, as the author adheres to his own experiences and interpretations. There is also an article on Hilbert's second problem as well as on the author's fundamental conjecture about second order logic.
Download or read book Memoirs Of A Proof Theorist Godel Other Logicians written by Nicholas Passell and published by World Scientific. This book was released on 2003-02-10 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a translation of the book Gödel, written in Japanese by Gaisi Takeuti, a distinguished proof theorist. The core of the book comprises a memoir of K Gödel, Takeuti's personal recollections, and his interpretation of Gödel's attitudes towards mathematical logic. It also contains Takeuti's recollection of association with some other famous logicians. Everything in the book is original, as the author adheres to his own experiences and interpretations. There is also an article on Hilbert's second problem as well as on the author's fundamental conjecture about second order logic.
Download or read book An Introduction to Proof Theory written by Paolo Mancosu and published by Oxford University Press. This book was released on 2021-08-12 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.
Download or read book Philosophy of Mathematics in the Twentieth Century written by Charles Parsons and published by Harvard University Press. This book was released on 2014-03-10 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these selected essays, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the past century: Brouwer, Hilbert, Bernays, Weyl, Gödel, Russell, Quine, Putnam, Wang, and Tait.
Download or read book Kurt G del and the Foundations of Mathematics written by Matthias Baaz and published by Cambridge University Press. This book was released on 2011-06-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.
Download or read book Advances in Mathematical Logic written by Toshiyasu Arai and published by Springer Nature. This book was released on 2022-01-24 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gaisi Takeuti was one of the most brilliant, genius, and influential logicians of the 20th century. He was a long-time professor and professor emeritus of mathematics at the University of Illinois at Urbana-Champaign, USA, before he passed away on May 10, 2017, at the age of 91. Takeuti was one of the founders of Proof Theory, a branch of mathematical logic that originated from Hilbert's program about the consistency of mathematics. Based on Gentzen's pioneering works of proof theory in the 1930s, he proposed a conjecture in 1953 concerning the essential nature of formal proofs of higher-order logic now known as Takeuti's fundamental conjecture and of which he gave a partial positive solution. His arguments on the conjecture and proof theory in general have had great influence on the later developments of mathematical logic, philosophy of mathematics, and applications of mathematical logic to theoretical computer science. Takeuti's work ranged over the whole spectrum of mathematical logic, including set theory, computability theory, Boolean valued analysis, fuzzy logic, bounded arithmetic, and theoretical computer science. He wrote many monographs and textbooks both in English and in Japanese, and his monumental monograph Proof Theory, published in 1975, has long been a standard reference of proof theory. He had a wide range of interests covering virtually all areas of mathematics and extending to physics. His publications include many Japanese books for students and general readers about mathematical logic, mathematics in general, and connections between mathematics and physics, as well as many essays for Japanese science magazines. This volume is a collection of papers based on the Symposium on Advances in Mathematical Logic 2018. The symposium was held September 18–20, 2018, at Kobe University, Japan, and was dedicated to the memory of Professor Gaisi Takeuti.
Download or read book Computer Aided Systems Theory EUROCAST 2017 written by Roberto Moreno-Díaz and published by Springer. This book was released on 2018-01-25 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNCS 10671 and 10672 constitutes the thoroughly refereed proceedings of the 16th International Conference on Computer Aided Systems Theory, EUROCAST 2017, held in Las Palmas de Gran Canaria, Spain, in February 2017. The 117 full papers presented were carefully reviewed and selected from 160 submissions. The papers are organized in topical sections on: pioneers and landmarks in the development of information and communication technologies; systems theory, socio-economic systems and applications; theory and applications of metaheuristic algorithms; stochastic models and applications to natural, social and technical systems; model-based system design, verification and simulation; applications of signal processing technology; algebraic and combinatorial methods in signal and pattern analysis; computer vision, deep learning and applications; computer and systems based methods and electronics technologies in medicine; intelligent transportation systems and smart mobility.
Download or read book Kurt G del written by William D. Brewer and published by Springer Nature. This book was released on 2022-09-08 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: During his lifetime, Kurt Gödel was not well known outside the professional world of mathematicians, philosophers and theoretical physicists. Early in his career, for his doctoral thesis and then for his Habilitation (Dr.Sci.), he wrote earthshaking articles on the completeness and provability of mathematical-logical systems, upsetting the hypotheses of the most famous mathematicians/philosophers of the time. He later delved into theoretical physics, finding a unique solution to Einstein’s equations for gravity, the ‘Gödel Universe’, and made contributions to philosophy, the guiding theme of his life. This book includes more details about the context of Gödel’s life than are found in earlier biographies, while avoiding an elaborate treatment of his mathematical/scientific/philosophical works, which have been described in great detail in other books. In this way, it makes him and his times more accessible to general readers, and will allow them to appreciate the lasting effects of Gödel’s contributions (the latter in a more up-to-date context than in previous biographies, many of which were written 15–25 years ago). His work spans or is relevant to a wide spectrum of intellectual endeavor, and this is emphasized in the book, with recent examples. This biography also examines possible sources of his unusual personality, which combined mathematical genius with an almost childlike naiveté concerning everyday life, and striking scientific innovations with timidity and hesitancy in practical matters. How he nevertheless had a long and successful career, inspiring many younger scholars along the way, with the help of his loyal wife Adele and some of his friends, is a fascinating story in human nature.
Download or read book European Philosophy of Science Philosophy of Science in Europe and the Viennese Heritage written by Maria Carla Galavotti and published by Springer Science & Business Media. This book was released on 2013-08-28 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume combines the theoretical and historical perspective focusing on the specific features of a European philosophy of science. On the occasion of the 20th anniversary of the Institute Vienna Circle the Viennese roots and influences will be addressed, in addition. There is no doubt that contemporary philosophy of science originated mainly in Europe beginning in the 19th century and has influenced decisively the subsequent development of globalized philosophy of science, esp. in North America. Recent research in this field documents some specific characteristics of philosophy of science covering the natural, social, and also cultural sciences in the European context up to the destruction and forced migration caused by Fascism and National Socialism. This European perspective with the integration of history and philosophy of science and the current situation in the philosophy of science after the transatlantic interaction and transformation, and the “return” after World War II raises the question of contemporary European characteristics in the philosophy of science. The role and function of the renowned Vienna Circle of Logical Empiricism and its impact and influence on contemporary philosophy of science is on the agenda, too. Accordingly, the general topic is dealt with in two parallel sessions representing systematic-formal as well as genetic-historical perspectives on philosophy of science in a European context up to the present.
Download or read book Artificial Intelligence Intellectual Property Cyber Risk and Robotics written by Ruth Taplin and published by Taylor & Francis. This book was released on 2023-12-30 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Artificial Intelligence (AI) is the most rapidly developing technology in the current Digital Age, but it is also the least defined, understood and adequately explained technological advance. This book brings together a group of leading experts who assess different aspects of AI from different disciplinary perspectives. The book argues that robots are not living systems but the creations of humans who must ultimately be accountable for the actions of the robots that they have invented. Robots do not have ownership entitlement. The book uses Intellectual Property Rights cases, evidence from roboticists, cybersecurity experts, Patent Court judges, technology officers, climate change scientists, economists, physicists and those from the legal profession to demonstrate that while AI can have very beneficial uses for many aspects of human economy and society, robots are not living systems autonomous from human decision making. This book will be useful to those in banking and insurance, cybersecurity, lawyers, judges, technology officers, economists, scientist inventors, computer scientists, large and small companies and postgraduate students.
Download or read book Incompleteness written by Rebecca Goldstein and published by W. W. Norton & Company. This book was released on 2006-01-31 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proof Theory written by Gaisi Takeuti and published by Courier Corporation. This book was released on 2013-01-01 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics. Suitable for advanced undergraduates and graduate students of mathematics, this long-out-of-print monograph forms a cornerstone for any library in mathematical logic and related topics. The three-part treatment begins with an exploration of first order systems, including a treatment of predicate calculus involving Gentzen's cut-elimination theorem and the theory of natural numbers in terms of Gödel's incompleteness theorem and Gentzen's consistency proof. The second part, which considers second order and finite order systems, covers simple type theory and infinitary logic. The final chapters address consistency problems with an examination of consistency proofs and their applications.
Download or read book A World Without Time written by Palle Yourgrau and published by Basic Books. This book was released on 2009-03-04 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is a widely known but little considered fact that Albert Einstein and Kurt Godel were best friends for the last decade and a half of Einstein's life. The two walked home together from Princeton's Institute for Advanced Study every day; they shared ideas about physics, philosophy, politics, and the lost world of German science in which they had grown up. By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist . Einstein endorsed this result-reluctantly, since it decisively overthrew the classical world-view to which he was committed. But he could find no way to refute it, and in the half-century since then, neither has anyone else. Even more remarkable than this stunning discovery, however, was what happened afterward: nothing. Cosmologists and philosophers alike have proceeded with their work as if Godel's proof never existed -one of the greatest scandals of modern intellectual history. A World Without Time is a sweeping, ambitious book, and yet poignant and intimate. It tells the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue from undeserved obscurity the brilliant work they did together.
Download or read book An Introduction to G del s Theorems written by Peter Smith and published by Cambridge University Press. This book was released on 2007-07-26 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.
Download or read book G del s Proof written by Ernest Nagel and published by Psychology Press. This book was released on 1989 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. A gripping combination of science and accessibility, Godel’s Proofby Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.
Download or read book The G delian Puzzle Book written by Raymond M. Smullyan and published by Courier Corporation. This book was released on 2013-08-21 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: These logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. No background in formal logic necessary.
