Paul Lorenzen Mathematician And Logician

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Paul Lorenzen Mathematician And Logician
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Author : Gerhard Heinzmann
language : en
Publisher: Springer Nature
Release Date : 2021-08-17
Paul Lorenzen Mathematician And Logician written by Gerhard Heinzmann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-17 with Mathematics categories.
This open access book examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics. The papers also explore how practitioners can implement Lorenzen’s systematical ideas in today’s debates on proof-theoretic semantics, databank management, and stochastics. Coverage details key contributions of Lorenzen to constructive mathematics, Lorenzen’s work on lattice-groups and divisibility theory, and modern set theory and Lorenzen’s critique of actual infinity. The contributors also look at the main problem of Grundlagenforschung and Lorenzen’s consistency proof and Hilbert’s larger program. In addition, the papers offer a constructive examination of a Russell-style Ramified Type Theory and a way out of the circularity puzzle within the operative justification of logic and mathematics. Paul Lorenzen's name is associated with the Erlangen School of Methodical Constructivism, of which the approach in linguistic philosophy and philosophy of science determined philosophical discussions especially in Germany in the 1960s and 1970s. This volume features 10 papers from a meeting that took place at the University of Konstanz.
Paul Lorenzen Mathematician And Logician
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Author : Gerhard Heinzmann
language : en
Publisher:
Release Date : 2021
Paul Lorenzen Mathematician And Logician written by Gerhard Heinzmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
This open access book examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics. The papers also explore how practitioners can implement Lorenzen's systematical ideas in today's debates on proof-theoretic semantics, databank management, and stochastics. Coverage details key contributions of Lorenzen to constructive mathematics, Lorenzen's work on lattice-groups and divisibility theory, and modern set theory and Lorenzen's critique of actual infinity. The contributors also look at the main problem of Grundlagenforschung and Lorenzen's consistency proof and Hilbert's larger program. In addition, the papers offer a constructive examination of a Russell-style Ramified Type Theory and a way out of the circularity puzzle within the operative justification of logic and mathematics. Paul Lorenzen's name is associated with the Erlangen School of Methodical Constructivism, of which the approach in linguistic philosophy and philosophy of science determined philosophical discussions especially in Germany in the 1960s and 1970s. This volume features 10 papers from a meeting that took place at the University of Konstanz.
The Legacy Of Kurt Sch Tte
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Author : Reinhard Kahle
language : en
Publisher: Springer Nature
Release Date : 2020-08-10
The Legacy Of Kurt Sch Tte written by Reinhard Kahle and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-10 with Mathematics categories.
This book on proof theory centers around the legacy of Kurt Schütte and its current impact on the subject. Schütte was the last doctoral student of David Hilbert who was the first to see that proofs can be viewed as structured mathematical objects amenable to investigation by mathematical methods (metamathematics). Schütte inaugurated the important paradigm shift from finite proofs to infinite proofs and developed the mathematical tools for their analysis. Infinitary proof theory flourished in his hands in the 1960s, culminating in the famous bound Γ0 for the limit of predicative mathematics (a fame shared with Feferman). Later his interests shifted to developing infinite proof calculi for impredicative theories. Schütte had a keen interest in advancing ordinal analysis to ever stronger theories and was still working on some of the strongest systems in his eighties. The articles in this volume from leading experts close to his research, show the enduring influence of his work in modern proof theory. They range from eye witness accounts of his scientific life to developments at the current research frontier, including papers by Schütte himself that have never been published before.
A Beautiful Math
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Author : Tom Siegfried
language : en
Publisher: National Academies Press
Release Date : 2006-09-21
A Beautiful Math written by Tom Siegfried and has been published by National Academies Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-21 with Science categories.
Millions have seen the movie and thousands have read the book but few have fully appreciated the mathematics developed by John Nash's beautiful mind. Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimov's dream closer to reality.
Revolutions And Revelations In Computability
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Author : Ulrich Berger
language : en
Publisher: Springer Nature
Release Date : 2022-06-25
Revolutions And Revelations In Computability written by Ulrich Berger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-25 with Computers categories.
This book constitutes the proceedings of the 18th Conference on Computability in Europe, CiE 2022, in Swansea, UK, in July 2022. The 19 full papers together with 7 invited papers presented in this volume were carefully reviewed and selected from 41 submissions. The motto of CiE 2022 was “Revolutions and revelations in computability”. This alludes to the revolutionary developments we have seen in computability theory, starting with Turing's and Gödel's discoveries of the uncomputable and the unprovable and continuing to the present day with the advent of new computational paradigms such as quantum computing and bio-computing, which have dramatically changed our view of computability and revealed new insights into the multifarious nature of computation.
The Mathematician Sophus Lie
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Author : Arild Stubhaug
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-12-04
The Mathematician Sophus Lie written by Arild Stubhaug 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 2001-12-04 with Mathematics categories.
Sophus Lie (1842-1899) is one of Norways greatest scientific talents. His mathematical works have made him famous around the world no less than Niels Henrik Abel. The terms "Lie groups" and "Lie algebra" are part of the standard mathematical vocabulary. In his comprehensive biography the author Arild Stubhaug introduces us to both the person Sophus Lie and his time. We follow him through: childhood at the vicarage in Nordfjordeid; his youthful years in Moss; education in Christiania; travels in Europe; and learn about his contacts with the leading mathematicians of his time.
What Is Information
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Author : Peter Janich
language : en
Publisher: U of Minnesota Press
Release Date : 2018-03-06
What Is Information written by Peter Janich and has been published by U of Minnesota Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-06 with Science categories.
A novel way of looking at information challenges longstanding dogmas—from a preeminent German thinker It is widely agreed that we live in an “information age,” but what exactly is information? This small, seemingly facile question is in fact surprisingly difficult, and it has occupied many of the best philosophical minds of the modern age. In this wholly original addition to the quest to understand information, German philosopher Peter Janich argues that our understanding of information is based in the much broader history of scientific naturalism—the belief that science is a fundamental aspect of the world and not a human contrivance. His novel critique of this widespread dogma grounds science in human life practices and wrestles with the very fundamentals of the scientific way of understanding reality. Offering new perspectives on the major contemporary fields of communications technology, neurobiology, and artificial intelligence, What Is Information? provides a deep look into humanity in an information age. Its arguments show ways of reconciling the sciences and the humanities, shining new light on the relationship of science to the natural world.
Mathematical Reasoning
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Author : Raymond Nickerson
language : en
Publisher: Taylor & Francis
Release Date : 2011-02-25
Mathematical Reasoning written by Raymond Nickerson and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-25 with Psychology categories.
The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition. This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the ‘truths’ of mathematics are discoveries or inventions, and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as ‘beautiful’? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction. This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book’s insights illuminating.
Hermann Gra Mann
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Author : Hans-Joachim Petsche
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-30
Hermann Gra Mann written by Hans-Joachim Petsche 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 2009-12-30 with Mathematics categories.
Hermann Günther Graßmann was one of the most remarkable personalities in 19th-century science. A "small-town genius", he developed a groundbreaking n-dimensional algebra of space and contributed to a revolution in the understanding of mathematics. His work fascinated great mathematicians such as W. R. Hamilton, J. W. Gibbs and A. N. Whitehead. This intellectual biography traces Graßmann’s steps towards scientific brilliance by untangling a complicated web of influences: the force of unsolved problems in mathematics, Friedrich Schleiermacher’s Dialectic, German Romanticism and life in 19th-century Prussia. The book also introduces the reader to the details of Graßmann’s mathematical work without neglecting his achievements in Sanskrit philology and physics. And, for the first time, it makes many original sources accessible to the English-language reader.
Multi Agent Systems
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Author : Vadim Malvone
language : en
Publisher: Springer Nature
Release Date : 2023-09-06
Multi Agent Systems written by Vadim Malvone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-06 with Computers categories.
This volume LNCS 14282 constitutes the refereed proceedings of the 20th European Conference EUMAS 2023, held in Naples, Italy, during September 2023. This volume includes 24 full papers and 5 short papers, carefully selected from 47 submissions. Additionally, the volume features 16 short papers, rigorously reviewed from 20 submissions for the PhD day. The conference focused on the theory and practice of autonomous agents and multi-agent systems, covering a wide range of topics.