Philosophy S Loss Of Logic To Mathematics
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Philosophy S Loss Of Logic To Mathematics
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Author : Woosuk Park
language : en
Publisher: Springer
Release Date : 2018-07-12
Philosophy S Loss Of Logic To Mathematics written by Woosuk Park and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-12 with Philosophy categories.
This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand Tarski’s and Gödel’s work, explaining why the problems they discussed are still unsolved. Finally, the book reports on some of the most influential positions in contemporary philosophy of mathematics, i.e., Maddy’s mathematical naturalism and Shapiro’s mathematical structuralism. Last but not least, the book introduces Biancani’s Aristotelian philosophy of mathematics as this is considered important to understand current philosophical issue in the applications of mathematics. One of the main purposes of the book is to stimulate readers to reconsider the Aristotelian position, which disappeared almost completely from the scene in logic and mathematics in the early twentieth century.
Logic S Lost Genius
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Author : Eckart Menzler-Trott
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-05-05
Logic S Lost Genius written by Eckart Menzler-Trott and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-05 with Mathematics categories.
Gerhard Gentzen (1909–1945) is the founder of modern structural proof theory. His lasting methods, rules, and structures resulted not only in the technical mathematical discipline called “proof theory” but also in verification programs that are essential in computer science. The appearance, clarity, and elegance of Gentzen's work on natural deduction, the sequent calculus, and ordinal proof theory continue to be impressive even today. The present book gives the first comprehensive, detailed, accurate scientific biography expounding the life and work of Gerhard Gentzen, one of our greatest logicians, until his arrest and death in Prague in 1945. Particular emphasis in the book is put on the conditions of scientific research, in this case mathematical logic, in National Socialist Germany, the ideological fight for “German logic”, and their mutual protagonists. Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an indispensable source of information on this important mathematician, his work, and his time. The volume is completed by two deep substantial essays by Jan von Plato and Craig Smoryński on Gentzen's proof theory; its relation to the ideas of Hilbert, Brouwer, Weyl, and Gödel; and its development up to the present day. Smoryński explains the Hilbert program in more than the usual slogan form and shows why consistency is important. Von Plato shows in detail the benefits of Gentzen's program. This important book is a self-contained starting point for any work on Gentzen and his logic. The book is accessible to a wide audience with different backgrounds and is suitable for general readers, researchers, students, and teachers.
Essays On Husserl S Logic And Philosophy Of Mathematics
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Author : Stefania Centrone
language : en
Publisher: Springer
Release Date : 2017-09-07
Essays On Husserl S Logic And Philosophy Of Mathematics written by Stefania Centrone and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-07 with Philosophy categories.
Essays on Husserl’s Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl’s work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl’s by considering their reception and elaboration by some of his disciples and followers, such as Oskar Becker and Jacob Klein, as well as their influence on some of the most significant logicians and mathematicians of the past century, such as Luitzen E. J. Brouwer, Rudolf Carnap, Kurt Gödel and Hermann Weyl. Most of the papers consider Husserl and another scholar – e.g. Leibniz, Kant, Bolzano, Brentano, Cantor, Frege – and trace out and contextualize lines of influence, points of contact, and points of disagreement. Each essay is written by an expert of the field, and the volume includes contributions both from the analytical tradition and from the phenomenological one.
Philosophy Of Science Logic And Mathematics In The 20th Century
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Author : Stuart G. Shanker
language : en
Publisher: Taylor & Francis
Release Date : 2023-05-09
Philosophy Of Science Logic And Mathematics In The 20th Century written by Stuart G. Shanker and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-09 with Philosophy categories.
The twentieth century witnessed the birth of analytic philosophy. This volume covers some of its key movements and philosophers, including Frege and Wittgenstein's Tractatus.
Abduction In Cognition And Action
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Author : John R. Shook
language : en
Publisher: Springer Nature
Release Date : 2021-05-29
Abduction In Cognition And Action written by John R. Shook and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-29 with Philosophy categories.
This book gathers together novel essays on the state-of-the-art research into the logic and practice of abduction. In many ways, abduction has become established and essential to several fields, such as logic, cognitive science, artificial intelligence, philosophy of science, and methodology. In recent years this interest in abduction’s many aspects and functions has accelerated. There are evidently several different interpretations and uses for abduction. Many fundamental questions on abduction remain open. How is abduction manifested in human cognition and intelligence? What kinds or types of abduction can be discerned? What is the role for abduction in inquiry and mathematical discovery? The chapters aim at providing answer to these and other current questions. Their contributors have been at the forefront of discussions on abduction, and offer here their updated approaches to the issues that they consider central to abduction’s contemporary relevance. The book is an essential reading for any scholar or professional keeping up with disciplines impacted by the study of abductive reasoning, and its novel development and applications in various fields.
An Historical Introduction To The Philosophy Of Mathematics A Reader
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Author : Russell Marcus
language : en
Publisher: Bloomsbury Publishing
Release Date : 2016-02-11
An Historical Introduction To The Philosophy Of Mathematics A Reader written by Russell Marcus and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-11 with Philosophy categories.
A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.
Social Constructivism As A Philosophy Of Mathematics
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Author : Paul Ernest
language : en
Publisher: SUNY Press
Release Date : 1998-01-01
Social Constructivism As A Philosophy Of Mathematics written by Paul Ernest and has been published by SUNY Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Philosophy categories.
Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.
Topics In Logic Philosophy And Foundations Of Mathematics And Computer Science
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Author : Stanisław Krajewski
language : en
Publisher: IOS Press
Release Date : 2007
Topics In Logic Philosophy And Foundations Of Mathematics And Computer Science written by Stanisław Krajewski and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This volume honors Professor Andrzej Grzegorczyk, the nestor of Polish logicians, on his 85th anniversary. The editors would like to express the respect and sympathy they have for him. His textbook The Outline of Mathematical Logic has been published in many editions and translated into several languages. It was this textbook that introduced many of us into the world of mathematical logic. Professor Grzegorczyk has made fundamental contributions to logic and to philosophy. His results, mainly on hierarchy of primitive recursive functions, known as the Grzegorczyk hierarchy, are of fundamental importance to theoretical computer science. In particular, they were precursory for the computational complexity theory. The editors would like to stress that this special publication celebrates a scientist who is still actively pursuing genuinely innovative directions of research. Quite recently, Andrzej Grzegorczyk gave a new proof of undecidability of the first order functional calculus. His proof does not use the arithmetization of Kurt Gödel. In recognition of his merits, the University of Clermont-Ferrand conferred to Professor Andrzej Grzegorczyk the Doctorat Honoris Causa. The work and life of Professor Andrzej Grzegorczyk is presented in the article by Professors Stanislaw Krajewski and Jan Wolenski. The papers in this collection have been submitted on invitational basis.
Constructibility And Mathematical Existence
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Author : Charles S. Chihara
language : en
Publisher: Clarendon Press
Release Date : 1990-04-12
Constructibility And Mathematical Existence written by Charles S. Chihara and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-04-12 with Philosophy categories.
This book is concerned with `the problem of existence in mathematics'. It develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. It explores the philosophical implications of such an approach in an examination of the writings of Field, Burgess, Maddy, Kitcher, and others.
The Oxford Dictionary Of Philosophy
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Author : Simon Blackburn
language : en
Publisher: OUP Oxford
Release Date : 2005-10-27
The Oxford Dictionary Of Philosophy written by Simon Blackburn and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-27 with Philosophy categories.
Comprehensive and authoritative, this dictionary provides wide-ranging and lively coverage of not only Western philosophical traditions, but also themes from Chinese, Indian, Islamic, and Jewish philosophy.