Logicism Renewed
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Logicism Renewed
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Author : Paul C. Gilmore
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-30
Logicism Renewed written by Paul C. Gilmore and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-30 with Mathematics categories.
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Logicism, as put forward by Bertrand Russell, was predicated on a belief that all of mathematics can be deduced from a very small number of fundamental logical principles. In this volume, the twenty-third publication in the Lecture Notes in Logic series, Paul C. Gilmore revisits logicism in light of recent advances in mathematical logic and theoretical computer science. Gilmore addresses the need for languages which can be understood by both humans and computers and, using Intensional Type Theory (ITT), provides a unified basis for mathematics and computer science. This yields much simpler foundations for recursion theory and the semantics of computer programs than those currently provided by category theory.
Philosophy Of Mathematics
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Author :
language : en
Publisher: Elsevier
Release Date : 2009-07-08
Philosophy Of Mathematics written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-08 with Philosophy categories.
One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics-Clearly written expositions of fundamental ideas and concepts-Definitive discussions by leading researchers in the field-Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included
Logic Colloquium 2005
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Author : Costas Dimitracopoulos
language : en
Publisher: Cambridge University Press
Release Date : 2008
Logic Colloquium 2005 written by Costas Dimitracopoulos and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Logic, Symbolic and mathematical categories.
The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of developments, and the rest of the papers are chosen to complement the invited talks. This 2007 volume includes surveys, tutorials, and selected research papers from the 2005 meeting. Highlights include three papers on different aspects of connections between model theory and algebra; a survey of major advances in combinatorial set theory; a tutorial on proof theory and modal logic; and a description of Bernay's philosophy of mathematics.
Recursion Theory
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Author : Joseph R. Shoenfield
language : en
Publisher: CRC Press
Release Date : 2018-04-27
Recursion Theory written by Joseph R. Shoenfield and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-27 with Mathematics categories.
This volume, which ten years ago appeared as the first in the acclaimed series Lecture Notes in Logic, serves as an introduction to recursion theory. The fundamental concept of recursion makes the idea of computability accessible to a mathematical analysis, thus forming one of the pillars on which modern computer science rests. The clarity and focus of this text have established it as a classic instrument for teaching and self-study that prepares its readers for the study of advanced monographs and the current literature on recursion theory.
Nonstandard Methods And Applications In Mathematics
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Author : Nigel J. Cutland
language : en
Publisher: CRC Press
Release Date : 2006-02-21
Nonstandard Methods And Applications In Mathematics written by Nigel J. Cutland and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-21 with Mathematics categories.
A conference on Nonstandard Methods and Applications in Mathematics (NS2002) was held in Pisa, Italy from June 12-16, 2002. Nonstandard analysis is one of the great achievements of modern applied mathematical logic. In addition to the important philosophical achievement of providing a sound mathematical basis for using infinitesimals in analysis, t
From Word To Sentence
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Author : Joachim Lambek
language : en
Publisher: Polimetrica s.a.s.
Release Date : 2008
From Word To Sentence written by Joachim Lambek and has been published by Polimetrica s.a.s. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Language Arts & Disciplines categories.
Theorem Proving In Higher Order Logics
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Author : Victor A. Carreño
language : en
Publisher:
Release Date : 2002
Theorem Proving In Higher Order Logics written by Victor A. Carreño and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Automatic theorem proving categories.
Logic Logic And Logic
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Author : George Boolos
language : en
Publisher: Harvard University Press
Release Date : 1998
Logic Logic And Logic written by George Boolos and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gödel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work on logic and the philosophy of mathematics. John Burgess has provided introductions to each of the three parts of the volume, and also an afterword on Boolos's technical work in provability logic, which is beyond the scope of this volume.
The Evolution Of Logic
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Author : W. D. Hart
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-23
The Evolution Of Logic written by W. D. Hart and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-23 with Philosophy categories.
Examines the relations between logic and philosophy over the last 150 years. Logic underwent a major renaissance beginning in the nineteenth century. Cantor almost tamed the infinite, and Frege aimed to undercut Kant by reducing mathematics to logic. These achievements were threatened by the paradoxes, like Russell's. This ferment generated excellent philosophy (and mathematics) by excellent philosophers (and mathematicians) up to World War II. This book provides a selective, critical history of the collaboration between logic and philosophy during this period. After World War II, mathematical logic became a recognized subdiscipline in mathematics departments, and consequently but unfortunately philosophers have lost touch with its monuments. This book aims to make four of them (consistency and independence of the continuum hypothesis, Post's problem, and Morley's theorem) more accessible to philosophers, making available the tools necessary for modern scholars of philosophy to renew a productive dialogue between logic and philosophy.
Origins And Varieties Of Logicism
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Author : Francesca Boccuni
language : en
Publisher: Taylor & Francis
Release Date : 2021-11-29
Origins And Varieties Of Logicism written by Francesca Boccuni and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-29 with Mathematics categories.
This book offers a plurality of perspectives on the historical origins of logicism and on contemporary developments of logicist insights in philosophy of mathematics. It uniquely provides up-to-date research and novel interpretations on a variety of intertwined themes and historical figures related to different versions of logicism. The essays, written by prominent scholars, are divided into three thematic sections. Part I focuses on major authors like Frege, Dedekind, and Russell, providing a historical and theoretical exploration of such figures in the philosophical and mathematical milieu in which logicist views were first expounded. Part II sheds new light on the interconnections between these founding figures and a number of influential other traditions, represented by authors like Hilbert, Husserl, and Peano, as well as on the reconsideration of logicism by Carnap and the logical empiricists. Finally, Part III assesses the legacy of such authors and of logicist themes for contemporary philosophy of mathematics, offering new perspectives on highly debated topics—neo-logicism and its extension to accounts of ordinal numbers and set-theory, the comparison between neo-Fregean and neo-Dedekindian varieties of logicism, and the relation between logicist foundational issues and empirical research on numerical cognition—which define the prospects of logicism in the years to come. This book offers a comprehensive account of the development of logicism and its contemporary relevance for the logico-philosophical foundations of mathematics. It will be of interest to graduate students and researchers working in philosophy of mathematics, philosophy of logic, and the history of analytic philosophy.