Logicism Renewed

Author : Paul C. Gilmore
Publisher : Cambridge University Press
Page : 128 pages
File Size : 40,6 Mb
Release : 2017-03-30
Category : Mathematics
ISBN : 9781108676939

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Logicism Renewed by Paul C. Gilmore Pdf

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.

Author : Anonim
Publisher : Elsevier
Page : 735 pages
File Size : 44,8 Mb
Release : 2009-07-08
Category : Philosophy
ISBN : 9780080930589

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Philosophy of Mathematics by Anonim Pdf

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

Author : Costas Dimitracopoulos
Publisher : Cambridge University Press
Page : 289 pages
File Size : 50,9 Mb
Release : 2008
Category : Logic, Symbolic and mathematical
ISBN : 9780521884259

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Logic Colloquium 2005 by Costas Dimitracopoulos Pdf

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.

Author : Joseph R. Shoenfield
Publisher : CRC Press
Page : 85 pages
File Size : 45,5 Mb
Release : 2018-04-27
Category : Mathematics
ISBN : 9781351419413

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Recursion Theory by Joseph R. Shoenfield Pdf

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.

Author : Nigel J. Cutland,Mauro Di Nasso,David A. Ross
Publisher : CRC Press
Page : 263 pages
File Size : 42,5 Mb
Release : 2006-02-21
Category : Mathematics
ISBN : 9781439865828

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Nonstandard Methods and Applications in Mathematics by Nigel J. Cutland,Mauro Di Nasso,David A. Ross Pdf

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

Author : Joachim Lambek
Publisher : Polimetrica s.a.s.
Page : 154 pages
File Size : 50,7 Mb
Release : 2008
Category : Language Arts & Disciplines
ISBN : 9788876991172

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From Word to Sentence by Joachim Lambek Pdf

Author : Victor A. Carreño,César A. Muñoz,Sofiène Tahar
Publisher : Unknown
Page : 200 pages
File Size : 45,8 Mb
Release : 2002
Category : Automatic theorem proving
ISBN : NASA:31769000474430

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Theorem Proving in Higher Order Logics by Victor A. Carreño,César A. Muñoz,Sofiène Tahar Pdf

Author : Francesca Boccuni,Andrea Sereni
Publisher : Taylor & Francis
Page : 419 pages
File Size : 50,6 Mb
Release : 2021-11-29
Category : Mathematics
ISBN : 9781000508116

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Origins and Varieties of Logicism by Francesca Boccuni,Andrea Sereni Pdf

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.

Author : A. J. Bueno
Publisher : Strategic Book Publishing & Rights Agency
Page : 390 pages
File Size : 52,8 Mb
Release : 2016-05-23
Category : Electronic
ISBN : 9781681812694

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Recuperation of Theological Principles against Ideo-logicist Incompetence by A. J. Bueno Pdf

This Recuperation, based on the epistemology of Book 1, confronts the logicist destruction in theology. The preface enjoins: “Logicism is deleterious in all sciences. We shall see how it can destroy Theology trying, for example, to replace reality with sacred texts, that is, with testimonies of Revelation.” The logicist sub-epistemology certainly favors the identification of Revelation with Bible, of faith with articles of faith, of enuntiabilia and concepts with reality. Writing his theological thesis on Bonaventure, J. Ratzinger was pleasantly surprised to discover that no one in the thirteenth century called the Bible the Revelation. But this does not mean that logicism began afterward, with Descartes, for example, reaching its apotheosis with the German idealism. This book explains how a peculiar symbiosis of nominalism (Ockham) and logicism impairs the sincere and orthodox initial search of Luther, who ends up developing a theology of the nomina-logicist sort source of ravings. Erasmus perceives it and tries to refute him, but is a victim of similar epistemological blunders. The book’s second part focuses on the issue of the integral education of young people and leads to the need of sacred theology. Is it advisable to teach young people metaphysics and ethics in a strictly philosophical way in order to provide a fundamental view of reality, a Weltanschauung, perhaps? The explicit answer of Aristotle and Thomas is a resounding no. Aquinas advocates teaching metaphysics within theology.

Author : Anonim
Publisher : Unknown
Page : 780 pages
File Size : 53,9 Mb
Release : 2002
Category : Logic, Symbolic and mathematical
ISBN : UOM:39015058994461

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Reports on Mathematical Logic by Anonim Pdf

Author : Sten Lindström,Erik Palmgren,Krister Segerberg,Viggo Stoltenberg-Hansen
Publisher : Springer Science & Business Media
Page : 509 pages
File Size : 50,9 Mb
Release : 2008-11-25
Category : Mathematics
ISBN : 9781402089268

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Logicism, Intuitionism, and Formalism by Sten Lindström,Erik Palmgren,Krister Segerberg,Viggo Stoltenberg-Hansen Pdf

This anthology reviews the programmes in the foundations of mathematics from the classical period and assesses their possible relevance for contemporary philosophy of mathematics. A special section is concerned with constructive mathematics.

Author : Joseph R. Pearce
Publisher : University Press of America
Page : 222 pages
File Size : 47,5 Mb
Release : 1994
Category : Philosophy
ISBN : 0819195782

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Analytical Sociology by Joseph R. Pearce Pdf

The focus on this volume is on logic and how the logic of foundational hierarchies may be applied to clarify the relationship between sociological theory and empirical research. The author articulates a logical calculus as a method for theory construction. Contents: Introduction; The Logical Foundations of Analytical Theory; Ontology and Analytical Sociological Theory; The Social Order and Social Structure; Neo-Marxist Theories of the State; An Application of Analytical Theory to Gramsci's and Althusser's Theories of the State; The Relationship Between Theory and Empirical Research; Conclusion; Bibliography; Index.

Author : Anonim
Publisher : Unknown
Page : 280 pages
File Size : 55,8 Mb
Release : 2006
Category : Library science
ISBN : UOM:39015066139471

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Alchemical Libraries Almanack by Anonim Pdf

Author : Khalid Arar,Deniz Örücü,Jane Wilkinson
Publisher : Routledge
Page : 239 pages
File Size : 52,5 Mb
Release : 2020-12-29
Category : Education
ISBN : 9781000282986

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Neoliberalism and Education Systems in Conflict by Khalid Arar,Deniz Örücü,Jane Wilkinson Pdf

Neoliberalism and Education Systems in Conflict: Exploring Challenges Across the Globe explores how neoliberal values are imprinted onto educational spaces and practices, and by consequence, fundamentally reshape how we come to understand the educational experience at the school or system level. Countries across the globe struggle with the residual effects of increased accountability, choice/voucher systems, and privatization. The first section of the book discusses the direct imprint of neoliberal policies on educational spaces. The next section examines the more indirect outcomes of neoliberalism, including the challenges of inequity, access, violence, racism, and social justice issues as a result of neoliberal ideologies. Each section of the book includes case studies about education systems across the globe, including Britain, Middle East, Turkey, United States, China, and Chile written by international contributors. Neoliberalism and Education Systems in Conflict is essential reading for educators, scholars, and faculty of educational leadership and policy globally.

Author : Paola Cantù,Georg Schiemer
Publisher : Springer Nature
Page : 333 pages
File Size : 40,5 Mb
Release : 2024-01-23
Category : Science
ISBN : 9783031421907

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Logic, Epistemology, and Scientific Theories - From Peano to the Vienna Circle by Paola Cantù,Georg Schiemer Pdf

This book provides a collection of chapters on the development of scientific philosophy and symbolic logic in the early twentieth century. The turn of the last century was a key transitional period for the development of symbolic logic and scientific philosophy. The Peano school, the editorial board of the Revue de Métaphysique et de Morale, and the members of the Vienna Circle are generally mentioned as champions of this transformation of the role of logic in mathematics and in the sciences. The scholarship contained provides a rich historical and philosophical understanding of these groups and research areas. Specifically, the contributions focus on a detailed investigation of the relation between structuralism and modern mathematics. In addition, this book provides a closer understanding of the relation between symbolic logic and previous traditions such as syllogistics. This volume also informs the reader on the relation between logic, the history and didactics in the Peano School. This edition appeals to students and researchers working in the history of philosophy and of logic, philosophy of science, as well as to researchers on the Vienna Circle and the Peano School.