Report From The 90 25 Philosophical Reflections On The Foundations Of Mathematics
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Report From The 90 25 Philosophical Reflections On The Foundations Of Mathematics
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Author : McGill University. Dept. of Mathematics and Statistics
language : en
Publisher:
Release Date : 1990
Report From The 90 25 Philosophical Reflections On The Foundations Of Mathematics written by McGill University. Dept. of Mathematics and Statistics and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
Canadiana
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Author :
language : en
Publisher:
Release Date : 1991-05
Canadiana written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-05 with Canada categories.
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.
Artificial Mathematical Intelligence
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Author : Danny A. J. Gómez Ramírez
language : en
Publisher: Springer Nature
Release Date : 2020-10-23
Artificial Mathematical Intelligence written by Danny A. J. Gómez Ramírez and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-23 with Mathematics categories.
This volume discusses the theoretical foundations of a new inter- and intra-disciplinary meta-research discipline, which can be succinctly called cognitive metamathematics, with the ultimate goal of achieving a global instance of concrete Artificial Mathematical Intelligence (AMI). In other words, AMI looks for the construction of an (ideal) global artificial agent being able to (co-)solve interactively formal problems with a conceptual mathematical description in a human-style way. It first gives formal guidelines from the philosophical, logical, meta-mathematical, cognitive, and computational points of view supporting the formal existence of such a global AMI framework, examining how much of current mathematics can be completely generated by an interactive computer program and how close we are to constructing a machine that would be able to simulate the way a modern working mathematician handles solvable mathematical conjectures from a conceptual point of view. The thesis that it is possible to meta-model the intellectual job of a working mathematician is heuristically supported by the computational theory of mind, which posits that the mind is in fact a computational system, and by the meta-fact that genuine mathematical proofs are, in principle, algorithmically verifiable, at least theoretically. The introduction to this volume provides then the grounding multifaceted principles of cognitive metamathematics, and, at the same time gives an overview of some of the most outstanding results in this direction, keeping in mind that the main focus is human-style proofs, and not simply formal verification. The first part of the book presents the new cognitive foundations of mathematics’ program dealing with the construction of formal refinements of seminal (meta-)mathematical notions and facts. The second develops positions and formalizations of a global taxonomy of classic and new cognitive abilities, and computational tools allowing for calculation of formal conceptual blends are described. In particular, a new cognitive characterization of the Church-Turing Thesis is presented. In the last part, classic and new results concerning the co-generation of a vast amount of old and new mathematical concepts and the key parts of several standard proofs in Hilbert-style deductive systems are shown as well, filling explicitly a well-known gap in the mechanization of mathematics concerning artificial conceptual generation.
The Palgrave Centenary Companion To Principia Mathematica
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Author : Bernard Linsky
language : en
Publisher: Springer
Release Date : 2013-11-29
The Palgrave Centenary Companion To Principia Mathematica written by Bernard Linsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-29 with Philosophy categories.
To mark the centenary of the 1910 to 1913 publication of the monumental Principia Mathematica by Alfred N. Whitehead and Bertrand Russell, this collection of fifteen new essays by distinguished scholars considers the influence and history of PM over the last hundred years.
Philosophy Of Mathematics In The Twentieth Century
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Author : Charles Parsons
language : en
Publisher: Harvard University Press
Release Date : 2014-03-17
Philosophy Of Mathematics In The Twentieth Century written by Charles Parsons 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 2014-03-17 with Philosophy categories.
In this illuminating collection, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the course of the past century. Parsons begins with a discussion of the Kantian legacy in the work of L. E. J. Brouwer, David Hilbert, and Paul Bernays, shedding light on how Bernays revised his philosophy after his collaboration with Hilbert. He considers Hermann Weyl's idea of a "vicious circle" in the foundations of mathematics, a radical claim that elicited many challenges. Turning to Kurt Gödel, whose incompleteness theorem transformed debate on the foundations of mathematics and brought mathematical logic to maturity, Parsons discusses his essay on Bertrand Russell's mathematical logic--Gödel's first mature philosophical statement and an avowal of his Platonistic view. Philosophy of Mathematics in the Twentieth Century insightfully treats the contributions of figures the author knew personally: W. V. Quine, Hilary Putnam, Hao Wang, and William Tait. Quine's early work on ontology is explored, as is his nominalistic view of predication and his use of the genetic method of explanation in the late work The Roots of Reference. Parsons attempts to tease out Putnam's views on existence and ontology, especially in relation to logic and mathematics. Wang's contributions to subjects ranging from the concept of set, minds, and machines to the interpretation of Gödel are examined, as are Tait's axiomatic conception of mathematics, his minimalist realism, and his thoughts on historical figures.
Founding Mathematics On Semantic Conventions
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Author : Casper Storm Hansen
language : en
Publisher: Springer Nature
Release Date : 2021-11-04
Founding Mathematics On Semantic Conventions written by Casper Storm Hansen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-04 with Mathematics categories.
This book presents a new nominalistic philosophy of mathematics: semantic conventionalism. Its central thesis is that mathematics should be founded on the human ability to create language – and specifically, the ability to institute conventions for the truth conditions of sentences. This philosophical stance leads to an alternative way of practicing mathematics: instead of “building” objects out of sets, a mathematician should introduce new syntactical sentence types, together with their truth conditions, as he or she develops a theory. Semantic conventionalism is justified first through criticism of Cantorian set theory, intuitionism, logicism, and predicativism; then on its own terms; and finally, exemplified by a detailed reconstruction of arithmetic and real analysis. Also included is a simple solution to the liar paradox and the other paradoxes that have traditionally been recognized as semantic. And since it is argued that mathematics is semantics, this solution also applies to Russell’s paradox and the other mathematical paradoxes of self-reference. In addition to philosophers who care about the metaphysics and epistemology of mathematics or the paradoxes of self-reference, this book should appeal to mathematicians interested in alternative approaches.
Symmetries In Physics
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Author : Katherine Brading
language : en
Publisher: Cambridge University Press
Release Date : 2003-12-04
Symmetries In Physics written by Katherine Brading 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 2003-12-04 with Science categories.
This book brings together philosophical discussions of symmetry in physics, highlighting the main issues and controversies. It covers all the fundamental symmetries of modern physics, as well as discussing symmetry-breaking and general interpretational issues. For each topic, classic texts are followed by review articles and short commentaries.
History And Philosophy Of Modern Mathematics
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Author : William Aspray
language : en
Publisher: U of Minnesota Press
Release Date : 1988
History And Philosophy Of Modern Mathematics written by William Aspray 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 1988 with Mathematics categories.
History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective. The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.
Current Debates In Philosophy Of Science
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Author : Cristián Soto
language : en
Publisher: Springer Nature
Release Date : 2023-08-28
Current Debates In Philosophy Of Science written by Cristián Soto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-28 with Science categories.
This volume collects previously unpublished contributions to the philosophy of science. What brings them together is a twofold goal: first and foremost, celebrating the name of Roberto Torretti, whose works in this and other areas have had –and continue to have– a significant impact on the international philosophy of science community; and second, the desire of advancing novel perspectives on various issues in the philosophy of science broadly construed. Roberto Torretti has made substantial contributions to current debates in the history and philosophy of science, the general philosophy of science, and the philosophy of physics and geometry. Among his landmark contributions, we find his investigations in the history and philosophy of geometry, as well as his systematic studies of Einstein's relativity theory. This volume convenes leading philosophers and early-career scholars compiling a fine collection of chapters addressing recent debates on Kantian philosophy of science, the general philosophy of science, and the history and philosophy of physics and mathematics.