Essays On The Foundations Of Mathematics By Moritz Pasch
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Essays On The Foundations Of Mathematics By Moritz Pasch
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Author : Stephen Pollard
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-03
Essays On The Foundations Of Mathematics By Moritz Pasch written by Stephen Pollard 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 2010-08-03 with Mathematics categories.
Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science; he provides axioms for the combinatorial reasoning essential to Hilbert’s program of consistency proofs; he explores "implicit definition" (a generalization of definition by abstraction) and indicates how this technique yields an "empiricist" reconstruction of set theory; he argues that we cannot fully understand the logical structure of mathematics without clearly distinguishing between decidable and undecidable properties; he offers a rare glimpse into the mind of a master of axiomatics, surveying in detail the thought experiments he employed as he struggled to identify fundamental mathematical principles; and much more. This volume will: Give English speakers access to an important body of work from a turbulent and pivotal period in the history of mathematics, help us look beyond the familiar triad of formalism, intuitionism, and logicism, show how deeply we can see with the help of a guide determined to present fundamental mathematical ideas in ways that match our human capacities, will be of interest to graduate students and researchers in logic and the foundations of mathematics.
Essays On The Foundations Of Mathematics By Moritz Pasch
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Author : Stephen Pollard
language : en
Publisher:
Release Date : 2010
Essays On The Foundations Of Mathematics By Moritz Pasch written by Stephen Pollard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science; he provides axioms for the combinatorial reasoning essential to Hilbert's program of consistency proofs; he explores "implicit definition" (a generalization of definition by abstraction) and indicates how this technique yields an "empiricist" reconstruction of set theory; he argues that we cannot fully understand the logical structure of mathematics without clearly distinguishing between decidable and undecidable properties; he offers a rare glimpse into the mind of a master of axiomatics, surveying in detail the thought experiments he employed as he struggled to identify fundamental mathematical principles; and much more. This volume will: Give English speakers access to an important body of work from a turbulent and pivotal period in the history of mathematics. Help us look beyond the familiar triad of formalism, intuitionism, and logicism. Show how deeply we can see with the help of a guide determined to present fundamental mathematical ideas in ways that match our human capacities. The book will be of interest to graduate students and researchers in logic and the foundations of mathematics.
The Prehistory Of Mathematical Structuralism
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Author : Erich H. Reck
language : en
Publisher: Oxford University Press
Release Date : 2020
The Prehistory Of Mathematical Structuralism written by Erich H. Reck and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.
This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysical aspects of structuralism.
Scientific Concepts And Investigative Practice
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Author : Uljana Feest
language : en
Publisher: Walter de Gruyter
Release Date : 2012-10-30
Scientific Concepts And Investigative Practice written by Uljana Feest and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-30 with Philosophy categories.
Recent philosophy and history of science has seen a surge of interest in the role of concepts in scientific research. Scholars working in this new field focus on scientific concepts, rather than theories, as units of analysis and on the ways in which concepts are formed and used rather than on what they represent. They analyze what has traditionally been called the context of discovery, rather than (or in addition to) the context of justification. And they examine the dynamics of research rather than the status of the finished research results. This volume provides detailed case studies and general analyses to address questions raised by these points, such as: - Can concepts be clearly distinguished from the sets of beliefs we have about their referents? - What - if any - sense can be made of the separation between concepts and theories? - Can we distinguish between empirical and theoretical concepts? - Are there interesting similarities and differences between the role of concepts in the empirical sciences and in mathematics? - What underlying notion of investigative practice could be drawn on to explicate the role of concept in such practice? - From a philosophical point of view, is the distinction between discovery and justification a helpful frame of reference for inquiring into the dynamics of research? - From a historiographical point of view, does a focus on concepts face the danger of falling back into an old-fashioned history of ideas?
Epistemology Knowledge And The Impact Of Interaction
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Author : Juan Redmond
language : en
Publisher: Springer
Release Date : 2016-04-28
Epistemology Knowledge And The Impact Of Interaction written by Juan Redmond and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-28 with Philosophy categories.
With this volume of the series Logic, Epistemology, and the Unity of Science edited by S. Rahman et al. a challenging dialogue is being continued. The series’ first volume argued that one way to recover the connections between logic, philosophy of sciences, and sciences is to acknowledge the host of alternative logics which are currently being developed. The present volume focuses on four key themes. First of all, several chapters unpack the connection between knowledge and epistemology with particular focus on the notion of knowledge as resulting from interaction. Secondly, new epistemological perspectives on linguistics, the foundations of mathematics and logic, physics, biology and law are a subject of analysis. Thirdly, several chapters are dedicated to a discussion of Constructive Type Theory and more generally of the proof-theoretical notion of meaning.Finally, the book brings together studies on the epistemic role of abduction and argumentation theory, both linked to non-monotonic approaches to the dynamics of knowledge.
From Dedekind To G Del
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Author : Jaakko Hintikka
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
From Dedekind To G Del written by Jaakko Hintikka 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 2013-03-09 with Philosophy categories.
Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy. From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics illustrates the much greater variety of the actual developments in the foundations during the period covered. The viewpoints that serve this purpose included the foundational ideas of working mathematicians, such as Kronecker, Dedekind, Borel and the early Hilbert, and the development of notions like model and modelling, arbitrary function, completeness, and non-Archimedean structures. The philosophers discussed include not only the household names in logic, but also Husserl, Wittgenstein and Ramsey. Needless to say, such logically-oriented thinkers as Frege, Russell and Gödel are not entirely neglected, either. Audience: Everybody interested in the philosophy and/or history of mathematics will find this book interesting, giving frequently novel insights.
Mathematics Unbound The Evolution Of An International Mathematical Research Community 1800 1945
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Author : Karen Hunger Parshall
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Mathematics Unbound The Evolution Of An International Mathematical Research Community 1800 1945 written by Karen Hunger Parshall 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 2002 with Mathematics categories.
Although today's mathematical research community takes its international character very much for granted, this ``global nature'' is relatively recent, having evolved over a period of roughly 150 years-from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom thegoal of mathematical research and cooperation transcended national boundaries. Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians andmathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only developments within component national mathematical communities, such as the growth of societies and journals, but also more wide-ranging political, philosophical, linguistic, and pedagogical issues. The resulting volume is essential reading for anyone interestedin the history of modern mathematics. It will be of interest to mathematicians, historians of mathematics, and historians of science in general.
From Kant To Hilbert Volume 2
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Author : William Bragg Ewald
language : en
Publisher: OUP Oxford
Release Date : 2005-04-21
From Kant To Hilbert Volume 2 written by William Bragg Ewald and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-21 with Mathematics categories.
Immanuel Kant's Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics while David Hilbert was the last great mainstream mathematician to pursue important nineteenth cnetury ideas. This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics—algebra, geometry, number theory, analysis, logic and set theory—with narratives to show how they are linked. Classic works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare are reproduced in reliable translations and many selections from writers such as Gauss, Cantor, Kronecker and Zermelo are here translated for the first time. The collection is an invaluable source for anyone wishing to gain an understanding of the foundation of modern mathematics.
Reading Mathematics In Early Modern Europe
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Author : Philip Beeley
language : en
Publisher: Routledge
Release Date : 2020-10-20
Reading Mathematics In Early Modern Europe written by Philip Beeley and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-20 with Literary Criticism categories.
Libraries and archives contain many thousands of early modern mathematical books, of which almost equally many bear readers’ marks, ranging from deliberate annotations and accidental blots to corrections and underlinings. Such evidence provides us with the material and intellectual tools for exploring the nature of mathematical reading and the ways in which mathematics was disseminated and assimilated across different social milieus in the early centuries of print culture. Other evidence is important, too, as the case studies collected in the volume document. Scholarly correspondence can help us understand the motives and difficulties in producing new printed texts, library catalogues can illuminate collection practices, while manuscripts can teach us more about textual traditions. By defining and illuminating the distinctive world of early modern mathematical reading, the volume seeks to close the gap between the history of mathematics as a history of texts and history of mathematics as part of the broader history of human culture.
Mathematical Thought From Ancient To Modern Times Volume 3
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Author : Morris Kline
language : en
Publisher: Oxford University Press
Release Date : 1990-03-01
Mathematical Thought From Ancient To Modern Times Volume 3 written by Morris Kline and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-03-01 with Mathematics categories.
This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the disciplines origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.