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Essays On The Foundations Of Mathematics By Moritz Pasch
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Book Synopsis Essays on the Foundations of Mathematics by Moritz Pasch by : Stephen Pollard
Download or read book Essays on the Foundations of Mathematics by Moritz Pasch written by Stephen Pollard and published by Springer Science & Business Media. This book was released on 2010-08-03 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Essays on the Foundations of Mathematics by Moritz Pasch by : Stephen Pollard
Download or read book Essays on the Foundations of Mathematics by Moritz Pasch written by Stephen Pollard and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Essays on the Foundations of Mathematics by : Moritz Pasch
Download or read book Essays on the Foundations of Mathematics written by Moritz Pasch and published by . This book was released on 2010 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Prehistory of Mathematical Structuralism by : Erich H. Reck
Download or read book The Prehistory of Mathematical Structuralism written by Erich H. Reck and published by Oxford University Press. This book was released on 2020 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 metaphysic.
Book Synopsis Scientific Concepts and Investigative Practice by : Uljana Feest
Download or read book Scientific Concepts and Investigative Practice written by Uljana Feest and published by Walter de Gruyter. This book was released on 2012-10-30 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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?
Book Synopsis Epistemology, Knowledge and the Impact of Interaction by : Juan Redmond
Download or read book Epistemology, Knowledge and the Impact of Interaction written by Juan Redmond and published by Springer. This book was released on 2016-04-28 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Mathematical Prelude to the Philosophy of Mathematics by : Stephen Pollard
Download or read book A Mathematical Prelude to the Philosophy of Mathematics written by Stephen Pollard and published by Springer. This book was released on 2014-05-12 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Gödel's theorems, interpretability, the hierarchy of sets, Frege arithmetic and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and real numbers and have some background in formal logic.
Book Synopsis From Dedekind to Gödel by : Jaakko Hintikka
Download or read book From Dedekind to Gödel written by Jaakko Hintikka and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800-1945 by : Karen Hunger Parshall
Download or read book Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800-1945 written by Karen Hunger Parshall and published by American Mathematical Soc.. This book was released on 2002 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis From Kant to Hilbert Volume 2 by : William Bragg Ewald
Download or read book From Kant to Hilbert Volume 2 written by William Bragg Ewald and published by Oxford University Press. This book was released on 1999 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work brings together a comprehensive selection of mathematical works from the period 1707-1930. During this time the foundations of modern mathematics were laid, and From Kant to Hilbert provides an overview of the foundational work in each of the main branches of mathmeatics with narratives showing how they were linked. Now available as a separate volume.
Book Synopsis Ernst Schröder on Algebra and Logic by : Stephen Pollard
Download or read book Ernst Schröder on Algebra and Logic written by Stephen Pollard and published by Springer. This book was released on 2023-07-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers English translations of three early works by Ernst Schröder (1841-1902), a mathematician and logician whose philosophical ruminations and pathbreaking contributions to algebraic logic attracted the admiration and ire of figures such as Dedekind, Frege, Husserl, and C. S. Peirce. Today he still engages the sympathetic interest of logicians and philosophers. The works translated record Schröder’s journey out of algebra into algebraic logic and document his transformation of George Boole’s opaque and unwieldy logical calculus into what we now recognize as Boolean algebra. Readers interested in algebraic logic and abstract algebra can look forward to a tour of the early history of those fields with a guide who was exceptionally thorough, unfailingly honest, and deeply reflective.
Book Synopsis Mathematical Thought From Ancient to Modern Times by : Morris Kline
Download or read book Mathematical Thought From Ancient to Modern Times written by Morris Kline and published by OUP USA. This book was released on 1990-03 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traces the development of mathematics from its beginnings in Babylonia and ancient Egypt to the work of Riemann and Godel in modern times.
Book Synopsis Space, Number, and Geometry from Helmholtz to Cassirer by : Francesca Biagioli
Download or read book Space, Number, and Geometry from Helmholtz to Cassirer written by Francesca Biagioli and published by Springer. This book was released on 2016-08-22 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such later scientific developments as non-Euclidean geometries and Einstein’s general theory of relativity called into question the certainty of Euclidean geometry and posed the problem of reconsidering space as an open question for empirical research. The transformation of the concept of space from a source of knowledge to an object of research can be traced back to a tradition, which includes such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which finds one of its clearest expressions in Hermann von Helmholtz’s epistemological works. Although Helmholtz formulated compelling objections to Kant, the author reconsiders different strategies for a philosophical account of the same transformation from a neo-Kantian perspective, and especially Hermann Cohen’s account of the aprioricity of mathematics in terms of applicability and Ernst Cassirer’s reformulation of the a priori of space in terms of a system of hypotheses. This book is ideal for students, scholars and researchers who wish to broaden their knowledge of non-Euclidean geometry or neo-Kantianism.
Book Synopsis Emergence of the Theory of Lie Groups by : Thomas Hawkins
Download or read book Emergence of the Theory of Lie Groups written by Thomas Hawkins and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: The great Norwegian mathematician Sophus Lie developed the general theory of transformations in the 1870s, and the first part of the book properly focuses on his work. In the second part the central figure is Wilhelm Killing, who developed structure and classification of semisimple Lie algebras. The third part focuses on the developments of the representation of Lie algebras, in particular the work of Elie Cartan. The book concludes with the work of Hermann Weyl and his contemporaries on the structure and representation of Lie groups which serves to bring together much of the earlier work into a coherent theory while at the same time opening up significant avenues for further work.
Book Synopsis Philosophy Today by : Edward Leroy Schaub
Download or read book Philosophy Today written by Edward Leroy Schaub and published by . This book was released on 1928 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Philosophy Today written by and published by . This book was released on 1928 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Monist written by Paul Carus and published by . This book was released on 1928 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vols. 2 and 5 include appendices.
