David Hilbert S Lectures On The Foundations Of Arithmetic And Logic 1917 1933

Author : William Ewald,Wilfried Sieg
Publisher : Springer-Verlag
Page : 1062 pages
File Size : 55,9 Mb
Release : 2013-05-14
Category : Mathematics
ISBN : 9783540694441

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David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933 by William Ewald,Wilfried Sieg Pdf

The core of Volume 3 consists of lecture notes for seven sets of lectures Hilbert gave (often in collaboration with Bernays) on the foundations of mathematics between 1917 and 1926. These texts make possible for the first time a detailed reconstruction of the rapid development of Hilbert’s foundational thought during this period, and show the increasing dominance of the metamathematical perspective in his logical work: the emergence of modern mathematical logic; the explicit raising of questions of completeness, consistency and decidability for logical systems; the investigation of the relative strengths of various logical calculi; the birth and evolution of proof theory, and the parallel emergence of Hilbert’s finitist standpoint. The lecture notes are accompanied by numerous supplementary documents, both published and unpublished, including a complete version of Bernays’s Habilitationschrift of 1918, the text of the first edition of Hilbert and Ackermann’s Grundzüge der theoretischen Logik (1928), and several shorter lectures by Hilbert from the later 1920s. These documents, which provide the background to Hilbert and Bernays’s monumental Grundlagen der Mathematik (1934, 1938), are essential for understanding the development of modern mathematical logic, and for reconstructing the interactions between Hilbert, Bernays, Brouwer, and Weyl in the philosophy of mathematics.

Author : William Ewald,Wilfried Sieg
Publisher : Springer
Page : 1062 pages
File Size : 48,9 Mb
Release : 2013-06-03
Category : Mathematics
ISBN : 3540205780

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David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933 by William Ewald,Wilfried Sieg Pdf

The core of Volume 3 consists of lecture notes for seven sets of lectures Hilbert gave (often in collaboration with Bernays) on the foundations of mathematics between 1917 and 1926. These texts make possible for the first time a detailed reconstruction of the rapid development of Hilbert’s foundational thought during this period, and show the increasing dominance of the metamathematical perspective in his logical work: the emergence of modern mathematical logic; the explicit raising of questions of completeness, consistency and decidability for logical systems; the investigation of the relative strengths of various logical calculi; the birth and evolution of proof theory, and the parallel emergence of Hilbert’s finitist standpoint. The lecture notes are accompanied by numerous supplementary documents, both published and unpublished, including a complete version of Bernays’s Habilitationschrift of 1918, the text of the first edition of Hilbert and Ackermann’s Grundzüge der theoretischen Logik (1928), and several shorter lectures by Hilbert from the later 1920s. These documents, which provide the background to Hilbert and Bernays’s monumental Grundlagen der Mathematik (1934, 1938), are essential for understanding the development of modern mathematical logic, and for reconstructing the interactions between Hilbert, Bernays, Brouwer, and Weyl in the philosophy of mathematics.

Author : William Ewald,Michael Hallett,Ulrich Majer,Wilfried Sieg
Publisher : Springer
Page : 0 pages
File Size : 42,9 Mb
Release : 2023-01-26
Category : Mathematics
ISBN : 3540206051

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David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1894-1917 by William Ewald,Michael Hallett,Ulrich Majer,Wilfried Sieg Pdf

Volume 2 focuses on notes for lectures on the foundations of the mathematical sciences held by Hilbert in the period 1894-1917. They document Hilbert’s first engagement with ‘impossibility’ proofs; his early attempts to formulate and address the problem of consistency, first dealt with in his work on geometry in the 1890s; his engagement with foundational problems raised by the work of Cantor and Dedekind; his early investigations into the relationship between arithmetic, set theory, and logic; his advocation of the use of the axiomatic method generally; his first engagement with the logical and semantical paradoxes; and the first formal attempts to develop a logical calculus. The Volume also contains Hilbert’s address from 1895 which formed the preliminary version of his famous Zahlbericht (1897).

Author : Michael Hallett,Ulrich Majer
Publisher : Springer Science & Business Media
Page : 708 pages
File Size : 53,8 Mb
Release : 2004-05-17
Category : Mathematics
ISBN : 3540643737

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David Hilbert’s Lectures on the Foundations of Geometry 1891–1902 by Michael Hallett,Ulrich Majer Pdf

This volume contains six sets of notes for lectures on the foundations of geometry held by Hilbert in the period 1891-1902. It also reprints the first edition of Hilbert’s celebrated Grundlagen der Geometrie of 1899, together with the important additions which appeared first in the French translation of 1900. The lectures document the emergence of a new approach to foundational study and contain many reflections and investigations which never found their way into print.

Author : Fernando Ferreira,Reinhard Kahle,Giovanni Sommaruga
Publisher : Springer Nature
Page : 209 pages
File Size : 50,6 Mb
Release : 2022-10-13
Category : Mathematics
ISBN : 9783030776572

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Axiomatic Thinking I by Fernando Ferreira,Reinhard Kahle,Giovanni Sommaruga Pdf

In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere. The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Göttingen as his main collaborator in foundational studies in the years to come. The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations. Chapter 8 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Author : Joel David Hamkins
Publisher : MIT Press
Page : 350 pages
File Size : 54,9 Mb
Release : 2021-02-02
Category : Mathematics
ISBN : 9780262362658

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Lectures on the Philosophy of Mathematics by Joel David Hamkins Pdf

An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Author : Gianluigi Oliveri,Claudio Ternullo,Stefano Boscolo
Publisher : Springer Nature
Page : 365 pages
File Size : 49,7 Mb
Release : 2022-03-08
Category : Science
ISBN : 9783030847067

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Objects, Structures, and Logics by Gianluigi Oliveri,Claudio Ternullo,Stefano Boscolo Pdf

This edited collection casts light on central issues within contemporary philosophy of mathematics such as the realism/anti-realism dispute; the relationship between logic and metaphysics; and the question of whether mathematics is a science of objects or structures. The discussions offered in the papers involve an in-depth investigation of, among other things, the notions of mathematical truth, proof, and grounding; and, often, a special emphasis is placed on considerations relating to mathematical practice. A distinguishing feature of the book is the multicultural nature of the community that has produced it. Philosophers, logicians, and mathematicians have all contributed high-quality articles which will prove valuable to researchers and students alike.

Author : Erich H. Reck,Georg Schiemer
Publisher : Oxford University Press
Page : 469 pages
File Size : 51,8 Mb
Release : 2020
Category : Mathematics
ISBN : 9780190641221

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The Prehistory of Mathematical Structuralism by Erich H. Reck,Georg Schiemer Pdf

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.

Author : Paolo Mancosu
Publisher : OUP Oxford
Page : 460 pages
File Size : 55,6 Mb
Release : 2008-06-19
Category : Philosophy
ISBN : 9780191559099

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The Philosophy of Mathematical Practice by Paolo Mancosu Pdf

Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, and developments at the intersection of history and philosophy of mathematics. But anyone familiar with contemporary philosophy of mathematics will be aware of the need for new approaches that pay closer attention to mathematical practice. This book is the first attempt to give a coherent and unified presentation of this new wave of work in philosophy of mathematics. The new approach is innovative at least in two ways. First, it holds that there are important novel characteristics of contemporary mathematics that are just as worthy of philosophical attention as the distinction between constructive and non-constructive mathematics at the time of the foundational debates. Secondly, it holds that many topics which escape purely formal logical treatment - such as visualization, explanation, and understanding - can nonetheless be subjected to philosophical analysis. The Philosophy of Mathematical Practice comprises an introduction by the editor and eight chapters written by some of the leading scholars in the field. Each chapter consists of short introduction to the general topic of the chapter followed by a longer research article in the area. The eight topics selected represent a broad spectrum of contemporary philosophical reflection on different aspects of mathematical practice: diagrammatic reasoning and representation systems; visualization; mathematical explanation; purity of methods; mathematical concepts; the philosophical relevance of category theory; philosophical aspects of computer science in mathematics; the philosophical impact of recent developments in mathematical physics.

Author : Jan von Plato
Publisher : Princeton University Press
Page : 400 pages
File Size : 51,7 Mb
Release : 2017-08-02
Category : Science
ISBN : 9781400885039

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The Great Formal Machinery Works by Jan von Plato Pdf

The information age owes its existence to a little-known but crucial development, the theoretical study of logic and the foundations of mathematics. The Great Formal Machinery Works draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution. Jan von Plato examines the contributions of figures such as Aristotle; the nineteenth-century German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schröder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. Von Plato shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Gödel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. Von Plato describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later. Shedding new light on this crucial chapter in the history of science, The Great Formal Machinery Works is essential reading for students and researchers in logic, mathematics, and computer science.

Author : Gabriele M. Mras,Paul Weingartner,Bernhard Ritter
Publisher : Walter de Gruyter GmbH & Co KG
Page : 565 pages
File Size : 42,7 Mb
Release : 2019-11-18
Category : Philosophy
ISBN : 9783110654547

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Philosophy of Logic and Mathematics by Gabriele M. Mras,Paul Weingartner,Bernhard Ritter Pdf

This volume presents different conceptions of logic and mathematics and discuss their philosophical foundations and consequences. This concerns first of all topics of Wittgenstein's ideas on logic and mathematics; questions about the structural complexity of propositions; the more recent debate about Neo-Logicism and Neo-Fregeanism; the comparison and translatability of different logics; the foundations of mathematics: intuitionism, mathematical realism, and formalism. The contributing authors are Matthias Baaz, Francesco Berto, Jean-Yves Beziau, Elena Dragalina-Chernya, Günther Eder, Susan Edwards-McKie, Oliver Feldmann, Juliet Floyd, Norbert Gratzl, Richard Heinrich, Janusz Kaczmarek, Wolfgang Kienzler, Timm Lampert, Itala Maria Loffredo D'Ottaviano, Paolo Mancosu, Matthieu Marion, Felix Mühlhölzer, Charles Parsons, Edi Pavlovic, Christoph Pfisterer, Michael Potter, Richard Raatzsch, Esther Ramharter, Stefan Riegelnik, Gabriel Sandu, Georg Schiemer, Gerhard Schurz, Dana Scott, Stewart Shapiro, Karl Sigmund, William W. Tait, Mark van Atten, Maria van der Schaar, Vladimir Vasyukov, Jan von Plato, Jan Woleński and Richard Zach.

Author : Philip A. Ebert,Marcus Rossberg
Publisher : Unknown
Page : 686 pages
File Size : 54,9 Mb
Release : 2019-09-05
Category : Electronic
ISBN : 9780198712084

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Essays on Frege's Basic Laws of Arithmetic by Philip A. Ebert,Marcus Rossberg Pdf

This volume is the first collective study of a foundational text in modern philosophy and logic, Gottlob Frege's Basic Laws of Arithmetic which appeared in two volumes in 1893 and 1903. Twenty-two Frege scholars discuss a wide range of philosophical and logical topics arising from Basic Lawsof Arithmetic, and demonstrate the technical and philosophical richness of the work. Their original contributions make vivid the importance of this magnum opus not just for Frege scholars but for the study of the history of logic, mathematics, and philosophy.

Author : Francesca Boccuni,Andrea Sereni
Publisher : Taylor & Francis
Page : 419 pages
File Size : 53,7 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 : Åsa Hirvonen,Juha Kontinen,Roman Kossak,Andrés Villaveces
Publisher : Walter de Gruyter GmbH & Co KG
Page : 438 pages
File Size : 49,6 Mb
Release : 2015-03-10
Category : Philosophy
ISBN : 9781614516873

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Logic Without Borders by Åsa Hirvonen,Juha Kontinen,Roman Kossak,Andrés Villaveces Pdf

In recent years, mathematical logic has developed in many directions, the initial unity of its subject matter giving way to a myriad of seemingly unrelated areas. The articles collected here, which range from historical scholarship to recent research in geometric model theory, squarely address this development. These articles also connect to the diverse work of Väänänen, whose ecumenical approach to logic reflects the unity of the discipline.

Author : Antonio Piccolomini d'Aragona
Publisher : Springer Nature
Page : 421 pages
File Size : 48,5 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9783031514067

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Perspectives on Deduction: Contemporary Studies in the Philosophy, History and Formal Theories of Deduction by Antonio Piccolomini d'Aragona Pdf