Die von Jens Timmermann besorgte Neuausgabe innerhalb der Philosophischen Bibliothek bietet den vollständigen Wortlaut der beiden Originalausgaben von 1781 und 1787. Der Kantische Text wurde unter Wahrung der Interpunktion und sprachlicher Eigenheiten sehr behutsam an die heutigen orthographischen Regeln angeglichen. Die semantisch bedeutenden Korrekturvorschläge späterer Herausgeber (nicht nur der Akademie-Ausgabe) sind, wo sie nicht in den Text Aufnahme gefunden haben, am Fuß der Seite verzeichnet. Alle wesentlichen Unterschiede zwischen den Originalausgaben sind durch Kursivdruck hervorgehoben, größere Abweichungen ganzer Textstücke - etwa (...) in der Einleitung und im Kapitel über Phaenomena und Noumena - wurden synoptisch gegenübergestellt, so daß Art und Umfang der Umarbeitung unmittelbar abgelesen werden können. Die durchgängig neu bearbeitete Studienausgabe folgt in den Grundprinzipien der seit 1926 in Forschung und Lehre maßgeblichen Ausgabe von Raymund Schmidt, die hiermit abgelöst wird. Sie wird ergänzt durch eine umfangreiche Bibliographie von Heiner Klemme sowie durch einen ausführlichen Personen- und Sachindex. (shrink)

Introduction: Science and Common Sense Long before the beginnings of modern civilization, men ac- quired vast funds of information about their environment. ...

Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...) audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. (shrink)

Klarheit in betreff dieser Sätze anstrebt, d. i. Einsicht in das Wesen der bei dem Vollzug und den ideal-möglichen Anwendungen solcher Sätze ins Spiel tretenden Erkenntnisweisen und der mit diesen sich wesensmäßig konstituierenden Sinngebungen und objektiven Gel- 1 11 S tungen • Sprachliche Erörterungen gehören r nun sicherlich zu den 1 r philosophisch I unerläßlichen Vorbereitungen für den Aufbau der [A 4] reinen Logik, weil nur durch ihre Mithilfe die eigentlichen Objekte der logischen Forschung und, in weiterer Folge, die wesentlichen (...) Arten und Unterschiede dieser Objekte zu unmißverständlicher 10 Klarheit herauszuarbeiten sind. Es handelt sich dabei aber nicht um 12 grammatische Erörterungen im r empirischen, auf irgendeine historisch gegebene Sprache bezogenen Sinn, sondern um Erörterun gen jener allgemeinsten Art, die zur weiteren Sphäre einer objekti ven Theorie der Erkenntnis und, was damit innigst zusammen- 13 15 hängt, einer rreinen Phänomenologie der Denk- und Erkenntniserlebnisse gehören. rDicse, wie die sie umspannende reine Phänomenologie der Erlebnisse überhaupt, hat es ausschließlich mit den in der Intuition erlaßbaren und analysierba ren Erlebnissen in reiner Wesensallgemeinheit zu tun, nicht aber mit 20 empirisch apperzipierten Erlebnissen als realen Fakten, als Erlebnis sen erlebender Menschen oder Tiere in der erscheinenden und als Erfahrungsfaktum gesetzten Welt. Die in der Wesensintuition direkt erfaßten Wesen und rein in den Wesen gründenden Zusammenhän ge bringt sie deskriptiv in Wesensbegriffen und gesetzlichen 25 Wesensaussagen zu reinem Ausdruck. Jede solche Aussage ist eine 1 14 apriorische im vorzüglichsten Sinne des Wortes. (shrink)

Steven French articulates and defends the bold claim that there are no objects in the world. He draws on metaphysics and philosophy of science to argue for structural realism--the position that we live in a world of structures--and defends a form of eliminativism about objects that sets laws and symmetry principles at the heart of ontology.

Das Ziel: Konstitutionssystem der Begriffe Das Ziel der vorliegenden Untersuchungen ist die Aufstellung eines erkenntnismäßig-logischen Systems der ...

Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.

The no-miracles argument for realism and the pessimistic meta-induction for anti-realism pull in opposite directions. Structural Realism---the position that the mathematical structure of mature science reflects reality---relieves this tension.

This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...

Develops a structuralist understanding of mathematics, as an alternative to set- or type-theoretic foundations, that respects classical mathematical truth while ...

Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.

Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.

This book expounds a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defense of realism about the metaphysics of mathematics--the view that mathematics (...) is about things that really exist. (shrink)

In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume ...

In this collection of essays one of the preeminent philosophers of science writing offers a reinterpretation of the enduring significance of logical positivism, the revolutionary philosophical movement centered around the Vienna Circle in the 1920s and 30s. Michael Friedman argues that the logical positivists were radicals not by presenting a new version of empiricism but rather by offering a new conception of a priori knowledge and its role in empirical knowledge. This collection will be mandatory reading for any philosopher or (...) historian of science interested in the history of logical positivism in particular or the evolution of modern philosophy in general. (shrink)

First published in 1903, _Principles of Mathematics_ was Bertrand Russell’s first major work in print. It was this title which saw him begin his ascent towards eminence. In this groundbreaking and important work, Bertrand Russell argues that mathematics and logic are, in fact, identical and what is commonly called mathematics is simply later deductions from logical premises. Highly influential and engaging, this important work led to Russell’s dominance of analytical logic on western philosophy in the twentieth century.

Category Theory has developed rapidly. This book aims to present those ideas and methods which can now be effectively used by Mathe­ maticians working in a variety of other fields of Mathematical research. This occurs at several levels. On the first level, categories provide a convenient conceptual language, based on the notions of category, functor, natural transformation, contravariance, and functor category. These notions are presented, with appropriate examples, in Chapters I and II. Next comes the fundamental idea of an adjoint (...) pair of functors. This appears in many substantially equivalent forms: That of universal construction, that of direct and inverse limit, and that of pairs offunctors with a natural isomorphism between corresponding sets of arrows. All these forms, with their interrelations, are examined in Chapters III to V. The slogan is "Adjoint functors arise everywhere". Alternatively, the fundamental notion of category theory is that of a monoid -a set with a binary operation of multiplication which is associative and which has a unit; a category itself can be regarded as a sort of general­ ized monoid. Chapters VI and VII explore this notion and its generaliza­ tions. Its close connection to pairs of adjoint functors illuminates the ideas of universal algebra and culminates in Beck's theorem characterizing categories of algebras; on the other hand, categories with a monoidal structure lead inter alia to the study of more convenient categories of topological spaces. (shrink)

This massive two-volume reference presents a comprehensive selection of the most important works on the foundations of mathematics. While the volumes include important forerunners like Berkeley, MacLaurin, and D'Alembert, as well as such followers as Hilbert and Bourbaki, their emphasis is on the mathematical and philosophical developments of the nineteenth century. Besides reproducing reliable English translations of classics works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare, William Ewald also includes selections from Gauss, Cantor, Kronecker, and Zermelo, all translated here for (...) the first time. (shrink)

In this insightful study of the common origins of analytic and continental philosophy, Friedman looks at how social and political events intertwined and influenced philosophy during the early twentieth century, ultimately giving rise to the two very different schools of thought. He shows how these two approaches, now practiced largely in isolation from one another, were once opposing tendencies within a common discussion. Already polarized by their philosophical disagreements, these approaches were further split apart by the rise of Naziism and (...) the resulting emigration of all influential German-speaking philosophers except for Heidegger. Although the book gives a general overview of the philosophical issues of the period, the author pays special attention to the relationships among three key twentieth-century philosophers: Rudolf Carnap, Ernst Cassirer, and Martin Heidegger. (shrink)

Analytic philosophy has become the dominant philosophical tradition in the English-speaking world. This book illuminates that tradition through a historical examination of a crucial period in its formation: the rejection of Idealism by Bertrand Russell and G.E. Moore at the beginning of the twentieth century, and the subsequent development of Russell's thought in the period before the First World War.

First published in 1903, _Principles of Mathematics_ was Bertrand Russell’s first major work in print. It was this title which saw him begin his ascent towards eminence. In this groundbreaking and important work, Bertrand Russell argues that mathematics and logic are, in fact, identical and what is commonly called mathematics is simply later deductions from logical premises. Highly influential and engaging, this important work led to Russell’s dominance of analytical logic on western philosophy in the twentieth century.

In this book, T. L. Short corrects widespread misconceptions of Peirce's theory of signs and demonstrates its relevance to contemporary analytic philosophy of language, mind and science. Peirce's theory of mind, naturalistic but nonreductive, bears on debates of Fodor and Millikan, among others. His theory of inquiry avoids foundationalism and subjectivism, while his account of reference anticipated views of Kripke and Putnam. Peirce's realism falls between 'internal' and 'metaphysical' realism and is more satisfactory than either. His pragmatism is not verificationism; (...) rather, it identifies meaning with potential growth of knowledge. Short distinguishes Peirce's mature theory of signs from his better-known but paradoxical early theory. He develops the mature theory systematically on the basis of Peirce's phenomenological categories and concept of final causation. The latter is distinguished from recent and similar views, such as Brandon's, and is shown to be grounded in forms of explanation adopted in modern science. (shrink)

Rudolf Carnap is widely regarded as one of the most important philosophers of the twentieth century. Born in Germany and later a US citizen, he was a founder of the philosophical movement known as Logical Empiricism. He was strongly influenced by a number of different philosophical traditions, and also by the German Youth Movement, the First World War, and radical socialism. This book places his central ideas in a broad cultural, political and intellectual context, showing how he synthesised many different (...) currents of thought to achieve a philosophical perspective that remains strikingly relevant in the twenty-first century. Its rich account of a philosopher's response to his times will appeal to all who are interested in the development of philosophy in the twentieth century. (shrink)

Die Leitgedanken meiner Untersuchungen über die Grundlagen der Mathematik, die ich - anknüpfend an frühere Ansätze - seit 1917 in Besprechungen mit P. BERNAYS wieder aufgenommen habe, sind von mir an verschiedenen Stellen eingehend dargelegt worden. Diesen Untersuchungen, an denen auch W. ACKERMANN beteiligt ist, haben sich seither noch verschiedene Mathematiker angeschlossen. Der hier in seinem ersten Teil vorliegende, von BERNAYS abgefaßte und noch fortzusetzende Lehrgang bezweckt eine Darstellung der Theorie nach ihren heutigen Ergebnissen. Dieser Ergebnisstand weist zugleich die Richtung (...) für die weitere Forschung in der Beweistheorie auf das Endziel hin, unsere üblichen Methoden der Mathematik samt und sonders als widerspruchsfrei zu erkennen. Im Hinblick auf dieses Ziel möchte ich hervorheben, daß die zeit weilig aufgekommene Meinung, aus gewissen neueren Ergebnissen von GÖDEL folge die Undurchführbarkeit meiner Beweistheorie, als irrtüm lich erwiesen ist. Jenes Ergebnis zeigt in der Tat auch nur, daß man für die weitergehenden Widerspruchsfreiheitsbeweise den finiten Stand punkt in einer schärferen Weise ausnutzen muß, als dieses bei der Be trachtung der elementaren Formallsmen erforderlich ist. Göttingen, im März 1934 HILBERT Vorwort zur ersten Auflage Eine Darstellung der Beweistheorie, welche aus dem HILBERTschen Ansatz zur Behandlung der mathematisch-logischen Grundlagenpro bleme erwachsen ist, wurde schon seit längerem von HILBERT ange kündigt. (shrink)

Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition (...) and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite. (shrink)

On knowledge and practices: a manifesto -- The web of practices -- Agents and frameworks -- Complementarity in mathematics -- Ancient Greek mathematics: a role for diagrams -- Advanced math: the hypothetical conception -- Arithmetic certainty -- Mathematics developed: the case of the reals -- Objectivity in mathematical knowledge -- The problem of conceptual understanding.

Kurt Godel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computation theory, as well as for the strong individuality of his writings on the philosophy of mathematics. Less well-known is his discovery of unusual cosmological models for Einstein's (...) equations, permitting "time-travel" into the past. This second volume of a comprehensive edition of Godel's works collects together all his publications from 1938 to 1974. Together with Volume I (Publications 1929-1936), it makes available for the first time in a single source all of his previously published work. Continuing the format established in the earlier volume, the present text includes introductory notes that provide extensive explanatory and historical commentary on each of the papers, a facing English translation of the one German original, and a complete bibliography. Succeeding volumes are to contain unpublished manuscripts, lectures, correspondence, and extracts from the notebooks. Collected Works is designed to be accessible and useful to as wide an audience as possible without sacrificing scientific or historical accuracy. The only complete edition available in English, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science. These volumes will also interest scientists and all others who wish to be acquainted with one of the great minds of the twentieth century. (shrink)

1 INTRODUCTION Above the other titles he might justly have claimed, Charles S. Peirce prized the title 'logician'. He expressed in several places his ...

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)