[PDF] Reading Freges Grundgesetze eBook

Author : Richard G. Heck
Publisher : Oxford University Press, USA
Page : 315 pages
File Size : 26,84 MB
Release : 2012-11-29
Category : Mathematics
ISBN : 0199233705

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Readership: Scholars and advanced students of philosophy of logic, philosophy of mathematics, and history of analytic philosophy

Author : Richard G. Heck Jr.
Publisher : OUP Oxford
Page : 315 pages
File Size : 34,58 MB
Release : 2012-11-29
Category : Philosophy
ISBN : 019165535X

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Gottlob Frege's Grundgesetze der Arithmetik, or Basic Laws of Arithmetic, was intended to be his magnum opus, the book in which he would finally establish his logicist philosophy of arithmetic. But because of the disaster of Russell's Paradox, which undermined Frege's proofs, the more mathematical parts of the book have rarely been read. Richard G. Heck, Jr., aims to change that, and establish it as a neglected masterpiece that must be placed at the center of Frege's philosophy. Part I of Reading Frege's Grundgesetze develops an interpretation of the philosophy of logic that informs Grundgesetze, paying especially close attention to the difficult sections of Frege's book in which he discusses his notorious 'Basic Law V' and attempts to secure its status as a law of logic. Part II examines the mathematical basis of Frege's logicism, explaining and exploring Frege's formal arguments. Heck argues that Frege himself knew that his proofs could be reconstructed so as to avoid Russell's Paradox, and presents Frege's arguments in a way that makes them available to a wide audience. He shows, by example, that careful attention to the structure of Frege's arguments, to what he proved, to how he proved it, and even to what he tried to prove but could not, has much to teach us about Frege's philosophy.

Author : Gottlob Frege
Publisher :
Page : 683 pages
File Size : 13,38 MB
Release : 2013-10
Category : Mathematics
ISBN : 0199281742

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This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik (1893 and 1903), with introduction and annotation. As the culmination of his ground-breaking work in the philosophy of logic and mathematics, Frege here tried to show how the fundamental laws of arithmetic could be derived from purely logical principles.

Author : Ryan Beaton
Publisher :
Page : 220 pages
File Size : 48,26 MB
Release : 2004
Category :
ISBN :

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"We first give a modern presentation of the formal language of Frege's Grundgesetze. There follows a comparison of the motivations for Frege's "Cumulative Type Theory" and for Russell's Type Theory and of the basic arithmetical definitions in each. Quine's New Foundations and, in particular, extensions of Jensen's modification, NFU, are introduced and consistency results are discussed. Finally, an interpretation is given in an NFU framework of a modified form of the Grundgesetze theory. It is shown that an "Axiom of Counting" necessary for arithmetic in NFU is needed in an analogous way for arithmetic in our interpretation; it is further demonstrated that from the statement of this axiom in NFU, the appropriate analogue is provable for our interpretation. The development of arithmetic in an NFU framework is seen essentially to be that intended by Frege in the Grundgesetze." --

Author : L. Haaparanta
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 38,18 MB
Release : 2012-12-06
Category : Philosophy
ISBN : 9400945523

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cake, even though it is typically given the pride of place in expositions in Frege's semantics. As a part of this attempted reversal of emphasis, Jaakko Hintikka has also called attention to the role Frege played in convincing almost everyone that verbs for being had to be treated as multiply ambiguous between the "is" of identity, the "is" of predication, the "is" of existence, and the "is" of class-inclusion - a view that had been embraced by few major figures (if any) before Frege, with the exception of John Stuart Mill and Augustus De Morgan. Hintikka has gone on to challenge this ambiguity thesis. At the same time, Frege's role in the genesis of another major twentieth-century philosophical movement, the phenomenological one, has become an important issue. Even the translation of Frege's key term "Bedeutung" as "reference" has become controversial. The interpretation of Frege is thus thrown largely back in the melting pot. In editing this volume, we have not tried to publish the last word on Frege. Even though we may harbor such ambitions ourselves, they are not what has led to the present editorial enterprise. What we have tried to do is to bring together some of the best ongoing work on Frege. Even though the ultimate judgment on our success lies with out readers, we want to register our satisfaction with all the contributions.

Author : Philip A. Ebert
Publisher :
Page : 686 pages
File Size : 19,41 MB
Release : 2019-09-05
Category :
ISBN : 0198712081

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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 : Gregory Landini
Publisher : Springer
Page : 187 pages
File Size : 20,5 MB
Release : 2012-02-10
Category : Philosophy
ISBN : 0230360157

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A new approach to reading Frege's notations that adheres to the modern view that terms and well-formed formulas are any disjoint syntactic categories. On this new approach, we can at last read Frege's notations in their original form revealing striking new solutions to many of the outstanding problems of interpreting his philosophy.

Author : Michael Beaney
Publisher : Wiley-Blackwell
Page : 432 pages
File Size : 31,66 MB
Release : 1997-07-07
Category : Philosophy
ISBN : 9780631194453

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This is the first single-volume edition and translation of Frege's philosophical writings to include all of his seminal papers and substantial selections from all three of his major works.

Author : Gisela Bengtsson
Publisher : Springer
Page : 186 pages
File Size : 14,81 MB
Release : 2018-01-12
Category : Mathematics
ISBN : 3319711865

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This volume collects nine essays that investigate the work of Gottlob Frege. The contributors address Frege’s work in relation to literature and fiction (Dichtung), the humanities (Geisteswissenschaften), and science (Wissenschaft). Overall, the essays consider internal connections between different aspects of Frege’s work while acknowledging the importance of its philosophical context. There are also further common strands between the papers, such as the relation between Frege’s and Wittgenstein’s approaches to philosophical investigations, the relation between Frege and Kant, and the place of Frege’s work in the philosophical landscape more generally. The volume is therefore of direct relevance to several current debates in philosophy in general, in addition to Frege and Wittgenstein research in particular. Even though Frege’s great significance for contemporary philosophy is not disputed, the question of how we are to understand the character and aims of his project is debated. The debate has a starting point in Frege’s specific conception of logic. The volume elucidates this conception as well as the relation between natural language and the Begriffsschrift. It will help philosophers, researchers, and students better understand the nuances of this great thinker. By extension, it will also help readers seeking to understand Wittgenstein’s approach to philosophical difficulties and his struggle to find an apt form of presentation for his philosophical investigations.