Download or read book The Basic Laws of Arithmetic written by Gottlob Frege and published by Univ of California Press. This book was released on 1967 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Frege written by Michael Dummett and published by Harvard University Press. This book was released on 1991 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: No one has figured more prominently in the study of the German philosopher Gottlob Frege than Michael Dummett. His magisterial Frege: Philosophy of Language is a sustained, systematic analysis of Frege's thought, omitting only the issues in philosophy of mathematics. 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 of Basic Laws of Arithmetic, establishing what parts of the philosopher's views can be salvaged and employed in new theorizing, and what must be abandoned, either as incorrectly argued or as untenable in the light of technical developments. Gottlob Frege (1848-1925) was a logician, mathematician, and philosopher whose work had enormous impact on Bertrand Russell and later on the young Ludwig Wittgenstein, making Frege one of the central influences on twentieth-century Anglo-American philosophy; he is considered the founder of analytic philosophy. His philosophy of mathematics contains deep insights and remains a useful and necessary point of departure for anyone seriously studying or working in the field.
Download or read book Reading Frege s Grundgesetze written by Richard G. Heck and published by Oxford University Press, USA. This book was released on 2012-11-29 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readership: Scholars and advanced students of philosophy of logic, philosophy of mathematics, and history of analytic philosophy
Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Foundations of Arithmetic written by Gottlob Frege and published by Northwestern University Press. This book was released on 1980-12 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Foundations of Arithmetic is undoubtedly the best introduction to Frege's thought; it is here that Frege expounds the central notions of his philosophy, subjecting the views of his predecessors and contemporaries to devastating analysis. The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly influenced developments in the philosophy of mathematics and in general ontology.
Download or read book Gottlob Frege Basic Laws of Arithmetic written by Gottlob Frege and published by . This book was released on 2013-10 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Functions and Generality of Logic written by Hourya Benis-Sinaceur and published by Springer. This book was released on 2015-06-24 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines three connected aspects of Frege’s logicism: the differences between Dedekind’s and Frege’s interpretation of the term ‘logic’ and related terms and reflects on Frege’s notion of function, comparing its understanding and the role it played in Frege’s and Lagrange’s foundational programs. It concludes with an examination of the notion of arbitrary function, taking into account Frege’s, Ramsey’s and Russell’s view on the subject. Composed of three chapters, this book sheds light on important aspects of Dedekind’s and Frege’s logicisms. The first chapter explains how, although he shares Frege’s aim at substituting logical standards of rigor to intuitive imports from spatio-temporal experience into the deductive presentation of arithmetic, Dedekind had a different goal and used or invented different tools. The chapter highlights basic dissimilarities between Dedekind’s and Frege’s actual ways of doing and thinking. The second chapter reflects on Frege’s notion of a function, in comparison with the notions endorsed by Lagrange and the followers of the program of arithmetization of analysis. It remarks that the foundational programs pursued by Lagrange and Frege are crucially different and based on a different idea of what the foundations of mathematics should be like. However, despite this contrast, the notion of function plays similar roles in the two programs, and this chapter emphasizes the similarities. The third chapter traces the development of thinking about Frege’s program in the foundations of mathematics, and includes comparisons of Frege’s, Russell’s and Ramsey’s views. The chapter discusses earlier papers written by Hintikka, Sandu, Demopoulos and Trueman. Although the chapter’s main focus is on the notion of arbitrary correlation, it starts out by discussing some aspects of the connection between this notion and Dedekind Theorem.
Download or read book Fixing Frege written by John P. Burgess and published by Princeton University Press. This book was released on 2005-07-25 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gottlob Frege's attempt to found mathematics on a grand logical system came to grief when Bertrand Russell discovered a contradiction in it. This book surveys consistent restrictions in both the old and new versions of Frege's system, determining just how much of mathematics can be reconstructed in each.
Download or read book Necessary Beings written by Bob Hale and published by Oxford University Press, USA. This book was released on 2013-09-19 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bob Hale presents a broadly Fregean approach to metaphysics, according to which ontology and modality are mutually dependent upon one another. He argues that facts about what kinds of things exist depend on facts about what is possible. Modal facts are fundamental, and have their basis in the essences of things—not in meanings or concepts.
Download or read book Frege Explained written by Joan Weiner and published by Open Court. This book was released on 2011-04-15 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the number one? How can we be sure that 2+2=4? These apparently ssimple questions have perplexed philosophers for thousands of years, but discussion of them was transformed by the German philosopher Gottlob Frege (1848-1925). Frege (pronounced Fray-guh)believed that arithmetic and all mathematics are derived from logic, and to prove this he developed a completely new approach to logic and numbers. Joan Weiner presents a very clear outline of Frege's life and ideas, showing how his thinking evolved through successive books and articles.
Download or read book A Companion to Analytic Philosophy written by A. P. Martinich and published by John Wiley & Sons. This book was released on 2008-04-15 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Companion to Analytic Philosophy is a comprehensive guide to many significant analytic philosophers and concepts of the last hundred years. Provides a comprehensive guide to many of the most significant analytic philosophers of the last one hundred years. Offers clear and extensive analysis of profound concepts such as truth, goodness, knowledge, and beauty. Written by some of the most distinguished philosophers alive, some of whom have entries in the book devoted to them.
Download or read book Conceptual Notation and Related Articles written by Gottlob Frege and published by Oxford Scholarly Classics. This book was released on 1972 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains English translations of Frege's early writings in logic and philosophy and of relevant reviews by other leading logicians. Professor Bynum has contributed a biographical essay, introduction, and extensive bibliography. ong Copy
Download or read book Essays on Frege s Basic Laws of Arithmetic written by Philip A. Ebert and published by . This book was released on 2019 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first collective study of a foundational text in modern philosophy and logic, Gottlob Frege's Basic Laws of Arithmetic. Twenty-two Frege scholars discuss a wide range of philosophical and logical topics arising from Basic Laws of Arithmetic, and demonstrate the technical and philosophical richness of this great work.
Download or read book Frege on Thinking and Its Epistemic Significance written by Pieranna Garavaso and published by Lexington Books. This book was released on 2014-11-12 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pieranna Garavaso and Nicla Vassallo investigate Gottlob Frege's notion of thinking (das Denken) to provide a new analysis of a largely unexplored area of the philosopher's work. Confronting Frege's deeply seated and widely emphasized anti-psychologism, Frege on Thinking and Its Epistemic Significance claims that the objective human science that Frege proposed can only be possible through a nuanced notion of thinking as neither merely psychological nor merely logical. Focusing on what Frege says about thinking in many passages from his works, Garavaso and Vassallo argue that Frege was engaged with issues that are still alive in contemporary debates, such as the definition of knowledge and the necessary role of language in conceptual thinking and in the expression of thoughts. Frege on Thinking and Its Epistemic Significance is essential not only for those interested in a new and original reading of Frege’s philosophy, but also for anyone engaged in epistemology, logic, psychology, philosophy of language, and the history of analytic philosophy.
Download or read book Frege in Perspective written by Joan Weiner and published by Cornell University Press. This book was released on 2018-05-31 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Not only can the influence of Gottlob Frege (1848-1925) be found in contemporary work in logic, the philosophy of mathematics, and the philosophy of language, but his projects—and the very terminology he employed in pursuing those projects—are still current in contemporary philosophy. This is undoubtedly why it seems so reasonable to assume that we can read Frege' s writings as if he were one of us, speaking to our philosophical concerns in our language. In Joan Weiner's view, however, Frege's words can be accurately interpreted only if we set that assumption aside. Weiner here offers a challenging new approach to the philosophy of this central figure in analytic philosophy. Weiner finds in Frege's corpus, from Begriffsschrift (1879) on, a unified project of remarkable ambition to which each of the writings in that corpus makes a distinct contribution—a project whose motivation she brings to life through a careful reading of his Foundations of Arithmetic. The Frege that Weiner brings into clear view is very different from the familiar figure. Far from having originated one of the standard positions on the nature of reference, Frege turns out not to have had positive doctrines on anything like what contemporary philosophers mean by "reference." Far from having served as a standard-bearer for those who take the realists' side of contemporary disputes with anti-realists, Frege turns out to have had no stake in either side of the controversy. Through Weiner's lens, Frege emerges as a thinker who has principled reasons for challenging the very assumptions and motivations that animate philosophers to dispute these doctrines. This lucidly written and accessible book will generate controversy among all readers with an interest in epistemology, philosophy of language, history of philosophy, and the philosophy of mathematics.
Download or read book The Frege Reader written by Michael Beaney and published by Wiley-Blackwell. This book was released on 1997-07-07 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Making up Numbers A History of Invention in Mathematics written by Ekkehard Kopp and published by Open Book Publishers. This book was released on 2020-10-23 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.
