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Author: Joan Weiner
Publisher: Open Court
ISBN: 0812697529
Category : Philosophy
Languages : en
Pages : 198
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Book Description
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.
Author: Joan Weiner
Publisher: Open Court
ISBN: 0812697529
Category : Philosophy
Languages : en
Pages : 198
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Book Description
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.
Author: Wolfgang Carl
Publisher: Cambridge University Press
ISBN: 9780521398169
Category : Philosophy
Languages : en
Pages : 236
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Book Description
This book provides a completely new and systematic account of Frege's philosophy by focusing on its cornerstone: the theory of sense and reference.
Author: Joan Weiner
Publisher: Oxford University Press, USA
ISBN:
Category : Mathematics
Languages : en
Pages : 168
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Book Description
What is the number one? How do we know that 2+2=4? These apparently simple questions are in fact notoriously difficult to answer, and in one form or other have occupied philosophers from ancient times to the present. Gottlob Frege's conviction that the truths of arithmetic, and mathematics more generally, are derived from self-evident logical truths formed the basis of a systematic project which revolutionized logic, and founded modern analytic philosophy. In this accessible and stimulating introduction, Joan Weiner traces the development of Frege's thought from his invention of a powerful new logical language in Begriffsschrift, through his explication of his project in the Foundations of Arithmetic and famous papers such as 'On Sense and Reference', to the brilliant, but ultimately doomed, presentation of the system in Basic Laws of Arithmetic. At each stage, she discusses Frege's motivations in a way which enables the modern reader to appreciate the originality, clarity, and profundity of his thought. Past Masters is a series of concise, lucid, authoritative introducitons to the thought of leading intellectual figures of the past whose ideas still influence the way we think today.
Author: Bob Hale
Publisher: Oxford University Press, USA
ISBN: 0199669570
Category : Language Arts & Disciplines
Languages : en
Pages : 309
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Book Description
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.
Author: Patricia Blanchette
Publisher: OUP USA
ISBN: 0199891613
Category : Mathematics
Languages : en
Pages : 207
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Book Description
In Frege's Conception of Logic Patricia A. Blanchette explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic. She argues that the fruitfulness of Frege's conception of logic, and the illuminating differences between that conception and those more modern views that have largely supplanted it, are best understood against the backdrop of a clear account of the role of conceptual analysis in logical investigation. The first part of the book locates the role of conceptual analysis in Frege's logicist project. Blanchette argues that despite a number of difficulties, Frege's use of analysis in the service of logicism is a powerful and coherent tool. As a result of coming to grips with his use of that tool, we can see that there is, despite appearances, no conflict between Frege's intention to demonstrate the grounds of ordinary arithmetic and the fact that the numerals of his derived sentences fail to co-refer with ordinary numerals. In the second part of the book, Blanchette explores the resulting conception of logic itself, and some of the straightforward ways in which Frege's conception differs from its now-familiar descendants. In particular, Blanchette argues that consistency, as Frege understands it, differs significantly from the kind of consistency demonstrable via the construction of models. To appreciate this difference is to appreciate the extent to which Frege was right in his debate with Hilbert over consistency- and independence-proofs in geometry. For similar reasons, modern results such as the completeness of formal systems and the categoricity of theories do not have for Frege the same importance they are commonly taken to have by his post-Tarskian descendants. These differences, together with the coherence of Frege's position, provide reason for caution with respect to the appeal to formal systems and their properties in the treatment of fundamental logical properties and relations.
Author: Gottlob Frege
Publisher: John Wiley & Sons
ISBN: 0631126945
Category : Mathematics
Languages : en
Pages : 146
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Book Description
A philosophical discussion of the concept of number In the book, The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, Gottlob Frege explains the central notions of his philosophy and analyzes the perspectives of predecessors and contemporaries. The book is the first philosophically relevant discussion of the concept of number in Western civilization. The work went on to significantly influence philosophy and mathematics. Frege was a German mathematician and philosopher who published the text in 1884, which seeks to define the concept of a number. It was later translated into English. This is the revised second edition.
Author: Gottlob Frege
Publisher: Univ of California Press
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 208
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Book Description
Author: Richard G. Heck Jr.
Publisher: OUP Oxford
ISBN: 019165535X
Category : Philosophy
Languages : en
Pages : 315
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Book Description
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: David Detmer
Publisher: Open Court
ISBN: 0812697979
Category : Philosophy
Languages : en
Pages : 226
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Book Description
Phenomenology is one of the most important and influential philosophical movements of the last one hundred years. It began in 1900, with the publication of a massive two-volume work, Logical Investigations, by a Czech-German mathematician, Edmund Husserl. It proceeded immediately to exert a strong influence on both philosophy and the social sciences. For example, phenomenology provided the central inspiration for the existentialist movement, as represented by such figures as Martin Heidegger in Germany and Jean-Paul Sartre in France. Subsequent intellectual currents in Europe, when they have not claimed phenomenology as part of their ancestry, have defined themselves in opposition to phenomenology. Thus, to give just one example, the first two works of Jacques Derrida, the father of deconstruction, were devoted to criticisms of Husserl’s phenomenological works. In the English-speaking world, where “analytic philosophy” dominates, phenomenology has recently emerged as a hot topic after decades of neglect. This has resulted from a dramatic upswing in interest in consciousness, the condition that makes all experience possible. Since the special significance of phenomenology is that it investigates consciousness, analytic philosophers have begun to turn to it as an underutilized resource. For the same reason, Husserl’s work is now widely studied by cognitive scientists. The current revival of interest in phenomenology also stems from the recognition that not every kind of question can be approached by means of experimental techniques. Not all questions are scientific in that sense. Thus, if there is to be knowledge in logic, mathematics, ethics, political philosophy, aesthetics, epistemology (theory of knowledge), psychology (from the inside), and the study of consciousness, among others, another method is clearly needed. Phenomenology is an attempt to rectify this. Its aim is to focus on the world as given in experience, and to describe it with unprecedented care, rigor, subtlety, and completeness. This applies not only to the objects of sense experience, but to all phenomena: moral, aesthetic, political, mathematical, and so forth. One can avoid the obscure problem of the real, independent existence of the objects of experience in these domains by focusing instead on the objects, as experienced, themselves, along with the acts of consciousness which disclose them. Phenomenology thus opens up an entirely new field of investigation, never previously explored. Rather than assuming, or trying to discern, what exists outside the realm of the mental, and what causal relations pertain to these extra-mental entities, we can study objects strictly as they are given, that is, as they appear to us in experience. This book explains what phenomenology is and why it is important. It focuses primarily on the works and ideas of Husserl, but also discusses important later thinkers, giving special emphasis to those whose contributions are most relevant to contemporary concerns. Finally, while Husserl’s greatest contributions were to the philosophical foundations of logic, mathematics, knowledge, and science, this book also addresses extensively the relatively neglected contribution of phenomenology to value theory, especially ethics, political philosophy, and aesthetics.
Author: Gregory Landini
Publisher: Springer
ISBN: 0230360157
Category : Philosophy
Languages : en
Pages : 187
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Book Description
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.
