Bemerkungen Über Die Grundlagen Der Mathematik PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Bemerkungen Über Die Grundlagen Der Mathematik PDF full book. Access full book title Bemerkungen Über Die Grundlagen Der Mathematik by Ludwig Wittgenstein. Download full books in PDF and EPUB format.
Author: Ludwig Wittgenstein
Publisher:
ISBN: 9780262730174
Category : Mathematics
Languages : de
Pages : 204
Get Book Here
Book Description
Author: Ludwig Wittgenstein
Publisher:
ISBN: 9780262730174
Category : Mathematics
Languages : de
Pages : 204
Get Book Here
Book Description
Author: Mike Hockney
Publisher: Magus Books
ISBN:
Category : Mathematics
Languages : en
Pages : 550
Get Book Here
Book Description
Perhaps nothing has been more misinterpreted than Gödel's incompleteness theorems. Stephen Hawking, adopting the popular misconception, said, "Thus mathematics is either inconsistent, or incomplete. The smart money is on incomplete." If mathematics is tautology, as Wittgenstein said, mathematics cannot be inconsistent and/or incomplete, and so Gödel's work cannot be about mathematics. If mathematics is not tautological, mathematics is mired in inconsistency and/or incompleteness, just as Stephen Hawking said, hence is unreliable. If mathematics is non-ontological, it cannot say anything about reality. If mathematics is ontological, it's the only thing that can say anything true about reality. There can't be a world where math is a bit true and a bit false. Either the world is wholly mathematical – in which case math and not science is how we must study the world – or the world isn't mathematical at all, in which case it's absurd for science to use math.
Author: Rebecca Goldstein
Publisher: W. W. Norton & Company
ISBN: 0393327604
Category : Biography & Autobiography
Languages : en
Pages : 299
Get Book Here
Book Description
"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Author: S.G. Shanker
Publisher: Taylor & Francis
ISBN: 1134947984
Category : Philosophy
Languages : en
Pages : 271
Get Book Here
Book Description
A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.
Author: Hao Wang
Publisher: Courier Corporation
ISBN: 0486171043
Category : Mathematics
Languages : en
Pages : 290
Get Book Here
Book Description
Noted logician discusses both theoretical underpinnings and practical applications, exploring set theory, model theory, recursion theory and constructivism, proof theory, logic's relation to computer science, and other subjects. 1981 edition, reissued by Dover in 1993 with a new Postscript by the author.
Author: Paul Livingston
Publisher: Routledge
ISBN: 113665674X
Category : Philosophy
Languages : en
Pages : 404
Get Book Here
Book Description
In this book, Livingston develops the political implications of formal results obtained over the course of the twentieth century in set theory, metalogic, and computational theory. He argues that the results achieved by thinkers such as Cantor, Russell, Godel, Turing, and Cohen, even when they suggest inherent paradoxes and limitations to the structuring capacities of language or symbolic thought, have far-reaching implications for understanding the nature of political communities and their development and transformation. Alain Badiou's analysis of logical-mathematical structures forms the backbone of his comprehensive and provocative theory of ontology, politics, and the possibilities of radical change. Through interpretive readings of Badiou's work as well as the texts of Giorgio Agamben, Jacques Lacan, Jacques Derrida, Gilles Deleuze, and Ludwig Wittgenstein, Livingston develops a formally based taxonomy of critical positions on the nature and structure of political communities. These readings, along with readings of Parmenides and Plato, show how the formal results can transfigure two interrelated and ancient problems of the One and the Many: the problem of the relationship of a Form or Idea to the many of its participants, and the problem of the relationship of a social whole to its many constituents.
Author: Severin Schroeder
Publisher: Routledge
ISBN: 100031829X
Category : Philosophy
Languages : en
Pages : 210
Get Book Here
Book Description
This book offers a detailed account and discussion of Ludwig Wittgenstein’s philosophy of mathematics. In Part I, the stage is set with a brief presentation of Frege’s logicist attempt to provide arithmetic with a foundation and Wittgenstein’s criticisms of it, followed by sketches of Wittgenstein’s early views of mathematics, in the Tractatus and in the early 1930s. Then (in Part II), Wittgenstein’s mature philosophy of mathematics (1937-44) is carefully presented and examined. Schroeder explains that it is based on two key ideas: the calculus view and the grammar view. On the one hand, mathematics is seen as a human activity — calculation — rather than a theory. On the other hand, the results of mathematical calculations serve as grammatical norms. The following chapters (on mathematics as grammar; rule-following; conventionalism; the empirical basis of mathematics; the role of proof) explore the tension between those two key ideas and suggest a way in which it can be resolved. Finally, there are chapters analysing and defending Wittgenstein’s provocative views on Hilbert’s Formalism and the quest for consistency proofs and on Gödel’s incompleteness theorems.
Author: Jaakko Hintikka
Publisher: Springer Science & Business Media
ISBN: 9401584788
Category : Philosophy
Languages : en
Pages : 585
Get Book Here
Book Description
Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy. From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics illustrates the much greater variety of the actual developments in the foundations during the period covered. The viewpoints that serve this purpose included the foundational ideas of working mathematicians, such as Kronecker, Dedekind, Borel and the early Hilbert, and the development of notions like model and modelling, arbitrary function, completeness, and non-Archimedean structures. The philosophers discussed include not only the household names in logic, but also Husserl, Wittgenstein and Ramsey. Needless to say, such logically-oriented thinkers as Frege, Russell and Gödel are not entirely neglected, either. Audience: Everybody interested in the philosophy and/or history of mathematics will find this book interesting, giving frequently novel insights.
Author: Hao Wang
Publisher: MIT Press
ISBN: 9780262261258
Category : Philosophy
Languages : en
Pages : 420
Get Book Here
Book Description
Hao Wang (1921-1995) was one of the few confidants of the great mathematician and logician Kurt Gödel. A Logical Journey is a continuation of Wang's Reflections on Gödel and also elaborates on discussions contained in From Mathematics to Philosophy. A decade in preparation, it contains important and unfamiliar insights into Gödel's views on a wide range of issues, from Platonism and the nature of logic, to minds and machines, the existence of God, and positivism and phenomenology. The impact of Gödel's theorem on twentieth-century thought is on par with that of Einstein's theory of relativity, Heisenberg's uncertainty principle, or Keynesian economics. These previously unpublished intimate and informal conversations, however, bring to light and amplify Gödel's other major contributions to logic and philosophy. They reveal that there is much more in Gödel's philosophy of mathematics than is commonly believed, and more in his philosophy than his philosophy of mathematics. Wang writes that "it is even possible that his quite informal and loosely structured conversations with me, which I am freely using in this book, will turn out to be the fullest existing expression of the diverse components of his inadequately articulated general philosophy." The first two chapters are devoted to Gödel's life and mental development. In the chapters that follow, Wang illustrates the quest for overarching solutions and grand unifications of knowledge and action in Gödel's written speculations on God and an afterlife. He gives the background and a chronological summary of the conversations, considers Gödel's comments on philosophies and philosophers (his support of Husserl's phenomenology and his digressions on Kant and Wittgenstein), and his attempt to demonstrate the superiority of the mind's power over brains and machines. Three chapters are tied together by what Wang perceives to be Gödel's governing ideal of philosophy: an exact theory in which mathematics and Newtonian physics serve as a model for philosophy or metaphysics. Finally, in an epilog Wang sketches his own approach to philosophy in contrast to his interpretation of Gödel's outlook.
Author: Juliet Floyd
Publisher: Cambridge University Press
ISBN: 1108616534
Category : Science
Languages : en
Pages : 96
Get Book Here
Book Description
For Wittgenstein mathematics is a human activity characterizing ways of seeing conceptual possibilities and empirical situations, proof and logical methods central to its progress. Sentences exhibit differing 'aspects', or dimensions of meaning, projecting mathematical 'realities'. Mathematics is an activity of constructing standpoints on equalities and differences of these. Wittgenstein's Later Philosophy of Mathematics (1934–1951) grew from his Early (1912–1921) and Middle (1929–33) philosophies, a dialectical path reconstructed here partly as a response to the limitative results of Gödel and Turing.
