Download or read book One Hundred Years of Russell s Paradox written by Godehard Link and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers collected in this volume represent the main body of research arising from the International Munich Centenary Conference in 2001, which commemorated the discovery of the famous Russell Paradox a hundred years ago. The 31 contributions and the introductory essay by the editor were (with two exceptions) all originally written for the volume. The volume serves a twofold purpose, historical and systematic. One focus is on Bertrand Russell's logic and logical philosophy, taking into account the rich sources of the Russell Archives, many of which have become available only recently. The second equally important aim is to present original research in the broad range of foundational studies that draws on both current conceptions and recent technical advances in the above-mentioned fields. The volume contributes therefore, to the well-established body of mathematical philosophy initiated to a large extent by Russell's work.
Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Outer Limits of Reason written by Noson S. Yanofsky and published by MIT Press. This book was released on 2016-11-04 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exploration of the scientific limits of knowledge challenges our deep-seated beliefs about our universe, our rationality, and ourselves. “A must-read for anyone studying information science.” —Publishers Weekly, starred review Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own intuitions about the world—including our ideas about space, time, and motion, and the complex relationship between the knower and the known. Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve: • perfectly formed English sentences that make no sense • different levels of infinity • the bizarre world of the quantum • the relevance of relativity theory • the causes of chaos theory • math problems that cannot be solved by normal means • statements that are true but cannot be proven Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.
Download or read book Incompleteness written by Rebecca Goldstein and published by W. W. Norton & Company. This book was released on 2006-01-31 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Download or read book Bertrand Russell and the Origins of the Set theoretic Paradoxes written by GARCIADIEGO and published by Birkhäuser. This book was released on 2013-03-09 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Xll Russell's published works include more than sixty books, several unpublished manuscripts, many hundreds of articles, dozens of radio and TV interviews and films, covering a wide spectrum of knowledge. His writings embrace discussions and analysis of such diverse topics as social sciences, foundations of mathematics, philosophy of physics, philosophy in general, religion, moral sciences, education, pacifism, natural sciences (including biology and physics), linguistics, statistics, probability, eco nomic theory, history, politics, international affairs and other topics. He corresponded with a large and diverse group of colleagues including both prominent and obscure figures in politics, the arts, humanities and scienc es. Russell's communication with his colleagues began in the late nine teenth century and was especially active through much of the twentieth century. In spite of being one of the most controversial public personali ties of his day (let us not forget that he went to prison twice, was dis missed from Cambridge University and was prevented from teaching at the College of the City of New York), his merits have been recognized and appreciated. He was awarded many medals, diplomas and honors, including the Nobel Prize for Literature in 1950.
Download or read book The Error of Russell written by Daniel J. Shepard and published by CreateSpace. This book was released on 2011-10-23 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This essay will begin where we, humankind, have lead ourselves as we attempted to slash our way through the jungle of life's seemingly endless paradoxes. These paradoxes, which life has persistently thrown across our path, are signposts for us. They are indicators that we do not have all the answers. They warn us to beware. They warn us there is something wrong with our perception of life; there is something wrong with our thinking. They have a function of their own, they direct us towards a state of understanding where we are, what we are, and why it is we exist. In this essay, we will be attempting to understand the likes of Russell, Wittgenstein, Frege, Plotinus, and back again to Russell as we attempt to move past parts of Heidegger. Our objective will be to step back in time in order to get back to today. What is the point of going to all this trouble just to get back to where we started? The point is to bring back with us a new perception regarding a simpler solution to Russell's paradox. Why is this important? Presently we have a solution to Russell's paradox, which involves a complex understanding of 'separation through exclusionism', which in turn represents what we do to people in society. We separate individuals and groups from our own groups and ourselves. Once having separated them from ourselves we exclude them from ourselves through a process of rejection, exclusionism, and separation. It is Russell's paradox, which provides the key to rectifying these constant actions of rejection. For this reason we will accompany Russell as he travels eighteen hundred years back in time. This trip will allow us to bring back with us a different solution to Russell's paradox. This trip will allow us to bring back a process known as 'separation through inclusion'. Now the name would seem to imply our creating a paradox to act as a solution to Russell's paradox but as we shall see it does nothing of the kind. What it does is allow us to find a much simpler solution to Russell's paradox. 'But what does this concept of 'separation through exclusion' as opposed to 'separation through inclusion' have to do with me?' you may ask. The process provides an alternative means to resolving a fundamental paradox of mathematics, which in turn can be applied directly to the process of understanding life. It is the simplistic resolution of complex paradoxes, which provides us with a simplistic understanding of life. It is through this process that we shall see 'Ockham's razor not only cuts away the complexity of science but becomes the primary tool for Husserl's bracketing . Ockham's Razor now becomes not only a principle axiom for science but now moves on to become a principle axiom of philosophy. This is an essay beginning in complexity and ending in simplicity. Why is it that we must begin in complexity rather than begin at the logical point of origin, the point of simplicity? We begin in complexity for it is through complexity that we presently have begun to understand Russell's paradox . Presently we have solved Russell's paradox in a complex fashion. This has led us to understanding life in a complex manner. We cannot understand the simplicity of life as long as the basics remain complex. The solution to this problem lies in the understanding of Russell's paradox. Once you understand the end of this essay, you will begin to understand why it is that we must go back and make a correctional adjustment to our journey as individuals and as specie. The question becomes, 'How far back in time must we travel to do all this?' We must go back 1700 years. Who will lead us on this backtracking expedition? The honors will go to Bertrand Russell himself. Russell verbalized the paradox in 1901. As such, it is Russell's paradox. Therefore, it will be Russell who will lead our backtracking expedition, which will lead us to an understanding of life.
Download or read book Perspectives on the History of Mathematical Logic written by Thomas Drucker and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers insights into the development of mathematical logic over the last century. Arising from a special session of the history of logic at an American Mathematical Society meeting, the chapters explore technical innovations, the philosophical consequences of work during the period, and the historical and social context in which the logicians worked. The discussions herein will appeal to mathematical logicians and historians of mathematics, as well as philosophers and historians of science.
Download or read book Exploring Theological Paradoxes written by Cyril Orji and published by Taylor & Francis. This book was released on 2022-08-31 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the question of theological paradox, exploring what it means and its place in theological method from a Christian perspective. Just as paradoxes are unavoidable in logic and mathematics, paradoxes are inevitable in religious and theological discourses. The chapters in this volume examine a number of cases, including the ‘Red Heifer paradox’, the ‘liar paradox’, and the ‘paradox of omnipotence’, and attention is given to Christian doctrines such as the Trinity and the Incarnation. Arguing for a renewed understanding and appreciation of the role of paradox, this study will be of interest to scholars of theology and the philosophy of religion.
Download or read book A Hundred Years of Philosophy written by John Passmore and published by . This book was released on 1968 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Fallacies and Paradoxes written by Bryan Bunch and published by Courier Corporation. This book was released on 2012-10-16 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stimulating, thought-provoking analysis of the most interesting intellectual inconsistencies in mathematics, physics, and language, including being led astray by algebra (De Morgan's paradox). 1982 edition.
Download or read book A Structural Account of Mathematics written by Charles S. Chihara and published by Clarendon Press. This book was released on 2004 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems areapplied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true.Chihara builds upon his previous work, in which he presented a new system of mathematics, the constructibility theory, which did not make reference to, or presuppose, mathematical objects. Now he develops the project further by analysing mathematical systems currently used by scientists to show howsuch systems are compatible with this nominalistic outlook. He advances several new ways of undermining the heavily discussed indispensability argument for the existence of mathematical objects made famous by Willard Quine and Hilary Putnam. And Chihara presents a rationale for the nominalisticoutlook that is quite different from those generally put forward, which he maintains have led to serious misunderstandings.A Structural Account of Mathematics will be required reading for anyone working in this field.
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 Principles of Mathematics written by Bertrand Russell and published by . This book was released on 2009-08 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics.
Download or read book A Brief History of the Paradox written by Roy Sorensen and published by Oxford University Press. This book was released on 2003-12-04 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Can God create a stone too heavy for him to lift? Can time have a beginning? Which came first, the chicken or the egg? Riddles, paradoxes, conundrums--for millennia the human mind has found such knotty logical problems both perplexing and irresistible. Now Roy Sorensen offers the first narrative history of paradoxes, a fascinating and eye-opening account that extends from the ancient Greeks, through the Middle Ages, the Enlightenment, and into the twentieth century. When Augustine asked what God was doing before He made the world, he was told: "Preparing hell for people who ask questions like that." A Brief History of the Paradox takes a close look at "questions like that" and the philosophers who have asked them, beginning with the folk riddles that inspired Anaximander to erect the first metaphysical system and ending with such thinkers as Lewis Carroll, Ludwig Wittgenstein, and W.V. Quine. Organized chronologically, the book is divided into twenty-four chapters, each of which pairs a philosopher with a major paradox, allowing for extended consideration and putting a human face on the strategies that have been taken toward these puzzles. Readers get to follow the minds of Zeno, Socrates, Aquinas, Ockham, Pascal, Kant, Hegel, and many other major philosophers deep inside the tangles of paradox, looking for, and sometimes finding, a way out. Filled with illuminating anecdotes and vividly written, A Brief History of the Paradox will appeal to anyone who finds trying to answer unanswerable questions a paradoxically pleasant endeavor.
Download or read book Mathematics and Metaphilosophy written by Justin Clarke-Doane and published by Cambridge University Press. This book was released on 2022-06-30 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Element discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the challenge to explain the (defeasible) justification of our mathematical beliefs ('the justificatory challenge'), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the challenge to explain their reliability ('the reliability challenge'), arises to the extent that we could have easily had different beliefs. The Element shows that mathematical facts are not, in general, empirically accessible, contra Quine, and that they cannot be dispensed with, contra Field. However, it argues that they might be so plentiful that our knowledge of them is unmysterious. The Element concludes with a complementary 'pluralism' about modality, logic and normative theory, highlighting its surprising implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap's pragmatism, transposed to the key of realism.
Download or read book Russell s Philosophy of Logical Analysis 1897 1905 written by J. Galaugher and published by Springer. This book was released on 2013-11-07 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This systematic and historical treatment of Russell's contributions to analytic philosophy, from his embrace of analysis in 1898 to his landmark theory of descriptions in 1905, draws important connections between his philosophically motivated conception of analysis and the technical apparatus he devised to facilitate analyses in mathematics
Download or read book The Value of Philosophy written by Bertrand Russell and published by . This book was released on 2017-10-05 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The Value of Philosophy" is one of the most important chapters of Bertrand's Russell's magnum Opus, The Problems of Philosophy. As a whole, Russell focuses on problems he believes will provoke positive and constructive discussion, Russell concentrates on knowledge rather than metaphysics: If it is uncertain that external objects exist, how can we then have knowledge of them but by probability. There is no reason to doubt the existence of external objects simply because of sense data.
