Download or read book The Fifth Impossibility written by Norman Manea and published by Yale University Press. This book was released on 2012-05-29 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring the language and psyche of the exiled writer, offers a critique of American writers and the author's fellow Romanian writers, answering questions on censorship and linguistic roots.

Download or read book Tales of Impossibility written by David S. Richeson and published by Princeton University Press. This book was released on 2021-11-02 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive look at four of the most famous problems in mathematics Tales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems—squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle—have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs—which demonstrated the impossibility of solving them using only a compass and straightedge—depended on and resulted in the growth of mathematics. Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viète, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems. Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries.

Download or read book A History of Mathematical Impossibility written by Jesper Lützen and published by Oxford University Press. This book was released on 2023-01-26 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the most famous results in mathematics are impossibility theorems stating that something cannot be done. Good examples include the quadrature of the circle by ruler and compass, the solution of the quintic equation by radicals, Fermat's last theorem, and the impossibility of proving the parallel postulate from the other axioms of Euclidean geometry. This book tells the history of these and many other impossibility theorems starting with the ancient Greek proof of the incommensurability of the side and the diagonal in a square. Lützen argues that the role of impossibility results have changed over time. At first, they were considered rather unimportant meta-statements concerning mathematics but gradually they obtained the role of important proper mathematical results that can and should be proved. While mathematical impossibility proofs are more rigorous than impossibility arguments in other areas of life, mathematicians have employed great ingenuity to circumvent impossibilities by changing the rules of the game. For example, complex numbers were invented in order to make impossible equations solvable. In this way, impossibilities have been a strong creative force in the development of mathematics, mathematical physics, and social science.

Download or read book Impossibility written by John D. Barrow and published by Oxford University Press, USA. This book was released on 1999 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Astronomer John Barrow takes an intriguing look at the limits of science, who argues that there are things that are ultimately unknowable, undoable, or unreachable.

Download or read book The Impossibility of Squaring the Circle in the 17th Century written by Davide Crippa and published by Springer. This book was released on 2019-03-06 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about James Gregory’s attempt to prove that the quadrature of the circle, the ellipse and the hyperbola cannot be found algebraically. Additonally, the subsequent debates that ensued between Gregory, Christiaan Huygens and G.W. Leibniz are presented and analyzed. These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise on the arithmetical quadrature of the circle. The author shows how the controversy around the possibility of solving the quadrature of the circle by certain means (algebraic curves) pointed to metamathematical issues, particularly to the completeness of algebra with respect to geometry. In other words, the question underlying the debate on the solvability of the circle-squaring problem may be thus phrased: can finite polynomial equations describe any geometrical quantity? As the study reveals, this question was central in the early days of calculus, when transcendental quantities and operations entered the stage. Undergraduate and graduate students in the history of science, in philosophy and in mathematics will find this book appealing as well as mathematicians and historians with broad interests in the history of mathematics.

Download or read book Possibility and Actuality written by Nicolai Hartmann and published by Walter de Gruyter. This book was released on 2013-03-22 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nicolai Hartmann's Possibility and Actuality is the second volume of a four-part investigation of ontology. It deals with such questions as: How do we know that something is really possible? Is the possible only the actual? Is the actual only the possible? What is the difference between ideal and real possibility? This groundbreaking work of modal analysis describes the logical relations between possibility, actuality, and necessity, and it provides insight into the relations between modes of knowledge and modes of being. Hartmann reviews the history of philosophical concepts of possibility and necessity, from ancient Megarian philosophy to Aristotle, to Medieval Scholasticism, to Leibniz, Kant, and Hegel. He explains the importance of modal analysis as a basic investigative tool, and he proposes an approach to understanding the nature of human existence that unifies the fields of ontology, modal logic, metaphysics, and epistemology. This brilliant and fascinating work is relevant to many topics of debate in contemporary philosophy, including the ontology of possible worlds, the metaphysics of modality, the logic of counterfactual conditionals, and modal epistemology. It illuminates the nature of real, ideal, logical, and epistemic possibility.

Download or read book The Law of Contracts written by Samuel Williston and published by . This book was released on 1920 with total page 1164 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Selections from Williston s Treatise on the Law of Contracts written by Samuel Williston and published by . This book was released on 1920 with total page 2676 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Ancient philosophy and the first to the thirteenth centuries v 2 14 th century to the French revolution with a glimpse into the 19 th century written by Frederick Denison Maurice and published by . This book was released on 1873 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Ancient philosophy and the first to the thirteenth centuries written by Frederick Denison Maurice and published by . This book was released on 1882 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Moral and Metaphysical Philosophy Ancient philosophy and the first to the thirteenth centuries written by Frederick Denison Maurice and published by . This book was released on 1873 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Foundations of Geometry written by David Hilbert and published by . This book was released on 1902 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Najm al D n al K tib s al Ris lah al Shamsiyyah written by Tony Street and published by NYU Press. This book was released on 2024-05-07 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: A scholarly edition of a classic textbook on logic Najm al-Dīn al-Kātibī’s al-Risālah al-Shamsiyyah is a scholarly edition and translation of The Rules of Logic, with commentary and notes. Composed by Najm al-Dīn al-Kātibī, a scholar of the Shāfiʿī school of law, al-Risālah al-Shamsiyyah is the most widely read introduction to logic in the Arabic-speaking world. It has probably enjoyed a longer shelf-life than any other logic textbook ever written, having been in use by madrasah students from the early eighth/fourteenth century up until the present day. Building on the theories of Avicenna, al-Rāzī, and other pioneers of logic, al-Kātibī discusses the many pitfalls of building arguments and setting out unambiguous claims in natural language. The enduring nature of the text is a testament to al-Kātibī and his impact on concepts of formal discourse and argument.

Download or read book Karl Barth s Infralapsarian Theology written by Shao Kai Tseng and published by InterVarsity Press. This book was released on 2016-02-17 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scholars of Karl Barth's theology have been unanimous in labeling him a supralapsarian, largely because Barth identifies himself as such. In this groundbreaking and thoroughly researched work, Shao Kai Tseng argues that Barth was actually an infralapsarian, bringing Barth into conversation with recent studies in Puritan theology.

Download or read book California Court of Appeal 2nd Appellate District Records and Briefs written by California (State). and published by . This book was released on with total page 838 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number of Exhibits: 17 Received document entitled: APPENDIX OF EXHIBITS AND OUT OF STATE AUTHORITIES TO PETITION FOR WRIT OF MANDATE

Download or read book On the Power of God written by Thomas Aquinas and published by Wipf and Stock Publishers. This book was released on 2004-06-11 with total page 727 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the thirteenth century, public disputation was not only a sort of ecclesiastical tournament arranged for an exceptional and solemn occasion, but also an integral part of a philosophical and theological course of study. At the University of Paris, for instance, public disputations were held frequently throughout the year. They were held more or less intermittently by other masters, but by Thomas with great frequency and regularity, especially during the three years of his first professorship at Paris when he held them twice a week during term. Thomas' disputations fall into seven series: on Truth; on the Power of God; on Evil; on the Incarnate Word; on Spiritual Creatures; and on the Virtures. These disputations on the power of God were written when Aquinas was about 40 and at the height of his intellectual powers. The exact time and place are unknown though it is likely that they were offered in either Anagni (1259-1261) or Rome (1265-67).

Download or read book On the Power of God written by Saint Thomas Aquinas and published by Aeterna Press. This book was released on 1992 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now, just as nothing suffers save by reason of a passive power, so nothing acts except by reason of the first act, namely the form. For it has been stated that this first act is so called from action. Now God is act both pure and primary, wherefore it is most befitting to him to act and communicate his likeness to other things: and consequently active power is most becoming to him: since power is called active forasmuch as it is a principle of action. We must also observe that our mind strives to describe God as a most perfect being. And seeing that it is unable to get at him save by likening him to his effects, while it fails to find any creature so supremely perfect as to be wholly devoid of imperfection, consequently it endeavours to describe him as possessing the various perfections it discovers in creatures, although each of those perfections is in some way at fault, yet so as to remove, from God whatever imperfection is connected with them. Aeterna Press