Aristotle on Mathematical Infinity


Author: Theokritos Kouremenos,Aristotle

Publisher: Franz Steiner Verlag

ISBN: 9783515068512

Category: Philosophy

Page: 131

View: 6301

Aristotle was the first not only to distinguish between potential and actual infinity but also to insist that potential infinity alone is enough for mathematics thus initiating an issue still central to the philosophy of mathematics. Modern scholarship, however, has attacked Aristotle's thesis because, according to the received doctrine, it does not square with Euclidean geometry and it also seems to contravene Aristotle's belief in the finitude of the physical universe. This monograph, the first thorough study of the issue, puts Aristotle's views on infinity in the proper perspective. Through a close study of the relevant Aristotelian passages it shows that the Stagirite's theory of infinity forms a well argued philosophical position which does not bear on his belief in a finite cosmos and does not undermine the Euclidean nature of geometry. The monograph draws a much more positive picture of Aristotle's views and reaffirms his disputed stature as a serious philosopher of mathematics. This innovative and stimulating contribution will be essential reading to a wide range of scholars, including classicists, philosophers of science and mathematics as well as historians of ideas.


Chronicles of Nick


Author: Sherrilyn Kenyon

Publisher: St. Martin's Griffin

ISBN: 9781429928601

Category: Young Adult Fiction

Page: 480

View: 1451

At fourteen, Nick Gautier thinks he knows everything about the world around him. Streetwise, tough, and savvy, his quick sarcasm is the stuff of legends. . .until the night when his best friends try to kill him. Saved by a mysterious warrior who has more fighting skills than Chuck Norris, the teenaged Nick is sucked into the realm of the Dark-Hunters: immortal vampire slayers who risk everything to save humanity. Nick quickly learns that the human world is only a veil for a much larger and more dangerous one: a world where the captain of the football team is a werewolf and the girl he has a crush on goes out at night to stake the undead. But before he can even learn the rules of this new world, his fellow students are turning into flesh-eating zombies--and he's next on the menu. As if starting high school isn't hard enough. . .now Nick has to hide his new friends from his mom, his chain saw from the principal, and keep the zombies and the demon Simi from eating his brains, all without getting grounded or suspended. How in the world is he supposed to do that?

To Infinity and Beyond

A Cultural History of the Infinite


Author: Eli Maor

Publisher: Princeton University Press

ISBN: 9780691025117

Category: Mathematics

Page: 284

View: 1415

Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher; from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes the mathematician's fascination with infinity--a fascination mingled with puzzlement. "Maor explores the idea of infinity in mathematics and in art and argues that this is the point of contact between the two, best exemplified by the work of the Dutch artist M. C. Escher, six of whose works are shown here in beautiful color plates."--Los Angeles Times "[Eli Maor's] enthusiasm for the topic carries the reader through a rich panorama."--Choice "Fascinating and enjoyable.... places the ideas of infinity in a cultural context and shows how they have been espoused and molded by mathematics."--Science

Understanding Infinity

The Mathematics of Infinite Processes


Author: Anthony Gardiner

Publisher: Courier Corporation

ISBN: 9780486425382

Category: Mathematics

Page: 308

View: 1539

Conceived by the author as an introduction to "why the calculus works," this volume offers a 4-part treatment: an overview; a detailed examination of the infinite processes arising in the realm of numbers; an exploration of the extent to which familiar geometric notions depend on infinite processes; and the evolution of the concept of functions. 1982 edition.

Numbers #3: Infinity


Author: Rachel Ward

Publisher: Scholastic Inc.

ISBN: 0545443024

Category: Juvenile Fiction

Page: 256

View: 8233

The mind-blowing conclusion to the chilling NUMBERS trilogy: Because everyone wants to live forever. No matter what it takes, Sarah's desperate to escape from the numbers. Always numbers. Sarah loves Adam, but can't bear the thought that every time he looks in her eyes, he can see her dying; can see her last day. It's 2029. Two years since the Chaos. Sarah and Adam are struggling to survive. She knows he always envisioned them together "'til death do us part." But will a child come between them? The child she loves. The child he saved. Little Mia was supposed to die that New Year's Day. The numbers don't lie. But somehow she changed her date. Mia's just a baby, oblivious to her special power. But ruthless people are hunting her down, determined to steal her secret. Because everyone wants to live forever.


New Research Frontiers


Author: Michael Heller,W. Hugh Woodin

Publisher: Cambridge University Press

ISBN: 1139495569

Category: Mathematics

Page: N.A

View: 8389

This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen world-renowned researchers in the fields of mathematics, physics, cosmology, philosophy and theology offer a rich intellectual exchange among various current viewpoints, rather than displaying a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity.

The Diagonal Infinity

Problems of Multiple Scales


Author: H. M. Hubey

Publisher: World Scientific

ISBN: 9789810230814

Category: Mathematics

Page: 522

View: 2786

CD-ROM consists of four directories: parametric plots, fractals, etc; nonlinear differential equations; fuzzy logics; and graphics files.

Infinity and Perspective


Author: Karsten Harries

Publisher: MIT Press

ISBN: 9780262582186

Category: Philosophy

Page: 392

View: 3277

A philosophical exploration of the origin and limits of the modern world.

Totality and Infinity

An Essay on Exteriority


Author: E. Levinas

Publisher: Springer Science & Business Media

ISBN: 9400993420

Category: Philosophy

Page: 297

View: 1726

Ever since the beginning of the modern phenomenological movement disciplined attention has been paid to various patterns of human experi ence as they are actually lived through in the concrete. This has brought forth many attempts to tind a general philosophical position which can do justice to these experiences without reduction or distQrtion. In France, the best known of these recent attempts have been made by Sartre in his Being and Nothingness and by Merleau-Ponty in his Phenomenol ogy of Perception and certain later fragments. Sartre has a keen sense for life as it is lived, and his work is marked by many penetrating descrip tions. But his dualistic ontology of the en-soi versus the pour-soi has seemed over-simple and inadequate to many critics, and has been seriously qualitied by the author himself in his latest Marxist work, The Critique of Dialetical Reason. Merleau-Ponty's major work is a lasting contri but ion to the phenomenology of the pre-objective world of perception. But asi de from a few brief hints and sketches, he was unable, before his unfortunate death in 1961, to work out carefully his ultimate philosophi cal point of view. This leaves us then with the German philosopher, Heidegger, as the only contemporary thinker who has formulated a total ontology which claims to do justice to the stable results of phenomenology and to the liv ing existential thought of our time.

Orders of Infinity

The "Infinitärcalcül" of Paul Du Bois-Reymond


Author: Godfrey Harold Hardy

Publisher: CUP Archive


Category: Mathematics

Page: 62

View: 3519

Originally published in 1910 as number twelve in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides an up-to-date version of Du Bois-Reymond's Infinitärcalcül by the celebrated English mathematician G. H. Hardy. This tract will be of value to anyone with an interest in the history of mathematics or the theory of functions.