The Passion Of Infinity

The Passion of Infinity generates a historical narrative surrounding the concept of the irrational as a threat which rational culture has made a series of attempts to understand and relieve. It begins with a reading of Sophocles' Oedipus as the paradigmatic figure of a reason that, having transgressed its mortal limit, becomes catastrophically reversed. It then moves through Aristotle's ethics, psychology and theory of tragedy, which redefine reason's collapses in moral-psychological rather than religious terms. By changing the way in which the irrational is conceived, and the nature of its relation to reason, Aristotle eliminates the concept of an irrationality which reason cannot in principle dissolve. The book culminates in an extensive reading of Kierkegaard's pseudonyms, who, in a critical retrieval of both Greek tragedy and Aristotle, prescribe their apparently pathological age a paradoxical task: develop a finite form of subjectivity willing to undergo an unthinkable thought ‐ allow the transcendence of a god to enter into the mind as well as the marrow, to make a tragic appearance in which a limit to the immanence of human reason can again be established.

What essentially is a garden? Is it a small plot of land that we put aside to cultivate our favorite vegetables or to grow flowers for our personal enjoyment? Or is it a symbol, a mirror, a reflection of our human passions? The topic of the present volume is the mysterious ways in which Imaginatio Creatix plays within the human ingrowness in natural life, transposing dreams, nostalgias, and enchantments.

'Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' Douglas Adams, Hitch-hiker's Guide to the Galaxy We human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the infinite is a journey into paradox. Here is a quantity that turns arithmetic on its head, making it feasible that 1 = 0. Here is a concept that enables us to cram as many extra guests as we like into an already full hotel. Most bizarrely of all, it is quite easy to show that there must be something bigger than infinity - when it surely should be the biggest thing that could possibly be. Brian Clegg takes us on a fascinating tour of that borderland between the extremely large and the ultimate that takes us from Archimedes, counting the grains of sand that would fill the universe, to the latest theories on the physical reality of the infinite. Full of unexpected delights, whether St Augustine contemplating the nature of creation, Newton and Leibniz battling over ownership of calculus, or Cantor struggling to publicise his vision of the transfinite, infinity's fascination is in the way it brings together the everyday and the extraordinary, prosaic daily life and the esoteric. Whether your interest in infinity is mathematical, philosophical, spiritual or just plain curious, this accessible book offers a stimulating and entertaining read.

'Science has never had an advocate quite like David Deutsch ... A computational physicist on a par with his touchstones Alan Turing and Richard Feynman, and a philosopher in the line of his greatest hero, Karl Popper. His arguments are so clear that to read him is to experience the thrill of the highest level of discourse available on this planet and to understand it' Peter Forbes, Independent In our search for truth, how far have we advanced? This uniquely human quest for good explanations has driven amazing improvements in everything from scientific understanding and technology to politics, moral values and human welfare. But will progress end, either in catastrophe or completion - or will it continue infinitely? In this profound and seminal book, David Deutsch explores the furthest reaches of our current understanding, taking in the Infinity Hotel, supernovae and the nature of optimism, to instill in all of us a wonder at what we have achieved - and the fact that this is only the beginning of humanity's infinite possibility. 'This is Deutsch at his most ambitious, seeking to understand the implications of our scientific explanations of the world ... I enthusiastically recommend this rich, wide-ranging and elegantly written exposition of the unique insights of one of our most original intellectuals' Michael Berry, Times Higher Education Supplement 'Bold ... profound ... provocative and persuasive' Economist 'David Deutsch may well go down in history as one of the great scientists of our age' Scotsman

In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.

This volume contains essays that examine infinity in early modern philosophy. The essays not only consider the ways that key figures viewed the concept. They also detail how these different beliefs about infinity influenced major philosophical systems throughout the era. These domains include mathematics, metaphysics, epistemology, ethics, science, and theology. Coverage begins with an introduction that outlines the overall importance of infinity to early modern philosophy. It then moves from a general background of infinity (before early modern thought) up through Kant. Readers will learn about the place of infinity in the writings of key early modern thinkers. The contributors profile the work of Descartes, Spinoza, Leibniz, and Kant. Debates over infinity significantly influenced philosophical discussion regarding the human condition and the extent and limits of human knowledge. Questions about the infinity of space, for instance, helped lead to the introduction of a heliocentric solar system as well as the discovery of calculus. This volume offers readers an insightful look into all this and more. It provides a broad perspective that will help advance the present state of knowledge on this important but often overlooked topic.

In Badiou, Infinity, and Subjectivity: Reading Hegel and Lacan after Badiou, Mohammad Reza Naderi elaborates on the trajectory of Alain Badiou’s philosophy by following a leading thread: the dominance of axiomatic thought and the category of mathematical infinity. According to this primary proposition, axiomatic thought is the only form of thinking adequate to the infinity of being. Using both primary and secondary literature, the author demonstrates two other major propositions: 1) The coherence of Badiou’s intellectual development from the early interventions to the publication of Being and Event, and 2) The formation of a theory Naderi calls “discipline.” By working through three dimensions of disciplinary thinking—interiority, novelty, and beginning—Naderi provides a new framework for understanding the inner structure of what Badiou calls “procedures of truths” and develops a new interpretation that ultimately reveals the inner logic of Badiou’s method.

Johannes Corrodi Katzenstein offers a contribution to the current debate on Kierkegaard, mostly concerning the rationality of religious belief and the presumed religious neutrality (autonomy) of philosophical and scientific thought. More specifically, his book is an attempt to relate Kierkegaard's theory of the stages of life (aesthetic, ethical, religious) to issues that have been of utmost concern to Anglo-American (analytical) philosophy, such as the nature of truth, rational knowledge, objectivity, etc. From this angle, Kierkegaard turns out to be not the irrationalist he has often been made into but rather the outspoken witness of a passion that guides all thinking, i.e. the passion to think what cannot be thought. An attempt is made to show that for Kierkegaard, anticipating some of the arguments of contemporary postsecular philosophy, the ideal of pure or autonomous reason inevitably has its basis in a pre-rational, often tacit commitment to an origin whose primary home is in religious faith. Rather than precluding dialogue, awareness of these deeper forces and starting-points of our various philosophical and scientific outlooks is a critical requirement for mutual understanding between secularist and religious perspectives and traditions competing for cultural and political dominance.