On The Brink Of Paradox

An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory. This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof. The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.

Centuries of self-imposed isolation have transformed Nulapeiron into a world unlike any other - a world of vast subterranean cities maintained by extraordinary organic technologies. For the majority of its peoples, however such wonders have little meaning. Denied their democratic rights and restricted to the impoverished lower levels, they are subjected to the brutal law of the Logic Lords and the Oracles, supra-human beings whose ability to truecast the future maintains the status quo. But all this is about to change. In a crowded marketplace a mysterious, beautiful woman is brutally cut down by a militia squad's graser fire. Amongst the horrified onlookers is young Tom Corcorigan. He recognizes her. Only the previous day she had presented him with a small, seemingly insignificant info-crystal. And only now, as the fire in the dying stranger's obsidian eyes fades, does he comprehend who - or what - she really was: a figure from legend, one of the fabled Pilots. What Tom has still to discover is that his crystal holds the key to understanding mu-space, and so to freedom itself. He doesn't know it yet, but he has been given a destiny to fulfill - nothing less than the rewriting of his future, and that of his world... Spectacularly staged, thrillingly written and set in a visionary future, Paradox places John Meaney at the forefront of science fiction in this new century.

Travel to the Stars . . . A Dream Fulfilled or Humankind's Worst Nightmare?Ed Walker's last mission almost ended in catastrophe. Although the NASA astronaut had been able to save the lives of his crewmates, he's still in danger of going down in history as the commander of the mission that wrecked the International Space Station. So he can hardly believe his luck when he's chosen to head the first manned exploration of the outer solar system.One of his new crew members is the young physicist David Holmes, who is studying the mysterious disappearance of three space probes.But as their spaceship approaches interstellar space, humanity's most pressing question is no longer: Are we alone in the universe? It is rather: Are we ready for the truth?For fans of Apollo 13, The Martian and Interstellar+++ Winner of the 2015 Storyteller Award at the Frankfurt International Bookfair +++

In The Progress Paradox, Gregg Easterbrook draws upon three decades of wide-ranging research and thinking to make the persuasive assertion that almost all aspects of Western life have vastly improved in the past century–and yet today, most men and women feel less happy than in previous generations. Detailing the emerging science of “positive psychology,” which seeks to understand what causes a person’s sense of well-being, Easterbrook offers an alternative to our culture of crisis and complaint. He makes a compelling case that optimism, gratitude, and acts of forgiveness not only make modern life more fulfilling but are actually in our self-interest. An affirming and constructive way of seeing life anew, The Progress Paradox will change the way you think about your place in the world–and about our collective ability to make it better.

Volume 4 in the 5-volume series titled Analytical Metaphysics. The essays in this volume are concerned with three main issues. First, what account can be given of the nature of a particular? Second, is identity over time a basic and irreducible relation, or can it be analysed? If so, what is the correct analysis? Third, what account can be offered of what it is to be actual? The final account of this volume involves the claim that actuality is a special property that is possessed by one, and only one, possible world.

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

Does the existence of evil call into doubt the existence of God? Show me the argument. Philosophy starts with questions, but attempts at answers are just as important, and these answers require reasoned argument. Cutting through dense philosophical prose, 100 famous and influential arguments are presented in their essence, with premises, conclusions and logical form plainly identified. Key quotations provide a sense of style and approach. Just the Arguments is an invaluable one-stop argument shop. A concise, formally structured summation of 100 of the most important arguments in Western philosophy The first book of its kind to present the most important and influential philosophical arguments in a clear premise/conclusion format, the language that philosophers use and students are expected to know Offers succinct expositions of key philosophical arguments without bogging them down in commentary Translates difficult texts to core arguments Designed to provides a quick and compact reference to everything from Aquinas’ “Five Ways” to prove the existence of God, to the metaphysical possibilities of a zombie world

International capital flow and domestic financial market structures explain why some countries are more vulnerable to banking crises.