Logic

In 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal to students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

The art of scientific investigation - Includes preparation, experimentation, chance, hypothesis, imagination, intuition and more.

An Unabridged, Digitally Enlarged Printing Of Volume I of III: Part I - MATHEMATICAL LOGIC - The Theory Of Deduction - Theory Of Apparent Variables - Classes And Relations - Logic And Relations - Products And Sums Of Classes - Part II - PROLEGOMENA TO CARDIANL ARITHMITIC - Unit Classes And Couples - Sub-Classes, Sub-Relations, And Relative Types - One-Many, Many-One, And One-One Relations - Selections - Inductive Relations

“I believe that it is right and proper for me, as a human being, to have an interest in the future, and what human civilization becomes in the future. One of those interests is the human pursuit of truth, which has strengthened slowly over the generations (for there was not always science). I wish to strengthen that pursuit further, in this generation. That is a wish of mine, for the Future. For we are all of us players upon that vast gameboard, whether we accept the responsibility or not. “And that makes your rationality my business. “Is this a dangerous idea? Yes, and not just pleasantly edgy 'dangerous.' People have been burned to death because some priest decided that they didn’t think the way they should. Deciding to burn people to death because they ‘don’t think properly’—that’s a revolting kind of reasoning, isn’t it? You wouldn’t want people to think that way, why, it’s disgusting. People who think like that, well, we’ll have to do something about them...“I agree! Here’s my Let’s argue against bad ideas but not set their bearers on fire.” Human intelligence is a an amazing capacity that has single-handedly put humans in a dominant position on Earth. When human intelligence defeats itself and goes off the rails, the fallout therefore tends to be a uniquely big deal. In How to Actually Change Your Mind , decision theorist Eliezer Yudkowsky asks how we can better identify and sort out our biases, integrate new evidence, and achieve lucidity in our daily lives. Because it really seems as though we should be able to do better— —and a three-pound all-purpose superweapon is a terrible thing to waste.