Kurt Godel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein s general relativity, as he proved that Einstein s theory allows for time machines.
The Godel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Godel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life.
This accessible book gives a new, detailed and elementary explanation of the Godel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences.

See also: http: //www.youtube.com/watch?v=REy9noY5Sg8

"

Kurt Godel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein's general relativity, as he proved that Einstein's theory allows for time machines. The Godel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin's groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Godel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life.This accessible book gives a new, detailed and elementary explanation of the Godel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book's writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8

"Tell me," Wittgenstein once asked a friend, "why do people always say, it was natural for man to assume that the sun went round the earth rather than that the earth was rotating?" His friend replied, "Well, obviously because it just looks as though the Sun is going round the Earth." Wittgenstein replied, "Well, what would it have looked like if it had looked as though the Earth was rotating?" What would it have looked like if we looked at all sciences from the viewpoint of Wittgenstein's philosophy? Wittgenstein is undoubtedly one of the most influential philosophers of the twentieth century. His complex body of work has been analysed by numerous scholars, from mathematicians and physicists, to philosophers, linguists, and beyond. This volume brings together some of his central perspectives as applied to the modern sciences and studies the influence they may have on the thought processes underlying science and on the world view it engenders. The contributions stem from leading scholars in philosophy, mathematics, physics, economics, psychology and human sciences; all of them have written in an accessible style that demands little specialist knowledge, whilst clearly portraying and discussing the deep issues at hand.