Logical life

Author: John Casti
Publisher:
Publish Date: 2002-11-01
Features: Kurt G?del was a giant of wisdom. His incompleteness theorems not only changed mathematics but also the entire scientific world and the philosophy built upon this theorem. G?del's theorems shattered the dream that logic would ultimately enable us to understand the entire world, while also raising many challenging questions: What are the limits of rational thinking? Can we fully understand the machines we have created? Can we decipher the workings of our own minds? How could mathematicians continue to work when their research lacked logical certainty? In this book, we finally meet the person behind these profound thoughts. John Casti and Werner De Bondt describe G?del as a complex figure—both worldly and reclusive, ambitious and stubborn. As a student during the most famous and creative period of Viennese culture, G?del was deeply influenced by the language philosopher Wittgenstein. He participated in the activities of the Vienna Circle, discussing the relationship between scientific theories, objective reality, and truth with the group members. Later, G?del went to the Institute for Advanced Study in Princeton. There, he became the companion Einstein had long sought and was regarded by Einstein as a kindred spirit.
After Einstein's death, G?del refused to eat out of fear of bacterial poisoning and ultimately died of starvation. But as Casti and De Bondt clearly demonstrate, G?del's influence is enduring. His work not only revolutionized mathematics but also impacted philosophy, linguistics, computer science, and perhaps even cosmology. The existence of truths that are knowable but necessarily unprovable—G?del's conclusion inspired waves of discoveries and innovations, from neural networks to computational theory. The dream of achieving complete, consistent knowledge of the end of human spirit—G?del's incompleteness theorems have thus erected a monument.