Philosophical reflection on formalism mentioning Kurt Gédel, Bertrand Russell, and David Hilbert

Known Unknowns 193 caused you to trip? You could go on forever, generating rules to cover every eventuality. Clearly, in the fuzzy world of human endeavor, truth and rules often part company. Yet, we all assume math- ematics is free of such uncertainty. Let me tell you this is not so. The brilliant mathematician Kurt Gédel proved see eee this when he was just 22, and his proof a es says something fundamental about the 4 rs /, : nature of knowledge. a has The story of his discovery involves some of the greatest mathematical thinkers in history. My introduction to it came about from a chance accident. I became ill in my first year at University (mononucleosis, otherwise know as glandular fever, if youre curious) and was eventu- ally sent home to recover. Lying in bed for two months is boring. So to pass the time my mother suggested I read Bertrand Russell's, The History of Western Philosophy. | think she figured I had plenty of time, so picked a thick book. This nearly 800-page tome charts the entire history of philosophy from the time of the ancient Greeks. I presumed Russell was a philosophy professor, but he was originally a mathematician. He was a mathematician. And because he lived and worked productively for almost all of his 97 years, spanning much of the 19" and 20" centuries, he crops up repeatedly as a central figure in many areas of intellectual life. Russell the politician, Russell the philosopher, Russell the mathematician and Russell the peace campaigner are all the same man — not, as I had incorrectly first guessed, a prolific family. In his early career, Bertrand Russell was a Fellow of Trinity College, Cambridge, working on a broad range of mathematical problems. Meanwhile, in Germany, his contem- porary David Hilbert, also a polymath, held the chair of mathematics at Gottingen University. Both men shared a common objective: to tidy up the loose ends in mathematics and set down the rules once and for all. This movement was called Formalism. Kurt Gédel Formalism David Hilbert and Bertrand Russell believed you should be able to set out all the rules of mathematics even though it might be a complicated affair. Without contradiction or inconsistency you should be able to HOUSE_OVERSIGHT_015883