Wednesday, July 11, 2007

Bertrand Russell's Logic, mathematics, and the Computer

One should read and study the works of Bertrand Russell. He has been described by great mathematicians as the greatest logician since Aristotle. Indeed, Russell showed that there were many forms of inferences than Aristotle had thought three thousand years ago. Aristotle tried to guard against fallacious reasoning by making a complete list – they might be called working rules – of all forms of deduction which are valid. Aristotle decided that these were nearly all syllogistic: for example, “All men are mortal, Socrates is a man, therefore Socrates is mortal.” Russell showed how much more there was to logic, and that syllogisms should have no such pre-eminence. But that is not all. When asked why Russell was a great logician, there is another important answer which is somewhat a paradoxical one; it was because he showed how little logic can do. Meantime, Russell not only insisted on the importance of philosophy and science to each other, he also tried to redefine the fundamental principles of mathematics on a few basic laws of logic. The whole project may have been misconceived and a grand failure, but it helped to make modern logic the analytical tool that it is today. Though he himself never realized it, Russell was, indeed, one of the founders of the modern computer age. Yes sir, that's the machine facing you right now at this very moment! Poch Suzara

No comments: