Topic Archive: Goedel
The road from Leibniz to Turing: from syllogisms to computations. Tribute to Alan Turing.
A group of brilliant innovators spanning three centuries were concerned with the nature of human reason. This endeavor led to the all-purpose digital computer. Except for Turing, none of them had any idea that his work might have such a tremendous application to our modern world. Leibniz saw far, but not that far. Boole could hardly have imagined that his algebra of logic would be used to design complex electronic circuits. Frege would have been amazed to find equivalents of his logical rules incorporated into computer programs for carrying out deductions. Cantor certainly never anticipated the ramifications of his diagonal method. Hilbert’s program to secure the foundations of mathematics was pointed in a very different direction. And Goedel, living his life of the mind, hardly thought of application to mechanical devices (M. Davis). However, Turing’s great vision has now been realized.