Inhabiting the uncomputable. Some reflections on Alan Turing’s research program

Abstract

Towards the end of the 1940s, Alan Turing had developed the idea that digital computers could reproduce human thinking and, in order to measure their intelligence, he proposed the famous “imitation game”, which later became known as the “Turing test”. Although it has sometimes been considered an operational definition of thinking or intelligence, in Turing’s view, the test only provided a sufficient condition for a machine’s behaviour to be considered intelligent. Turing arrived at these conclusions based on his work, which began in the 1930s, in the field of mathematical logic to demonstrate the unsolvability of David Hilbert’s Entscheidungsproblem. The present article aims to revisit some of Turing’s ideas on mathematical methods of proof, intelligence and computing machines, in order to demonstrate the fundamental influence they had on his pioneering research programme on artificial intelligence.