Best known for his Incompleteness Theorem, Kurt Gödel (1906-1978) is considered one of the most important mathematicians and logicians of the 20th century. By showing that the establishment of a set of axioms encompassing all of mathematics would never succeed, he revolutionized the world of mathematics, logic and philosophy.
John Randolph Lucas is a former Fellow and Tutor of Merton College, Oxford and remains an emeritus member of the University Faculty of Philosophy. He is a Fellow of the British Academy.
Although best known for his paper "Minds, Machines and Gödel", where he argues that an automaton cannot represent a human mathematician, Lucas has written widely on a diverse range of topics. His main area of research has focused on philosophy of mathematics, especially the implications of Gödel’s incompleteness theorem, the philosophy of mind, free will and determinism, the philosophy of science with special reference to special relativity, causality, political philosophy, ethics and business ethics, and the philosophy of religion. He is the author of Reason and Reality, A Treatise on Time & Space, Spacetime and Electromagnetism and On Justice.
Q: When did you first become acquainted with Kurt Gödel and his Incompleteness Theorems? And what was it about his work that impressed you?
A: I first heard a mention of a strange piece of work that coded things with prime numbers in June 1948, talking to a tutor about switching from Mathematics to "Greats" (Philosophy and Ancient History). I probably was trying to explain a thought that had come to me earlier at school when I had been listening to an essay by one of my contemporaries, who was putting forward an extremely materialistic world-view. I countered that if such a view was true, there was no room for truth or rational conviction: he could not hope to persuade me that it was true; if I came to believe it, it would only be because he had successfully manipulated my nervous system, not because it was true, and I had been rationally convinced by his arguments.While I was reading philosophy as an undergraduate, I made considerable use of this type of argument, using it to refute the Verification Principle, Marxism, and Freudianism. But I found great difficulty in formulating it in a water-tight way. There were great difficulties in securing self-reference. Russell’s Theory of Types stood in the way of most of my efforts. Gödel, however, had managed to circumvent the difficulties. So when my Junior Research Fellowship at Merton was coming to an end, I decided to go to Princeton, and really master it.
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