Lucas was educated at Winchester College and then, as a pupil of R.M. Hare, among others, at Balliol College, Oxford.[2] He studied first mathematics, then Greats (Greek, Latin, Philosophy and Ancient History), obtaining first class honours in both. He sat for Finals in 1951, and took his MA in 1954. He spent the 1957–58 academic year at Princeton University, studying mathematics and logic. For 36 years, until his 1996 retirement, he was a Fellow and Tutor of Merton College, Oxford, and he remained an emeritus member of the University Faculty of Philosophy. He was a Fellow of the British Academy.[3]
The son of a Church of England clergyman, and an Anglican himself, Lucas described himself as "a dyed-in-the-wool traditional Englishman." He had four children (Edward, Helen, Richard and Deborah) with Morar Portal, among them Edward Lucas, a former journalist at The Economist.
In addition to his philosophical career, Lucas had a practical interest in business ethics. He helped found the Oxford Consumers' Group,[4] and was its first chairman in 1961–3, serving again in 1965.
Determinism ↔ For any human h there exists at least one (deterministic) logical systemL(h) which reliably predicts h's actions in all circumstances.
For any logical system L a sufficiently skilled mathematical logician (equipped with a sufficiently powerful computer if necessary) can construct some statements T(L) which are true but unprovable in L. (This follows from Gödel's first theorem.)
If a human m is a sufficiently skillful mathematical logician (equipped with a sufficiently powerful computer if necessary) then if m is given L(m), he or she can construct T(L(m)) and determine that they are true—which L(m) cannot do.
Hence L(m) does not reliably predict m's actions in all circumstances.
It is implausible that the qualitative difference between mathematical logicians and the rest of the population is such that the former have free will and the latter do not.
His argument was strengthened by the discovery by Hava Siegelmann in the 1990s that sufficiently complex analogue recurrent neural networks are more powerful than Turing Machines.[6]
Space, time and causality
Lucas wrote several books on the philosophy of science and space-time (see below). In A treatise on time and space[7] he introduced a transcendental derivation of the Lorenz Transformations based on Red and Blue exchanging messages (in Russian and Greek respectively) from their respective frames of reference which demonstrates how these can be derived from a minimal set of philosophical assumptions.
In The Future Lucas gives a detailed analysis of tenses and time, arguing that "the Block universe gives a deeply inadequate view of time. It fails to account for the passage of time, the pre-eminence of the present, the directedness of time and the difference between the future and the past"[8] and in favour of a tree structure in which there is only one past or present (at any given point in spacetime) but a large number of possible futures. "We are by our own decisions in the face of other men's actions and chance circumstances weaving the web of history on the loom of natural necessity"[9]
2003. An Engagement with Plato's Republic (with B.G. Mitchell). ISBN0-7546-3366-7
2006. Reason and Reality, freely available as a series of .pdf files on Lucas's website (below). Also available as Reason and Reality: An Essay in Metaphysics by J. R. Lucas (494 pages, December 2009): Hardback is ISBN978-1-934297-04-9 and Softback is ISBN978-1-934297-06-3
2016. Value Economics: The Ethical Implications of Value for New Economic Thinking (with M.R. Griffiths). ISBN9781349958986
2021. L’economia del valore (Italian translation, also with M.R. Griffiths).ISBN9788804729099
