John Randolph Lucas (18 June 1929 – 5 April 2020) was a British philosopher.

Biography

Lucas was educated at

Winchester College Winchester College is a public school (fee-charging independent day and boarding school) in Winchester, Hampshire, England. It was founded by William of Wykeham in 1382 and has existed in its present location ever since. It is the oldest of ...

and then, as a pupil of R.M. Hare, among others, at

Balliol College, Oxford Balliol College () is one of the constituent colleges of the University of Oxford in England. One of Oxford's oldest colleges, it was founded around 1263 by John I de Balliol, a landowner from Barnard Castle in County Durham, who provided the ...

. 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 Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...

, studying mathematics and logic. For 36 years, until his 1996 retirement, he was a Fellow and Tutor of

Merton College, Oxford Merton College (in full: The House or College of Scholars of Merton in the University of Oxford) is one of the constituent colleges of the University of Oxford in England. Its foundation can be traced back to the 1260s when Walter de Merton, ...

, and he remained an emeritus member of the University Faculty of Philosophy. He was a Fellow of the

British Academy The British Academy is the United Kingdom's national academy for the humanities and the social sciences. It was established in 1902 and received its royal charter in the same year. It is now a fellowship of more than 1,000 leading scholars s ...

. Lucas is perhaps best known for his paper "

Minds, Machines and Gödel "Minds, Machines and Gödel" is J. R. Lucas's 1959 philosophical paper in which he argues that a human mathematician cannot be accurately represented by an algorithmic automaton. Appealing to Gödel's incompleteness theorem, he argues that for a ...

," arguing that an

automaton An automaton (; plural: automata or automatons) is a relatively self-operating machine, or control mechanism designed to automatically follow a sequence of operations, or respond to predetermined instructions.Automaton – Definition and More ...

cannot represent a human mathematician, attempting to refute

computationalism In philosophy of mind, the computational theory of mind (CTM), also known as computationalism, is a family of views that hold that the human mind is an information processing system and that cognition and consciousness together are a form of c ...

. An author with diverse teaching and research interests, Lucas wrote on the

philosophy of mathematics The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people' ...

, especially the implications of Gödel's incompleteness theorem, the

philosophy of mind Philosophy of mind is a branch of philosophy that studies the ontology and nature of the mind and its relationship with the body. The mind–body problem is a paradigmatic issue in philosophy of mind, although a number of other issues are add ...

free will and determinism Free may refer to: Concept * Freedom, having the ability to do something, without having to obey anyone/anything * Freethought, a position that beliefs should be formed only on the basis of logic, reason, and empiricism * Emancipate, to procure ...

, the

philosophy of science Philosophy of science is a branch of philosophy concerned with the foundations, methods, and implications of science. The central questions of this study concern what qualifies as science, the reliability of scientific theories, and the ultim ...

including one book on physics co-authored with Peter E. Hodgson,

causality Causality (also referred to as causation, or cause and effect) is influence by which one event, process, state, or object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the cau ...

political philosophy Political philosophy or political theory is the philosophical study of government, addressing questions about the nature, scope, and legitimacy of public agents and institutions and the relationships between them. Its topics include politics, ...

, ethics and

business ethics Business ethics (also known as Corporate Ethics) is a form of applied ethics or professional ethics, that examines ethical principles and moral or ethical problems that can arise in a business environment. It applies to all aspects of business c ...

, and the

philosophy of religion Philosophy of religion is "the philosophical examination of the central themes and concepts involved in religious traditions". Philosophical discussions on such topics date from ancient times, and appear in the earliest known texts concerning p ...

. The son of a

Church of England The Church of England (C of E) is the established Christian church in England and the mother church of the international Anglican Communion. It traces its history to the Christian church recorded as existing in the Roman province of Brit ...

clergyman, and an Anglican himself, Lucas described himself as "a dyed-in-the-wool traditional Englishman." He had four children
EdwardHelenRichard
and Deborah) with Morar Portal, among them Edward Lucas, a former journalist at ''

The Economist ''The Economist'' is a British weekly newspaper printed in demitab format and published digitally. It focuses on current affairs, international business, politics, technology, and culture. Based in London, the newspaper is owned by The Eco ...

''. In addition to his philosophical career, Lucas had a practical interest in

. He helped found the Oxford Consumers' Group, and was its first chairman in 1961–3, serving again in 1965.

Philosophical contributions

Free will

Lucas (1961) began a lengthy and heated

debate Debate is a process that involves formal discourse on a particular topic, often including a moderator and audience. In a debate, arguments are put forward for often opposing viewpoints. Debates have historically occurred in public meetings, a ...

over the implications of

Gödel's incompleteness theorems Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the phil ...

for the anthropic mechanism thesis, by arguing that: #

Determinism Determinism is a philosophical view, where all events are determined completely by previously existing causes. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and cons ...

↔ For any human ''h'' there exists at least one (deterministic)

logical system A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A for ...

''L''(''h'') which reliably predicts ''hs actions in all circumstances. # For any logical system ''L'' a sufficiently skilled

mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of forma ...

ian (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 ''ms actions in all circumstances. # Hence ''m'' has

free will Free will is the capacity of agents to choose between different possible courses of action unimpeded. Free will is closely linked to the concepts of moral responsibility, praise, culpability, sin, and other judgements which apply only to ac ...

. # 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 Hava Siegelmann is a professor of computer science. Her academic position is in the school of Computer Science and the Program of Neuroscience and Behavior at the University of Massachusetts Amherst; she is the director of the school's Biologica ...

in the 1990s that sufficiently complex analogue recurrent neural networks are more powerful than

Turing Machine A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer alg ...

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'' 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 In the philosophy of space and time, eternalism is an approach to the ontological nature of time, which takes the view that all existence in time is equally ''real'', as opposed to presentism or the growing block universe theory of time, in wh ...

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" 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"''The Future'' (1989), p. 4.

Timeline

*1942-7. Scholar of

*1947–51. Attended

on a scholarship. *1951. BA with 1st Class Honours, Greats. *1951-3. Harmsworth Senior Scholar,

. *1952. John Locke Scholarship,

Oxford University Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...

. *1953-6. Junior Research Fellow,

. *1956-9. Fellow and Assistant Tutor,

Corpus Christi College, Cambridge Corpus Christi College (full name: "The College of Corpus Christi and the Blessed Virgin Mary", often shortened to "Corpus"), is a constituent college of the University of Cambridge. From the late 14th century through to the early 19th centur ...

. *1957-8. Jane Eliza Procter Visiting Fellow,

. *1959–60.

Leverhulme The Leverhulme Trust () is a large national grant-making organisation in the United Kingdom. It was established in 1925 under the will of the 1st Viscount Leverhulme (1851–1925), with the instruction that its resources should be used to suppo ...

Research Fellow, the

University of Leeds , mottoeng = And knowledge will be increased , established = 1831 – Leeds School of Medicine1874 – Yorkshire College of Science1884 - Yorkshire College1887 – affiliated to the federal Victoria University1904 – University of Leeds , ...

. *1960–96. Fellow and Tutor of

. *1988. Elected a Fellow of the

. *1990-6. Reader in Philosophy,

. *1991-3. President, British Society for the Philosophy of Science.

Books

*1966. ''Principles of Politics''. *1970. '' The Concept of Probability''. *1970. ''The Freedom of the Will''. *1972
''The Nature of Mind''
(with A. J. P. Kenny, H. C. Longuet-Higgins, and C. H. Waddington; 1972

Gifford Lectures The Gifford Lectures () are an annual series of lectures which were established in 1887 by the will of Adam Gifford, Lord Gifford. Their purpose is to "promote and diffuse the study of natural theology in the widest sense of the term – in o ...

) *1973
''The Development of Mind''
(with A. J. P. Kenny, H.C.Longet-Higgins, and C.H.Waddington; 1973

) *1973. '' A Treatise on Time and Space''. *1976. '' Freedom and Grace''. *1976. ''Democracy and Participation''. *1978. ''Butler's Philosophy of Religion Vindicated''. *1980. '' On Justice''. *1985. ''Space, Time and Causality: an essay in natural philosophy''. *1989. '' The Future: an essay on God, temporality, and truth'' *1990. ''Spacetime and Electromagnetism'' (with Peter E. Hodgson) . *1993. '' Responsibility''. *1997. ''Ethical Economics'' (with M. R. Griffiths). *2000. ''Conceptual Roots of Mathematics''. *2003. ''An Engagement with Plato's Republic'' (with B.G. Mitchell). *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 and Softback is *2016. ''Value Economics: The Ethical Implications of Value for New Economic Thinking'' (with M.R. Griffiths). *2021. ''L’economia del valore'' (Italian translation, also with M.R. Griffiths).