James F. Thomson (1921–1984) was a British philosopher who devised the puzzle of

Thomson's lamp Thomson's lamp is a philosophical puzzle based on infinites. It was devised in 1954 by British philosopher James F. Thomson, who used it to analyze the possibility of a supertask, which is the completion of an infinite number of tasks. Conside ...

, to argue against the possibility of

supertask In philosophy, a supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time. Supertasks are called hypertasks when the number of operations becomes uncountably infinite. A hypertask that in ...

s (a word he also coined)

Academic career

Thomson was born in London in 1921 and graduated from the

University of London The University of London (UoL; abbreviated as Lond or more rarely Londin in Post-nominal letters, post-nominals) is a collegiate university, federal Public university, public research university located in London, England, United Kingdom. The ...

in 1949. He was an assistant in the Department of Philosophy, and John Stuart Mill Scholar at

University College, London University College London (Trade name, branded as UCL) is a Public university, public research university in London, England. It is a Member institutions of the University of London, member institution of the Federal university, federal Uni ...

, from 1949–1950. He was Commonwealth Fund Fellow at Harvard and Princeton from 1950–1951; assistant lecturer at University College from 1951–1953 and University Lecturer in Moral Science at the

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

from 1953–1956. Thomson was appointed Fellow and Tutor in Philosophy, Corpus Christi College,

Oxford Oxford () is a City status in the United Kingdom, cathedral city and non-metropolitan district in Oxfordshire, England, of which it is the county town. The city is home to the University of Oxford, the List of oldest universities in continuou ...

, in 1956, and also University Lecturer at

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

. He was visiting professor at Columbia from 1961–1962, and in 1963 he was appointed professor of philosophy at

MIT The Massachusetts Institute of Technology (MIT) is a private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and sc ...

Family life

In 1962 he married the American philosopher

Judith Jarvis Thomson Judith Jarvis Thomson (October 4, 1929November 20, 2020) was an American philosopher who studied and worked on ethics and metaphysics. Her work ranges across a variety of fields, but she is most known for her work regarding the thought experimen ...

. They separated in 1976 and divorced in 1980; they remained colleagues until James Thomson’s death in 1984.

Thomson's lamp

In a seminal 1954 article which followed on from the work of

Max Black Max Black (February 24, 1909 – August 27, 1988) was a Russian-born British-American philosopher who was a leading figure in analytic philosophy in the years after World War II. He made contributions to the philosophy of language, the philosoph ...

, Thomson considered the successful completion of an infinite number of tasks within a given time, to which he gave the name

supertasks In philosophy, a supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time. Supertasks are called hypertasks when the number of operations becomes uncountably infinite. A hypertask that inc ...

. To disprove the possibility of supertasks, he introduced Thomson's lamp, a thought experiment similar to

Zeno's paradoxes Zeno's paradoxes are a series of philosophical arguments presented by the ancient Greek philosopher Zeno of Elea (c. 490–430 BC), primarily known through the works of Plato, Aristotle, and later commentators like Simplicius of Cilicia. Zeno de ...

. This problem involves the mathematical

summation In mathematics, summation is the addition of a sequence of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, pol ...

of an infinite

divergent series In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit. If a series converges, the individual terms of the series mus ...

such as Grandi's. A lamp (which may be on or off at the start of the thought-experiment) is flicked on and off an infinite number of times within a 2-minute period. This corresponds to the ordered sequence t=0, t=0.5, t=0.75, t=0.875, ... According to Thomson, although the lamp must be either on or off at the end of the experiment when t=1, the state of the lamp – after an infinite number of switches – is also completely undetermined (i.e. the sequence has no limit). This apparent contradiction led him to reject the possibility of the experiment, and therefore the possibility of supertasks. However,

Paul Benacerraf Paul Joseph Salomon Benacerraf (; 26 March 1930 – 13 January 2025) was a French-born American philosopher working in the field of the philosophy of mathematics who taught at Princeton University his entire career, from 1960 until his retirement ...

in a 1962 paperBenacerraf, Paul. "Tasks, super-tasks, and modern eleatics", ''Journal of Philosophy'' LIX (1962), pp.765-784. successfully criticised Thomson's argument, by pointing out that the states of the lamp during the experiment do not logically determine the final state of the lamp when t=1. Thomson's conditions for the experiment are insufficiently complete, since only instants of time before t≡1 are considered. Benacerraf's essay led to a renewed interest in infinity-related problems,

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...

and the foundation of supertask theory.

Selected bibliography

*''A note on truth''. Analysis, 1949 *''The argument from analogy and our knowledge of other minds''. Mind, 1951 *''Some Remarks on Synonymy''. Analysis, 1952 *''Symposium: Reducibility''. (with Warnock, G. J. and Braithwaite, R. B.) Aristotelian Society, 1952 *''On Referring''. The Journal of Symbolic Logic, 1953 *''Tasks and super-tasks''. Analysis, 1954 *''Recent Criticisms of Russell's Analysis of Existence.'' The Journal of Symbolic Logic, 1956 *''What Achilles should have said to the Tortoise''. Ratio, 1960 *''On some paradoxes''. Analytical Philosophy, 1962 *''Is existence a predicate?'' Aquinas Society, 1963 *''What is the will?'' in Freedom and the Will (ed Pears, D.F.) New York: St. Martin's Press, 1963 *''In defense of material implication''. Journal of Philosophy, 1966 *''Truth-bearers and the Trouble about Propositions''. The Journal of Philosophy, 1969 *''Comments on Professor Benacerraf's Paper'' in ''Zeno's Paradoxes'' (ed. Salmon, W.), Bobbs-Merrill, 1970 *''In Defense of ⊃''. (1963/4) The Journal of Philosophy, 1990 (posth.)

References

{{DEFAULTSORT:Thomson, James F. 1921 births 1984 deaths 20th-century British philosophers Alumni of the University of London Academics of University College London Academics of the University of Cambridge Columbia University faculty Fellows of Corpus Christi College, Oxford MIT School of Humanities, Arts, and Social Sciences faculty British expatriates in the United States

Academic career

Family life

Thomson's lamp

Selected bibliography

See also

References