James F. Thomson (philosopher)
Encyclopedia
James F. Thomson was a British philosopher who devised the puzzle of Thomson's lamp
(a variation on Zeno's paradox), to argue against the possibility of supertask
s (a word he also coined.)
in 1949. He was an assistant in the Department of Philosophy, and John Stuart Mill Scholar at University College, London, 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
from 1953–1956. Thomson was appointed Fellow and Tutor in Philosophy, Corpus Christi College
, Oxford
, in 1956, and also University Lecturer at Columbia University
. He was visiting professor at Columbia from 1961–1962, and in 1963 he was appointed professor of philosophy at MIT.
. They separated in 1976 and divorced in 1980; they remained colleagues until James Thomson’s death in 1984.
, Thomson considered the successful completion of an infinite number of tasks within a given time, to which he gave the name supertasks.
To disprove the possibility of supertasks, he introduced Thomson's lamp, a thought experiment similar to Zeno's paradoxes. This problem involves the mathematical summation
of an infinite divergent series
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
in a 1962 paper 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
and the foundation of supertask theory.
Thomson's lamp
Thomson's lamp is a puzzle that is a variation on Zeno's paradoxes. It was devised by philosopher James F. Thomson, who also coined the term supertask....
(a variation on Zeno's paradox), to argue against the possibility of supertask
Supertask
In philosophy, a supertask is a quantifiably infinite number of operations that occur sequentially within a finite interval of time. Supertasks are called "hypertasks" when the number of operations becomes innumerably infinite. The term supertask was coined by the philosopher James F...
s (a word he also coined.)
Academic career
Thomson was born in London in 1921 and graduated from the University of LondonUniversity of London
-20th century:Shortly after 6 Burlington Gardens was vacated, the University went through a period of rapid expansion. Bedford College, Royal Holloway and the London School of Economics all joined in 1900, Regent's Park College, which had affiliated in 1841 became an official divinity school of the...
in 1949. He was an assistant in the Department of Philosophy, and John Stuart Mill Scholar at University College, London, 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
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
from 1953–1956. Thomson was appointed Fellow and Tutor in Philosophy, Corpus Christi College
Corpus Christi College
Corpus Christi College can refer to the following colleges:*Corpus Christi College, Cambridge*Corpus Christi College, Oxford*Corpus Christi College *Corpus Christi College, Melbourne...
, Oxford
Oxford
The city of Oxford is the county town of Oxfordshire, England. The city, made prominent by its medieval university, has a population of just under 165,000, with 153,900 living within the district boundary. It lies about 50 miles north-west of London. The rivers Cherwell and Thames run through...
, in 1956, and also University Lecturer at Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
. He was visiting professor at Columbia from 1961–1962, and in 1963 he was appointed professor of philosophy at MIT.
Family life
In 1962 he married the American philosopher Judith Jarvis ThomsonJudith Jarvis Thomson
Judith Jarvis Thomson is an American moral philosopher and metaphysician, best known for her use of thought experiments to make philosophical points.- Career :...
. 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 BlackMax Black
Max Black was a British-American philosopher, who was a leading influential figure in analytic philosophy in the first half of the twentieth century. He made contributions to the philosophy of language, the philosophy of mathematics and science, and the philosophy of art, also publishing studies...
, Thomson considered the successful completion of an infinite number of tasks within a given time, to which he gave the name supertasks.
To disprove the possibility of supertasks, he introduced Thomson's lamp, a thought experiment similar to Zeno's paradoxes. This problem involves the mathematical summation
Summation
Summation is the operation of adding a sequence of numbers; the result is their sum or total. If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation. The numbers to be summed may be integers, rational numbers,...
of an infinite divergent series
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 limit....
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
Limit of a sequence
The limit of a sequence is, intuitively, the unique number or point L such that the terms of the sequence become arbitrarily close to L for "large" values of n...
). This apparent contradiction led him to reject the possibility of the experiment, and therefore the possibility of supertasks.
However, Paul Benacerraf
Paul Benacerraf
Paul Joseph Salomon Benacerraf is an American philosopher working in the field of the philosophy of mathematics who has been teaching at Princeton University since he joined the faculty in 1960. He was appointed Stuart Professor of Philosophy in 1974, and recently retired as the James S....
in a 1962 paper 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
Infinitism
Infinitism is the view that knowledge may be justified by an infinite chain of reasons. It belongs to epistemology, the branch of philosophy that considers the possibility, nature, and means of knowledge.-Epistemological infinitism:...
, set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
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.)
See also
- British philosophyBritish philosophyBritish philosophy refers to the philosophical tradition of the people of the United Kingdom and of its citizens abroad.-Roger Bacon:Roger Bacon, O.F.M. , also known as Doctor Mirabilis , was an English philosopher and Franciscan friar who placed considerable emphasis on empirical methods...
- Moral philosophy
- Ross–Littlewood paradoxRoss–Littlewood paradoxThe Ross–Littlewood paradox is a hypothetical problem in abstract mathematics and logic designed to illustrate the seemingly paradoxical, or at least non-intuitive, nature of infinity...
- Zeno machineZeno machineIn mathematics and computer science, Zeno machines are a hypothetical computational model related to Turing machines that allows a countably infinite number of algorithmic steps to be performed in finite time...