Richard Carl Jeffrey (August 5, 1926 – November 9, 2002) was an American
philosopher
A philosopher is a person who practices or investigates philosophy. The term ''philosopher'' comes from the grc, φιλόσοφος, , translit=philosophos, meaning 'lover of wisdom'. The coining of the term has been attributed to the Greek th ...
,
logician, and
probability theorist. He is best known for developing and championing the philosophy of
radical probabilism and the associated
heuristic of
probability kinematics, also known as
Jeffrey conditioning.
Life and career
Born in
Boston, Massachusetts, Jeffrey served in the
U.S. Navy during
World War II. As a graduate student he studied under
Rudolf Carnap
Rudolf Carnap (; ; 18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism. He ...
and
Carl Hempel
Carl Gustav "Peter" Hempel (January 8, 1905 – November 9, 1997) was a German writer, philosopher, logician, and epistemologist. He was a major figure in logical empiricism, a 20th-century movement in the philosophy of science. He is espec ...
. He received his
M.A. from the
University of Chicago in 1952 and his
Ph.D. from
Princeton in 1957. After holding academic positions at
MIT,
City College of New York
The City College of the City University of New York (also known as the City College of New York, or simply City College or CCNY) is a public university within the City University of New York (CUNY) system in New York City. Founded in 1847, Cit ...
,
Stanford University
Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...
, and the
University of Pennsylvania, he joined the faculty of Princeton in 1974 and became a professor
emeritus
''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...
there in 1999. He was also a visiting professor at the
University of California, Irvine.
Jeffrey, who died of
lung cancer at the age of 76, was known for his sense of humor, which often came through in his breezy writing style. In the preface of his posthumously published ''Subjective Probability'', he refers to himself as "a fond foolish old fart dying of a surfeit of
Pall Malls".
Philosophical work
As a philosopher, Jeffrey specialized in
epistemology and
decision theory. He is perhaps best known for defending and developing the
Bayesian approach to probability.
Jeffrey also wrote, or co-wrote, two widely used and influential
logic textbooks: ''Formal Logic: Its Scope and Limits'', a basic introduction to logic, and ''Computability and Logic'', a more advanced text dealing with, among other things, the famous negative results of twentieth-century logic such as
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research i ...
and
Tarski's indefinability theorem.
Radical probabilism
In
frequentist statistics
Frequentist inference is a type of statistical inference based in frequentist probability, which treats “probability” in equivalent terms to “frequency” and draws conclusions from sample-data by means of emphasizing the frequency or pro ...
,
Bayes' theorem
In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For examp ...
provides a useful rule for updating a probability when new frequency data becomes available. In Bayesian statistics, the theorem itself plays a more limited role. Bayes' theorem connects probabilities that are held simultaneously. It does not tell the learner how to update probabilities when new evidence becomes available over time. This subtlety was first pointed out in terms by
Ian Hacking
Ian MacDougall Hacking (born February 18, 1936) is a Canadian philosopher specializing in the philosophy of science. Throughout his career, he has won numerous awards, such as the Killam Prize for the Humanities and the Balzan Prize, and been ...
in 1967.
However, adapting Bayes' theorem, and adopting it as a rule of updating, is a temptation. Suppose that a learner forms probabilities ''P''
old(''A''&''B'')=''p'' and ''P''
old(''B'')=''q''.
If the learner subsequently learns that ''B'' is true, nothing in the axioms of probability or the results derived therefrom tells him how to behave. He might be tempted to adopt Bayes' theorem by analogy and set his ''P''
new(''A'') = ''P''
old(''A'' , ''B'') = ''p''/''q''.
In fact, that step, Bayes' rule of updating, can be justified, as necessary and sufficient, through a ''dynamic''
Dutch book argument that is additional to the arguments used to justify the axioms. This argument was first put forward by
David Lewis in the 1970s though he never published it.
That works when the new data is certain.
C. I. Lewis had argued that "If anything is to be probable then something must be certain". There must, on Lewis' account, be some certain facts on which probabilities were
conditioned. However, the principle known as
Cromwell's rule declares that nothing, apart from a logical law, can ever be certain, if that. Jeffrey famously rejected Lewis' ''dictum'' and quipped, "It's probabilities all the way down." He called this position ''radical probabilism''.
In this case Bayes' rule isn't able to capture a mere subjective change in the probability of some critical fact. The new evidence may not have been anticipated or even be capable of being articulated after the event. It seems reasonable, as a starting position, to adopt the
law of total probability and extend it to updating in much the same way as was Bayes' theorem.
: ''P''
new(''A'') = ''P''
old(''A'' , ''B'')''P''
new(''B'') + ''P''
old(''A'' , not-''B'')''P''
new(not-''B'')
Adopting such a rule is sufficient to avoid a Dutch book but not necessary. Jeffrey advocated this as a rule of updating under radical probabilism and called it probability kinematics. Others have named it Jeffrey conditioning.
It is not the only sufficient updating rule for radical probabilism. Others have been advocated including
E. T. Jaynes'
maximum entropy principle and
Brian Skyrms'
principle of reflection.
Jeffrey conditioning can be generalized from partitions to arbitrary condition events by giving it a frequentist semantics.
See also
*
Bayesian epistemology
Selected bibliography
* ''Formal Logic: Its Scope and Limits''. 1st ed. McGraw Hill, 1967.
** 2nd ed. McGraw Hill, 1981.
** 3rd ed. McGraw Hill, 1990.
** 4th ed.,
John P. Burgess
John Patton Burgess (born 5 June 1948) is an American philosopher. He is John N. Woodhull Professor of Philosophy at Princeton University where he specializes in logic and philosophy of mathematics.
Education and career
Burgess received his Ph.D ...
(editor), Hackett Publishing, 2006,
* ''The Logic of Decision''. 2nd ed. University of Chicago Press, 1990.
* ''Probability and the Art of Judgment''. Cambridge University Press, 1992.
* ''Computability and Logic'' (with
George Boolos and
John P. Burgess
John Patton Burgess (born 5 June 1948) is an American philosopher. He is John N. Woodhull Professor of Philosophy at Princeton University where he specializes in logic and philosophy of mathematics.
Education and career
Burgess received his Ph.D ...
). 4th ed. Cambridge University Press, 2002.
* ''Subjective Probability: The Real Thing''. Cambridge University Press, 2004.
References
External links
His website at Princeton; includes several manuscripts, including ''Subjective Probability''by philosophe
Mathias Rissethe then forthcoming entry on Jeffreyin the
Dictionary of Modern American Philosophersbr>
and Remarks on Dick Jeffrey given during his 2003 Memorial Service rchived on Wayback Machine">Wayback_Machine.html" ;"title="rchived on Wayback Machine">rchived on Wayback Machine
Stanford Encyclopedia of Philosophy entry on Bayes' Theorem(discusses Jeffrey conditioning)
Tribute, by Brian Skyrms''In Memory of Richard Jeffrey: Some Reminiscences, and Some Reflections on The Logic Of Decision'' by Alan Hájek {Archived on Wayback Machine].
Guide to the Richard C. Jeffrey Papers, 1934-2002 ASP.2003.02, Archives of Scientific Philosophy, Special Collections Department, University of Pittsburgh)
{{DEFAULTSORT:Jeffrey, Richard
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