Richard Carl Jeffrey (August 5, 1926 – November 9, 2002) was an American philosopher,

logician Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

, and probability theorist. He is best known for developing and championing the philosophy of

radical probabilism Radical probabilism is a hypothesis in philosophy, in particular epistemology, and probability theory that holds that no facts are known for certain. That view holds profound implications for statistical inference. The philosophy is particularly ass ...

and the associated

heuristic A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate ...

probability kinematics Radical probabilism is a hypothesis in philosophy, in particular epistemology, and probability theory that holds that no facts are known for certain. That view holds profound implications for statistical inference. The philosophy is particularly ass ...

, also known as Jeffrey conditioning.

Life and career

Born in Boston, Massachusetts, Jeffrey served in the

U.S. Navy The United States Navy (USN) is the maritime service branch of the United States Armed Forces and one of the eight uniformed services of the United States. It is the largest and most powerful navy in the world, with the estimated tonnage o ...

during

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing ...

. As a graduate student he studied under Rudolf Carnap and Carl Hempel. He received his

M.A. A Master of Arts ( la, Magister Artium or ''Artium Magister''; abbreviated MA, M.A., AM, or A.M.) is the holder of a master's degree awarded by universities in many countries. The degree is usually contrasted with that of Master of Science. Tho ...

from the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

in 1952 and his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

from

Princeton 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 ni ...

in 1957. After holding academic positions at

MIT The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the m ...

, City College of New York, Stanford University, and the

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...

, he joined the faculty of Princeton in 1974 and became a professor emeritus there in 1999. He was also a visiting professor at the

University of California, Irvine The University of California, Irvine (UCI or UC Irvine) is a public land-grant research university in Irvine, California. One of the ten campuses of the University of California system, UCI offers 87 undergraduate degrees and 129 graduate and p ...

. Jeffrey, who died of

lung cancer Lung cancer, also known as lung carcinoma (since about 98–99% of all lung cancers are carcinomas), is a malignant lung tumor characterized by uncontrolled cell growth in tissues of the lung. Lung carcinomas derive from transformed, malign ...

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 Epistemology (; ), or the theory of knowledge, is the branch of philosophy concerned with knowledge. Epistemology is considered a major subfield of philosophy, along with other major subfields such as ethics, logic, and metaphysics. Epis ...

and

decision theory Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical ...

. He is perhaps best known for defending and developing the

Bayesian Thomas Bayes (/beɪz/; c. 1701 – 1761) was an English statistician, philosopher, and Presbyterian minister. Bayesian () refers either to a range of concepts and approaches that relate to statistical methods based on Bayes' theorem, or a followe ...

approach to probability. Jeffrey also wrote, or co-wrote, two widely used and influential

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...

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 and

Tarski's indefinability theorem Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics. Informally, the theorem states that ''arithmetical truth ...

Radical probabilism

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 pr ...

, Bayes' theorem 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 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 In gambling, a Dutch book or lock is a set of odds and bets, established by the bookmaker, that ensures that the bookmaker will profit—at the expense of the gamblers—regardless of the outcome of the event (a horse race, for example) on which ...

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 Clarence Irving Lewis (April 12, 1883 – February 3, 1964), usually cited as C. I. Lewis, was an American academic philosopher. He is considered the progenitor of modern modal logic and the founder of conceptual pragmatism. First a noted logic ...

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 Cromwell's rule, named by statistician Dennis Lindley, states that the use of prior probabilities of 1 ("the event will definitely occur") or 0 ("the event will definitely not occur") should be avoided, except when applied to statements that ar ...

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 In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which can be realized via several distinct eve ...

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 Edwin Thompson Jaynes (July 5, 1922 – April 30, 1998) was the Wayman Crow Distinguished Professor of Physics at Washington University in St. Louis. He wrote extensively on statistical mechanics and on foundations of probability and statisti ...

maximum entropy principle The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge about a system is the one with largest entropy, in the context of precisely stated prior data (such as a proposition ...

and

Brian Skyrms Brian Skyrms (born 1938) is an American philosopher, Distinguished Professor of Logic and Philosophy of Science and Economics at the University of California, Irvine, and a professor of philosophy at Stanford University. He has worked on problem ...

principle of reflection A principle is a proposition or value that is a guide for behavior or evaluation. In law, it is a rule that has to be or usually is to be followed. It can be desirably followed, or it can be an inevitable consequence of something, such as the law ...

. Jeffrey conditioning can be generalized from partitions to arbitrary condition events by giving it a frequentist semantics.

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 (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 George Stephen Boolos (; 4 September 1940 – 27 May 1996) was an American philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology. Life Boolos is of Greek-Jewish descent. He graduated with an A.B. i ...

and John P. Burgess). 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 Jeffrey
in the

Dictionary of Modern American Philosophers ''The Dictionary of Modern American Philosophers'' is a 2005 four-volume biographical reference work edited by John R. Shook, then of Oklahoma State University, published by Thoemmes Continuum. Its consulting editors were Richard T. Hull, Bruce ...

br>and Remarks on Dick Jeffrey given during his 2003 Memorial Service
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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 1926 births 2002 deaths 20th-century American non-fiction writers 20th-century American philosophers 20th-century essayists 21st-century American non-fiction writers 21st-century American philosophers 21st-century essayists American logicians American male essayists American male non-fiction writers American philosophy academics Analytic philosophers City College of New York faculty Deaths from lung cancer Epistemologists People from Boston Philosophers of logic Philosophers of science Philosophy writers Princeton University alumni Stanford University Department of Philosophy faculty University of Chicago alumni University of Pennsylvania faculty 20th-century American male writers 21st-century American male writers