**Updated**

Below is my updated version of a preliminary bibliography on probability and Keynes’s theory of probability. Suggestions are welcome!

**GENERAL BIBLIOGRAPHY**

Bunge, M. 1981. “Four Concepts of Probability,”

*Applied Mathematical Modelling*5: 306–312.

Bunge, Mario. 1988. “Two Faces and Three Masks of Probability,” in Evandro Agazzi (ed.),

*Probability in the Sciences*. Kluwer Academic, Dordrecht and London. 27–50.

Fine, T. 1973.

*Theories of Probability*. Academic Press, Waltham, MA.

De Finetti, Bruno. 1972.

*Probability, Induction and Statistics: The Art of Guessing*. Wiley, London and New York.

De Finetti, Bruno. 1990.

*Theory of Probability: A Critical Introductory Treatment*. Wiley, Chichester.

Galavotti, M. C. 2005.

*Philosophical Introduction to Probability*. CSLI Publications, Stanford.

Gillies, D. 1973.

*An Objective Theory of Probability*. Methuen, London.

Gillies, D. 2000.

*Philosophical Theories of Probability*. Routledge, London.

Hacking, Ian. 1975.

*The Emergence of Probability: A Philosophical Study of Early Ideas about Probability, Induction and Statistical Inference*. Cambridge University Press, London.

Hacking, Ian. 2006.

*The Emergence of Probability: A Philosophical Study of Early Ideas about Probability, Induction and Statistical Inference*(2nd edn.). Cambridge University Press, Cambridge.

Howson, C. and Urbach, P. 1993.

*Scientific Reasoning: The Bayesian Approach*(2nd edn.). Open Court, La Salle, IL.

Johns, Richard. 2002.

*A Theory of Physical Probability*. University of Toronto Press, Toronto.

Kyburg, Henry E. and Mariam Thalos. 2002.

*Probability is the Very Guide of Life: The Philosophical Uses of Chance*. Eurospan, London.

Mellor, D. H. 2005.

*Probability: A Philosophical Introduction*. Routledge, London.

Salmon, Wesley Charles. 1967.

*Foundations of Scientific Inference*. University of Pittsburgh Press, Pittsburgh.

Savage, Leonard Jimmie. 1972.

*The Foundations of Statistics*(2nd rev. edn.). Dover, New York.

Schum, David A. 2001.

*The Evidential Foundations of Probabilistic Reasoning*. Northwestern University Press, Evanston, Ill.

Skyrms, B. 2000.

*Choice and Chance*(4th edn.). Wadsworth, Belmont, CA.

Taleb, Nassim Nicholas. 2007.

*The Black Swan: The Impact of the Highly Improbable*. Allen Lane, London.

Taleb, Nassim Nicholas. 2005.

*Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets*(2nd edn.), Random House, New York.

von Plato, J. 1994.

*Creating Modern Probability*. Cambridge University Press, Cambridge.

Weatherford, Roy. 1982.

*Philosophical Foundations of Probability Theory*. Routledge & Kegan Paul, London.

**Reviews of Keynes’s**

*Treatise on Probability*[Anonymous?] W. L. C. 1922. “A Treatise on Probability by John Maynard Keynes,”

*Journal of the Institute of Actuaries (1886-1994)*53.1: 78–83.

[Anonymous?] W. L. C. 1923. “A Treatise on Probability. by J. M. Keynes,”

*Journal of the American Statistical Association*18.141: 678–682.

[Anonymous]. 1924 “A Treatise on Probability by J.-M. Keynes,”

*Revue de Métaphysique et de Morale*31.1: 11–12.

Borel, Émile. 1924. “A propos d’un traité de probabilités,”

*Revue philosophique*98: 321–326.

Broad, C. D. 1922. “A Treatise on Probability. by J. M. Keynes,”

*Mind*n.s. 31.121: 72–85.

Costello, Harry T. 1923. “A Treatise on Probability by John Maynard Keynes,”

*The Journal of Philosophy*20.11: 301–306.

De Laguna, Theodore. 1930. “On Keynes’ Theory of Probability,”

*The Philosophical Review*39.3: 227–242.

Edgeworth, Francis Ysidro. 1922. “A Treatise on Probability by John Maynard Keynes,”

*Journal of the Royal Statistical Society*85.1: 107–113.

Edgeworth, Francis Ysidro. 1922. “The Philosophy of Chance,”

*Mind*n.s. 31.123: 257–283.

Fisher, R. A. 1923. “Mr. Keynes’s Treatise on Probability,”

*Eugenics Review*14: 46–50.

Foster, William S. 1922. “A Treatise on Probability by John Maynard Keynes,”

*The American Journal of Psychology*33.3: 439–442.

Joseph, H. W. B. 1923. “Mr. Keynes on Probability,”

*Mind*n.s. 32.128: 408–431.

Lewis, Clarence Irving. 1922. “A Treatise on Probability by John Maynard Keynes,”

*The Philosophical Review*. 31.2: 180–186.

Pigou, A. C. 1921. “A Treatise on Probability,”

*The Economic Journal*31.124: 507–512.

Ramsey, Frank. P. 1922. “Mr. Keynes on Probability,”

*Cambridge Magazine*1.1: 3–5. [Reprinted in Ramsey 1989.]

Ramsey, Frank. P. 1926. “Truth and Probability,” in

*The Foundations of Mathematics and Other Logical Essays*. Kegan Paul, Trench, Trubner & Co, London.

Ramsey, Frank. P. 1989. “Mr Keynes on Probability,”

*British Journal for the Philosophy of Science*40: 219–222.

Russell, Bertrand. 1922. “A Treatise on Probability by John Maynard Keynes,”

*The Mathematical Gazette*11.159: 119–125. [Reprinted in Russell 1948.]

Russell, Bertrand. 1948. “A Treatise on Probability by John Maynard Keynes,”

*The Mathematical Gazette*32.300: 152–159.

Sheppard, W. F. 1923. “Probability and Statistics,”

*The Mathematical Gazette*11.167: 405–409.

Wilson, E. B. 1923. “Keynes on Probability,”

*Bulletin of the American Mathematical Society*29.7: 319-322.

Wolf, A. 1922. “Studies in Probability. I. Probability,”

*Economica*4: 87–97.

**KEYNES AND PROBABILITY**

Basili, Marcello and Carlo Zappia. 2009. “Keynes’s ‘Non-Numerical’ Probabilities and Non-Additive Measures,”

*Journal of Economic Psychology*30.3: 419–430.

Basili, Marcello and Carlo Zappia. 2010. “Ambiguity and Uncertainty in Ellsberg and Shackle,”

*Cambridge Journal of Economics*34: 449–474.

Bateman, Bradley W. 1987. “Keynes’s Changing Conception of Probability,”

*Economics and Philosophy*3: 97-119.

Bateman, Bradley W. 1988. “G. E. Moore and J. M. Keynes: A Missing Chapter in the History of the Expected Utility Model,”

*American Economic Review*78: 1098–1106.

Brady, Michael Emmett, 1983.

*The Foundation of Keynes’s Macrotheory: His Logical Theory of Probability and its Application in the General Theory and After*, Ph.D. Dissertation, University of California, Riverside.

Brady, Michael Emmett, 1987. “J. M. Keynes’ Theory of Evidential Weight: Its Relation to Information Processing Theory and Application in the General Theory,”

*Synthese*71: 37–60.

Brady, Michael Emmett, 1988. “J. M. Keynes’s Position on the General Applicability of Mathematical, Logical and Statistical Methods in Economics and Social Science,”

*Synthese*76.1: 1–24.

Brady, Michael Emmett and Howard B. Lee, 1989. “Dynamics of Choice Behavior: The Logical Relation between Linear Objective Probability and Nonlinear Subjective Probability,”

*Psychological Reports*64: 91-97.

Brady, Michael Emmett, 1993. “J. M. Keynes’s Theoretical Approach to Decision-Making under Conditions of Risk and Uncertainty,”

*The British Journal for the Philosophy of Science*44.2: 357–376.

Brady, Michael Emmett, 1994. “On the Application of J. M. Keynes’s Approach to Decision Making,”

*International Studies in the Philosophy of Science*8.2: 99–112.

Brady, Michael Emmett, 2010. “A Comparison-Contrast of Adam Smith, J.M. Keynes and Jeremy Bentham on Probability, Risk, Uncertainty, Optimism-Pessimism and Decision Making with Applications Concerning Banking, Insurance and Speculation,” SSRN Working Paper Series.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1728225

Brady, Michael Emmett and Rogério Arthmar, 2010. “Keynes’ Lower-Upper Bound Interval Approach to Probability,” SSRN Working Paper Series (February 2).

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1546726

Brady, Michael Emmett, 2010. “How to Use Keynes’s Conventional Coefficient of Risk and Weight, c, to clear up Misunderstandings and Confusions about Keynes’s Views on the use on his Principle of Indifference Versus the use of Laplace’s Principle of Nonsufficient Reason,” SSRN Working Paper Series (November 27).

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1716043

Brady, Michael Emmett, 2011. “Comparing J. M. Keynes’s and F. von Hayek’s Differing Definitions of Uncertainty as it relates to Knowledge: Keynes’s Unavailable or Missing Knowledge Concept versus Hayek’s Dispersal of Knowledge Concept,” SSRN Working Paper Series.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1751569

Brady, Michael Emmett, 2011. “Keynes, Mathematics and Probability: A Reappraisal,” SSRN Working Paper Series, August 31.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1920569

Brady, Michael Emmett. 2011. “The ‘Early’ Logical Empiricism of J. M. Keynes versus the Rhetoric of Subjectivism,” SSRN Working Paper Series, August 31

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1920578

Brady, Michael Emmett. 2012. “John Maynard Keynes’s Upper and Lower Valued Probabilities: A Study of How Statisticians, Philosophers, Logicians, Historians, and Economists Failed to Comprehend Keynes’s Breakthrough Application of G.Boole’s Interval Approach to Probability in the 20th Century,” January 30

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1996129

Brady, Michael Emmett and Rogério Arthmar. 2012. “Keynes, Boole and the Interval Approach to Probability,”

*History of Economic Ideas*20.3: 65–84.

Carabelli, Anna M. 1988.

*On Keynes’s Method*, Macmillan, Basingstoke.

Carabelli, Anna M. 2002. “Speculation and Reasonableness: a non-Bayesian Theory of Rationality,” in S. Dow and J. Hillard (eds.),

*Keynes, Uncertainty and the Global Economy: Beyond Keynes*(Vol. 2), Edward Elgar, Cheltenham UK and Northampton MA. 165–185.

Cottrell, A. 1993. “Keynes’s Theory of Probability and its Relevance to His Economics: Three Theses,”

*Economics and Philosophy*9: 25–51.

Crocco, M. 2000. “The Future’s Unknowability: Keynes’s Probability, Probable Knowledge and the Decision to Innovate,” in F. Louçã and M. Perlman (eds.),

*Is Economics an Evolutionary Science?*Edward Elgar, Cheltenham.

Crocco, M. 2002. “The Concept of Degrees of Uncertainty in Keynes, Shackle, and Davidson,”

*Nova Economia*12.2: 11–28.

Davis, John B. 1994.

*Keynes’s Philosophical Development*. Cambridge University Press, Cambridge.

Davis, John B. 2003. “The Relationship between Keynes’s Early and Later Philosophical Thinking,” in Jochen Runde and Sohei Mizuhara (eds.),

*The Philosophy of Keynes’ Economics: Probability, Uncertainty and Convention*. Routledge, London and New York. 100–110.

Davidson, P. 1982–1983. “Rational Expectations: A Fallacious Foundation for Studying Crucial Decision-making Processes,”

*Journal of Post-Keynesian Economics*5.2: 182-198.

Davidson, Paul. 1991. “Is Probability Theory Relevant for Uncertainty? A Post Keynesian Perspective,”

*Journal of Economic Perspectives*5.1: 129-143.

De Carvalho, Fernando J. Cardim. 1988. “Keynes on Probability, Uncertainty, and Decision Making,”

*Journal of Post Keynesian Economics*11.1: 66-81.

Dequech, David. 1997. “Uncertainty in a Strong Sense: Meaning and Sources,”

*Economic Issues*2.2: 21–43.

Dequech, David. 2008. “Varieties of Uncertainty: A Survey of the Economic Literature,”

http://ideas.repec.org/p/anp/en2008/200807211223070.html

Dequech, David. 2011. “Uncertainty: A Typology and Refinements of Existing Concepts,”

*Journal of Economic Issues*45.3: 621-640.

Dickens, Edwin. 2008. “Keynes’s Theory of Probability, Investment Behaviour, and Behavioral Finance,” in L. Randall Wray and Mathew Forstater (eds.),

*Keynes and Macroeconomics After 70 years: Critical Assessments of the General Theory*, Edward Elgar, Cheltenham, UK and Northampton, MA.

Dow, Sheila C. 1994. “Uncertainty,” in Philip Arestis and Malcolm Sawyer (eds.),

*The Elgar Companion to Radical Political Economy*. Edward Elgar, Aldershot. 434–438.

Dow, Sheila C. 1995. “Uncertainty about Uncertainty,” in S. C. Dow and J. Hillard (eds.).

*Keynes, Knowledge and Uncertainty*. Edward Elgar, Aldershot. 117–127.

Dow, Sheila C. 2012. “Uncertainty about Uncertainty,” in Sheila C. Dow,

*Foundations for New Economic Thinking: A Collection of Essays*. Palgrave Macmillan, Basingstoke. 72–82.

Dow, Sheila C. 2012.

*Foundations for New Economic Thinking: A Collection of Essays*. Palgrave Macmillan, Basingstoke.

Ellsberg, Daniel. 1961. “Risk, Ambiguity and the Savage Axioms,”

*Quarterly Journal of Economics*75: 643–669.

Ellsberg, Daniel. 2001 [].

*Risk, Ambiguity and Decision*. Garland, New York and London.

Feduzi, Alberto. 2007. “On the Relationship between Keynes’s Conception of Evidential Weight and the Ellsberg Paradox,”

*Journal of Economic Psychology*28: 545–565.

Fitzgibbons, Athol. 1988.

*Keynes’s Vision: A New Political Economy*, Clarendon, Oxford.

Gerrard, B. 2003. “Keynesian Uncertainty: What Do We Know?,” in Jochen Runde and Sohei Mizuhara (eds.),

*The Philosophy of Keynes’ Economics: Probability, Uncertainty and Convention*. Routledge, London and New York. 239–251.

Gillies, Donald. 2006. “Keynes and Probability,” in R. Backhouse and B. Bateman (eds.),

*The Cambridge Companion to Keynes*Cambridge University Press, Cambridge and New York. 199-216.

Gillies, Donald. 2003. “Probability and Uncertainty in Keynes’s Economics,” in Jochen Runde and Sohei Mizuhara (eds.),

*The Philosophy of Keynes’ Economics: Probability, Uncertainty and Convention*. Routledge, London and New York. 111–129.

Gilles, Dostaler. 2007.

*Keynes and his Battles*. Edward Elgar, Cheltenham.

Hailperin, Theodore. 1986.

*Boole’s Logic and Probability: A Critical Exposition from the Standpoint of Contemporary Algebra, Logic, and Probability Theory*(2nd rev. edn.), North-Holland, Amsterdam and New York.

Jespersen, Jesper. 2009.

*Macroeconomic Methodology: A Post-Keynesian Perspective*. Edward Elgar, Cheltenham, UK and Northampton, MA. Appendix 1. pp.126-131

Kelsey D. and J. Quiggin. 1992. “Theories of Choice under Ignorance and Uncertainty,”

*Journal of Economic Surveys*6.2: 133-153.

Keynes, J. M. 1921.

*A Treatise on Probability*(1st edn.), Macmillan, London.

Lavoie, M. 2009.

*An Introduction to Post-Keynesian Economics*(rev. edn.). Palgrave Macmillan, Basingstoke.

Lawson, Tony. 1985. “Uncertainty and Economic Analysis,”

*Economic Journal*95: 909-927.

Lawson, Tony. 1988. “Probability and Uncertainty in Economic Analysis,”

*Journal of Post Keynesian Economics*11.1: 38-65.

Lawson, Tony. 1993. “Keynes and Conventions,”

*Cambridge University Review of Social Economy*51: 174-200.

McCann, Charles R. 1994.

*Probability Foundations of Economic Theory*. Routledge, London.

McCann, Charles, R. 2003. “On the Nature of Keynesian Probability,” in Jochen Runde and Sohei Mizuhara (eds.),

*The Philosophy of Keynes’ Economics: Probability, Uncertainty and Convention*. Routledge, London and New York. 37-45.

Mandelbrot, Benoit B. 1997.

*Fractals and Scaling in Finance: Discontinuity, Concentration, Risk*. Springer, New York.

Mandelbrot, Benoit B. and Richard L. Hudson. 2004.

*The (Mis)behavior of Markets: A Fractal View of Risk, Ruin, and Reward*. Basic Books, New York.

Meeks, J. G. T. 1991. “Keynes on the Rationality of Decision Procedures under Uncertainty: The Investment Decision,” in J. G. T. Meeks (ed.),

*Thoughtful Economic Man: Essays on Rationality, Moral Rules and Benevolence*. Cambridge University Press, Cambridge. l26-160.

Moggridge, D. E. 1992.

*Maynard Keynes: An Economist’s Biography*, Routledge, London. pp. 143-166.

Narayanan, Sunder. 1994. “Comments on M. E. Brady’s Extension to J. M. Keynes’ Decision Rule,”

*Psychological Reports*75.1: 126.

O’Donnell, R. M. 1989.

*Keynes: Philosophy, Economics and Politics: The Philosophical Foundations of Keynes’s Thought and their Influence on his Economics and Politics*, Macmillan, Basingstoke.

O’Donnel, R. 2003. “The Thick and the Think of Controversy,” in Jochen Runde and Sohei Mizuhara (eds.),

*The Philosophy of Keynes’ Economics: Probability, Uncertainty and Convention*. Routledge, London and New York. 85–99.

Ramsey, F. P. 1989 [1922]. “Mr Keynes on Probability,”

*British Journal for the Philosophy of Science*40.2: 219-222.

Roncaglia, Alessandro. 2009. “Keynes and Probability: An Assessment,”

*European Journal of the History of Economic Thought*16.3: 489-510.

Rotheim, Roy J. 1988. “Keynes and the Language of Probability and Uncertainty,”

*Journal of Post Keynesian Economics*11.1: 82-99.

Rowbottom, D. P. 2007. “The Insufficiency of the Dutch Book Argument,”

*Studia Logica*87.1: 65-71.

Runde, Jochen. 1990. “Keynesian Uncertainty and the Weight of Arguments,”

*Economics and Philosophy*6.2: 275–292.

Runde, Jochen. 1991. “Keynesian Uncertainty and Stability of Beliefs,”

*Review of Political Economy*3: 125–145.

Runde, Jochen. 1994. “Keynes After Ramsey—In Defence of A Treatise on Probability,”

*Studies in History and Philosophy of Science*25.1: 97-121.

Runde, Jochen. 1995. “Risk, Uncertainty and Bayesian Decision Theory: A Keynesian View,” in S. C. Dow and J. Hillard (eds.),

*Keynes, Knowledge and Uncertainty.*Edward Elgar, Aldershot, UK. 197–210.

Runde, Jochen. 1995. “Chances and Choices: Some Notes on Probability and Belief in Economic Theory,”

*The Monist*78: 330–351.

Runde, Jochen. 1998. “Frank Knight’s Discussion of the Meaning of Risk and Uncertainty,”

*Cambridge Journal of Economics*22.5: 539-546.

Runde, Jochen. 2000. “Shackle on Probability,” in Stephen F. Frowen and Peter Earl (eds.),

*Economics as an Art of Thought: Essays in Memory of G. L. S. Shackle*. Routledge, New York.

Runde, Jochen and Sohei Mizuhara (eds.). 2003.

*The Philosophy of Keynes’ Economics: Probability, Uncertainty and Convention*. Routledge, London and New York.

Ryder, J. M. 1981. “Consequences of a Simple Extension of the Dutch Book Argument,”

*The British Journal for the Philosophy of Science*32.2: 164–167.

Syll, Lars Pålsson. 2007.

*John Maynard Keynes*SNS Förlag, Stockholm.

Skidelsky, R. J. A. 1992.

*John Maynard Keynes: The Economist as Saviour, 1920–1937*(vol. 2), Macmillan, London.

**My Posts**

“Degrees of Uncertainty,” November 24, 2011.

“Michael Emmett Brady on Keynes’s Probability Theory in Mises and Rothbard,” November 29, 2011.

Some comments on the bibliography...

ReplyDelete1.) The following articles don't deal with

A Treatise on Probabilitydirectly.Brady, Michael Emmett, 1990. “The Mathematical Development of Keynes’s Aggregate Supply Function in the General Theory,” History of Political Economy 22.1: 167-172.

Brady, Michael Emmett, 1994. “Keynes, Pigou and the Supply Side of the General Theory,” History of Economics Review 21: 34–46.

Brady, Michael Emmett, 1994. “A Note on the Keynes-Pigou Controversy,” History of Political Economy 26.4: 697–705.

2.) How could you forget to include Bruno de Finetti, who also helped create the axioms of choice as posed by Subjective Expected Utility?

3.) You forget to indicate where the article by F.P. Ramsey republished in

The British Journal for the Philosophy of Sciencein 1989 was originally published from.4.) You forget to note the original completion date of Daniel Ellsberg's doctoral thesis. Although it was published in 2001, it was actually finished in 1962.

5.) If my memory serves me right, S.C. Dow's 1995 and 2012 pieces are virtually identical.

6.) Some sources that cited J.M. Keynes's work on probability you could have mentioned in this bibliography but did not for whatever reason include: Rudolf Carnap, L.J. Cohen, Irving J. Good, E.T. Jaynes, B.O. Koopman, Henry Kyburg, Isaac Levi, David W. Miller, and Bertrand Russell.

7.) Some sources on modern decision theory that you might wanted to have referenced include Itzhak Gilboa, David Schmeidler, Yakov Ben-Haim, John Quiggin, Mark J. Machina, and Peter Wakker.

Mostly fixed. I will look into (6) and (7) at a later stage.

DeleteGotcha. Oh yes...I believe there was a review of

DeleteA Treatise on Probabilityby the French mathematician Emile Borel, but I don't remember where and when it was published and whether it was written in French or in English.In French:

DeleteBorel, Émile. 1924. "A propos d'un traité de probabilités,"

Revue philosophique98: 321-326.Now also added.

I just found this on arXiv: Robert, Christian P. "Reading Keynes' Treatise on Probability", 2010

ReplyDeleteMaybe it will be of use!

Absolutely splendid.

ReplyDeleteAnd if their is one work among all in your list that I especially would like to recommend, it has to be R. M. O’Donnell's "Keynes: Philosophy, Economics and Politics: The Philosophical Foundations of Keynes’s Thought and their Influence on his Economics and Politics." A masterpiece.

A few more things I forgot to add:

ReplyDelete1.) I don't think the following review of

A Treatise on Probabilitywas done anonymously at all:[Anonymous?] F. Y. E. 1922. “A Treatise on Probability by John Maynard Keynes,”

Journal of the Royal Statistical Society85.1: 107–113.In fact, I believe that's Francis Ysidro Edgeworth's review. F.Y. Edgeworth wrote two reviews on J.M. Keynes's book - one in that journal, and I believe the other was published in

Mind.2.) There is another article by Marcello Basili and Carlo Zappia that involves J.M. Keynes and probability theory. In fact, it was published a year before their 2010 article in the

Cambridge Journal of Economics. The other article by them, which I feel is of far greater importance, is their 2009 article in theJournal of Economic Psychology. I've sent you a PDF copy of their 2009 article before, Lord Keynes.3.) I believe that Dr. Michael Emmett Brady has five more pieces that were published in

Psychological Reportsthat involveA Treatise on Probability. Also, there was a piece that did comment on Dr. Michael Emmett Brady's research on J.M. Keynes's conventional coefficient of risk and weight by a Sunder Narayanan in the August 1994 issue ofPsychological Reports.Thanks, have fixed most of these.

Delete