### Adam SAdam Smith and J M Keynes on Insurance: Both give the same imprecise answer

#### Abstract

In 1776, Adam Smith, using his imprecise theory of probability, which was presented on pp.106-113 and p.714 of his *The Wealth of Nations*, showed that the firms composing the insurance industry do not use precise probability and do not need to use precise probability. All they need to do is to be able to establish a lower bound on the probable risk by the use of imprecise probability.

In 1921, J M Keynes, using his imprecise theory of probability, on pp.22-34 of the *A Treatise on Probability*, likewise showed that the firms composing the insurance industry do not use precise probability and do not need to use precise probability. All they need to do is to be able to establish a lower bound on the probable risk.

The analysis of both Smith and Keynes is based on their theories of imprecise probability and the existence of uncertainty.

The interesting questions are why no academician in the 18^{th} through the 21^{st} centuries has realized what Smith had done and why no academician in the 20th through the 21st centuries has realized what Keynes had done, which was to explicitly base their analysis on imprecise probability.

Apparently, no academician, especially economists and philosophers, in the 18^{th} through 21^{st} century actually read and/ or understood what Smith was doing in *The Wealth of Nations* while no academician, especially economists and philosophers, in the 20^{th} through the early part of the 21^{st} century, actually read and/or understood what Keynes was doing in his *A Treatise on Probability.*

This then leads to the following conclusion. Academicians from the 18^{th} through the 21 centuries have not read and/or understood the two most fundamental texts written in the last 250 years. This observation lends additional hard evidence to support Hishiyama’s 1969 conjecture, which was that the A Treatise on Probability was never read. To this we add the fact that either Smith’s Wealth of Nations has not been read or it has never been understood.

#### Full Text:

PDF#### References

Ashraf, N. , Camerer , C. ,and Lowenstein,

F.(2005).”Adam Smith, Behavioral Economist”,

Journal of Economic Perspectives,19,no.3, pp.131-

Bentham, Jeremy .(I789).Defense of Usury.

Kessinger Publishing, pp.1-74.

Bentham, Jeremy,(1787).The Principles of Morals

and Legislation. Nabu Press. NY; NY.

.

Boole, George. (1854). An Investigation of the Laws

of Thought on Which are Founded the

Mathematical Theories of Logic and Probability.

New York: Dover Publications, [1958].

Brady, Michael Emmett and Arthmar, Rogerio.

(2010).A Road Map for Economists, Logicians,

Philosophers ,Mathematicians, Statisticians,

Psychologists and Decision Theorists Seeking to

Follow the Mathematical Structure of Keynes’s

Approach to Specifying Lower and Upper Bounds

for Probabilities in the A Treatise on Probability,

(1973).Available at SSRN:

http://ssrn.com/abstract=1618445.

Brady, Michael Emmett and

Arthmar,Rogerio.2012.Keynes,Boole, and the

Interval approach to Probability. History of

Economic Ideas, 20,3, pp.65-84.

______. (2004a). J. M. Keynes’ Theory of Decision

Making, Induction, and Analogy. The Role of

Interval Valued Probability in His Approach.

Philadelphia, Pennsylvania: Xlibris Corporation.

______. (2004b). Essays on John Maynard Keynes

and …. Philadelphia, Pennsylvania: Xlibris

Corporation.

Breban, L. and Lapidus, A.(2019).Adam Smith on lotteries: an interpretation and formal restatement. The European Journal of the history of economic thought,26,no.1,pp.157-197

.Gregg, Samuel.(2010).”Smith Versus Keynes

:Economics and Political Economy in the Post Crisis

Economy”, Harvard Journal of Law and Public

Policy,Vol.33,no.2,pp.443-464.

Hailperin, T. (1965). Best possible inequalities for

the probability of a logical function of events.

American Mathematical Monthly, 72, 343-359.

______. (1986). Boole’s Logic and Probability.

Amsterdam: North-Holland. 2nd edition.

______. (1996). Sentential Probability Logic.

Bethlehem: Lehigh University Press.

Hansen, P., Jaumard, B. & de Aragão , M. P. (1993).

Boole’s Conditions of Possible Experience and

Reasoning under Uncertainty. Relatório Técnico,

DCC-12/93.

Hansen, P. et al. (2000). Probabilistic satisfiability

with imprecise probabilities. International Journal of

Approximate Reasoning, 24, 171-189.

Hishiyama,I.(1969). The Logic Of Uncertainty according to J. M.

Keynes. Kyoto University Economic Review , 39,no.1,pp. 22-44.

Hishiyama, I. (2011). A Critical Reorientation of Keynes’s Economic and

Philosophical Thoughts. In Silva Brandolini and R. Scazzieri, (eds.),Fundamental

Uncertainty: Rationality and Plausible Reasoning. Palgrave Macmillan;London,pp.232-271.

Keynes, J. M. (1921). A Treatise on Probability. The

Collected Writings of John Maynard Keynes

(CWJMK) vol. VIII. London: Macmillan, 1973.

______. F. P. Ramsey. In Essays in Biography,

CWJMK (pp. 335-346), vol. X, London: Macmillan for

the Royal Economic Society (reprinted from The

New Statesman and Nation, 3 October 1931).

Keynes, J.M. (1921). A Treatise on Probability.

London: Macmillan.

Keynes, J.M. (1937). “The General Theory of

Employment”. Quarterly Journal of Economics

:209-223.

Keynes, J.M. ( 1964). The General Theory of

Employment, Interest and Money, New York:

Harcourt, Brace and World.

Keynes, J.M. (1972). Essays in Biography. Vol. X,

The Collected Writings of John Maynard Keynes

(CWJMK), D. Moggridge (ed.). London: Macmillan.

Keynes, J . M. (1946).The Balance of Payments in

the United States. Economic Journal,Vol.56, no.

, June, pp.172-187.

Kyburg, H. E. Jr., & Smokler, H. E. (Eds.), Studies in

Subjective Probability. New York: Wiley.

Kyburg, H. E. Jr. (1970). Probability and Inductive

Logic. New York: Macmillan.

______. 1995. Keynes as a philosopher. In Cottrell,

A. F. & Lawlor, M. S. (Eds.), New Perspectives on

Keynes. Durham: Duke University Press.

______. (2003). Are there degrees of belief?,

Journal of Applied Logic, 1, 139-149.

______. (2006). Belief, evidence, and conditioning,

Philosophy of Science, 73, 42-65.

Levi, I. (1967). Gambling with Truth. New York:

Knopf.

______. (1974). On indeterminate probabilities.

Journal of Philosophy, 71, 391-418.

______. (2001). Introduction. In Ellsberg, D. (Ed.)

Risk, Ambiguity and Decision. New York: Routledge.

Skidelsky, Robert .(1983).John Maynard Keynes:

Volume 1: Hopes Betrayed 1883-1920 . Penguin

Books (January 1, 1994).

Skidelsky , Robert .(1992).John Maynard Keynes:

Volume 2: The Economist as Savior, 1920-1937 .

Penguin Books (January 1, 1995).

Skidelsky , Robert .(2001).John Maynard Keynes,

Vol. 3: Fighting for Freedom, 1937-1946. Viking

Adult (December 3 ,2001).

Smith, Adam.(1776).The Wealth of Nations. Modern

(Cannan) Library Edition with the foreword by Max

Lerner. N.Y.,N.Y.

Smith, Adam.(1759). The Theory of Moral

Sentiments. Sixth edition,1790.

.

### Refbacks

- There are currently no refbacks.

Copyright (c) 2023 Michael Emmett Brady

This work is licensed under a Creative Commons Attribution 4.0 International License.

This work is licensed under a Creative Commons Attribution 4.0 International License.