Adam Smith as an Example of Samuelson’s 1952 Point That Mathematics Can Be Written Out in the English Language: On Smith’s Anti-Utilitarianism Based on the Differences Between Precise and Imprecise Probability Presented in 1776 in the Wealth of Nations

Abstract

In the Wealth of Nations in 1776, Smith gave two clearly worked out mathematical examples involving a comparison- contrast examining the concepts of precise probability (exact, definite, linear, numerical) and imprecise probability(inexact, indefinite, nonlinear, non numerical) that must incorporate uncertainty, which means there is missing or unavailable evidence that is not available to the decision maker at the time that he must make a choice between two or more different alternative options or alternatives. Smith’s analysis is carefully presented on pp. 106-113 and pp. 419-423 of the Modern Library edition of the Wealth of Nations edited by Cannon with the foreword by Max Lerner. It is interesting that there has not been a single academic economist, philosopher, historian, sociologist, psychologist, political scientist, social scientist or decision theorist in the 244 years since Smith published the Wealth of Nations in 1776 to note this fact. The fact that Smith believed that the use of precise probability, as advocated by Jeremy Bentham, who was Smith’s great intellectual opponent and adversary, was possible only under very special conditions, explains why Smith rejected utilitarianism as an ethical system and foundation for the science of economics-the requirement for precise probabilities and precise outcomes was, in general, not possible, due to the fact of missing or unavailable relevant information data ,knowledge or evidence that the decision maker would need to estimate the consequences in the future of his present decision to act. An example of this severe misunderstanding and confusion of Smith’s approach to decision making can be seen, for just one instance, in the 2016 paper by Hollander Thus, discussions about whether Smith was a utilitarian ,partly a utilitarian, whatever that may mean, not a utilitarian or anti-utilitarian are all besides the point once it is realized that Smith completely rejected the additivity and linearity of the probability calculus upon which Bentham based his utilitarianism on, that all men can calculate. Smith realized that Bentham’s belief in the ability to calculate future consequences was extremely limited. Apparently, economists can’t read the English Language that Smith used to express his mathematical analysis of his approach to decision making in the Wealth of Nations. The belief that Smith did not use mathematical analysis in the Wealth of Nations can only be a conclusion reached by economists who are themselves mathematically illiterate, inept, innumerate or severely confused about how mathematical arguments and analysis can be presented. This leads to the conclusion that the M. Friedman, G. Becker, and G. Stigler school of economics, that is taught at the University of Chicago, can have nothing to do at all with Adam Smith’s Wealth of Nations because they base all of their economic analysis on precise probability, which is an approach that is identical to that expressed in the original work of Jeremy Bentham in chapter IV of the Principles of Morals and Legislation (1787).