Adam Smith rejected the use of the mathematical laws of the calculus of probabilities because the basic information-data-knowledge provided in the real world of decision making did not allow a decision maker to specify precise, definite, exact, numerical probabilities or discover the probability distributions. This means that Smith rejected the classical interpretation of probability of La Place and the Bernoulli brothers, the limiting frequency-relative frequency interpretation of probability, and the personalist, subjectivist, psychological Bayesian approach used by all neoclassical schools of thought because all of these approaches to probability claim that ALL probabilities can be represented by a single numeral between 0 and 1 and the decision maker knows the probability distributions. Smith, like Keynes, rejects this immediately. Thus, Smith’s inductive or logical concept of probability, like Keynes’s, only approaches mathematical probability in the limit. Adam Smith recognized that economic decision makers were confronted with knowledge structures that were not sharp and clear, but cloudy and amorphous. However, decision makers were still able to use the concept of probability in the weaker, interval sense of the concept of probability that was first thought to have been advocated by George Boole and later, with much greater force, by John Maynard Keynes in his two Fellowship dissertations, submitted in 1907 and 1908, respectively, and his A Treatise on Probability (1921). Instead of sharp, definite, determinate, calculated, and exact probabilistic estimates or distributions, inexact, indefinite, indeterminate, and imprecise estimates of probabilities could be derived and used so that decision makers were able to make choices among different possible options that concerned the future in a rational fashion. An important conclusion of this paper is that it was Adam Smith who first explicitly recognized that the mathematical concept of probability is not applicable, in general, in real world decision making. Smith also rejects the normative and prescriptive roles of mathematical probability in decision making. Adam Smith applied his approach to probability and uncertainty by analyzing the economic decisions made by human beings in choosing a particular profession and organizing various insurance markets to cover the risk of loss. Smith’s risk is however, not the standard deviation of the Normal probability distribution used by "Modern" economists, since important data/information/knowledge is missing and not available to the decision maker at the point in time that he is required to make a decision
