1Carlo Zappia’s book Uncertainty in Economics: A History is part of the book series Springer Studies in the History of Economic Thought (SSHET). It was previously published in Italian, Incertezza in economia (Carocci, Roma, 2024). The book has seven chapters : “Introduction”; “The Art of Conjecturing: Probability and Utility”; “Uncertainty According to Knight and Keynes”; “Von Neumann, Morgenstern and Decision Under Risk”; “Ramsey, De Finetti and Savage: Decision Under Uncertainty”; “Uncertainty as Ambiguity: Ellsberg and the Paradoxes of Decision Theory”; “Modern Uncertainty and the Return to Keynes”. The aim of the book is the following.
The book introduces the economic theories that have placed uncertainty at the core of economic discourse. Covering the works of John Maynard Keynes and Frank Knight, as well as those of John von Neumann, Oskar Morgenstern, and Leonard Savage, it reconstructs the complex history of how economists have analyzed uncertainty, as distinct from risk, in the twentieth century. The text delves into the question of the extent to which uncertainty is a measurable entity, focusing on the perspective of those authors who have attempted to demonstrate its irreducibility to risk, with particular regard to Daniel Ellsberg and the ensuing current decision theory. (book cover)
2A good book. This book by Carlo Zappia is truly a good book on uncertainty. And an original book within the existing literature. And a useful book. Especially useful for students studying decision theory in economics and finance, but also useful for those simply interested in understanding uncertainty, given that the concept of uncertainty is elusive, even once we understand that uncertainty is different from the calculable risk of numerical probabilities—an initial step that is already difficult for many to accept.
3In fact, uncertainty, like probability, depends on the probability theory used, on the epistemology we presuppose, sometimes tacitly. For example, probability can be empirical, like the frequency of occurrences; it can be classical, like in the game of dice or like in the classic urn with equally probable outcomes. But it can also be cognitive, like probable judgments. Moreover, it can represent a rational, logical judgment shared by most, given the reasons underlying it, or it can also represent a merely reasonable judgment (i.e., having some reason to believe, unrelated to the truth). Or probability can be an individual subjective judgment, unconnected to any idea of reason. However, this individual subjective judgement is sometimes associated with coherence rules that limit the irrational freedoms of individual subjective judgment. Furthermore, probability can be numerical (such as the precise calculation of probabilities in a probability distribution function), it can be a betting ratio in a gamble, or it can be imprecise, such as an interval between probable numbers. Or probability can be quantitative but not numerical (in this case we can call it qualitative or ordinal probability), such as that represented by orders of probability, in which the relationship of plus or minus, or equal, between probabilities holds. Probability can also be objective (such as frequency, or rational judgment, or even just reasonable judgment). Or, probability can be merely subjective, as in gambling. Furthermore, probability can be epistemological, that is, tied to one of the various available theories of knowledge; or it can be ontological, that is, tied to a theory of the intrinsic structure of reality, of the material world, and of events. Finally, probability can be tied to a theory of chance, whether objective or subjective.
4Another interesting aspect of Zappia’s book is that it shows us how the notion of uncertainty is not only based on the problematic notion of probability but also has roots in the evolution of utility theory, from cardinal utility to ordinal utility to expected utility. Thus, probability and utility are—and have been—historically and theoretically intertwined. Probability and utility are two of the pillars of economic thought. Since Jacob Bernoulli’s Ars conjectandi (1713) and Daniel Bernoulli’s Specimen theoriae novae de mensura sortis (1738) probability and utility are intertwined, arriving at the modern notion of subjective expected utility. As you can see, the book navigates a real maze.
5This book by Zappia helps us navigate this tangle of concepts, sometimes similar and sometimes conflicting; it also guides us through a historical-theoretical reconstruction of the various interpretations of probability, utility, and uncertainty that have overlapped seamlessly over time. It is a fascinating work of ordering and untangling a topic that, for me and for many, is fascinating.
6Some sections of the short and concise book, as is inevitable in a book intended primarily for students, are more elaborate and in-depth; others guide the reader from one focus to another, selected by Zappia as relevant. This is a relevant choice that I agree with. It is a guided and carefully selected journey through a field so impervious to the inexperienced reader, who would otherwise become lost in a vain search for the true notion of uncertainty.
7In his book, Zappia also guides us through some of the major controversies surrounding probability and utility, which also represent developments in modern economics. For example, he carefully reconstructs the controversies that still haunt interpreters of John Maynard Keynes’s economic theory and those concerning the development of expected utility to the discovery of the paradoxes of choice.
8Regarding the first controversy, the one concerning Keynes, Zappia addresses several questions. One is whether Keynes ultimately accepted Ramsey’s criticisms of his probability theory, set out in his Treatise on Probability, published in 1921. Zappia also addresses the question of whether Keynes became a follower of the subjectivist Ramsey and whether he ultimately became—in his 1936 General Theory—a Peircean pragmatist. He also addresses the question of whether Keynes—while acknowledging the limitations of his logical approach to probability—in his mature work, The General Theory, retained the old distinction—present in his Treatise on Probability—between logical-reasonable judgment (on which his vision of economic theory is also based) and the subjective or intersubjective conventions of the market, which Keynes viewed as the idols of the market. Another issue Zappia also discusses is whether the market, according to Keynes, exhibits subjective and pragmatic attitudes. Keynes’s description of the market certainly anticipates the later behaviorist analyses of Kahneman, Twersky, and Taleb, but, in my opinion, the economic theory with which Keynes approaches market analysis cannot itself be subjective and pragmatist; that is, Keynes cannot, as he himself points out, follow the idols of the market. Keynes cannot be an idolater of the market. Nor, again in Keynes’s view, can economic policy be. Therefore, economic theory and policy must be reasonable, that is, based on reasons, even if they are partial reasons. Otherwise, economic theory and policy could not be justified against the attacks launched by liberalism and neoliberalism.
9In this regard, Chapter 2 of the book (on uncertainty according to Knight and Keynes) is very interesting. Zappia addresses the problem of economists’ historical misidentifying of Keynes’s position on uncertainty with that of Knight. A recent illustration is Sunstein (2025). This chapter clearly reconstructs Knight and Keynes’s two different positions on probability, on the role of Knight’s theory of profits, and on Knight’s connection between uncertainty and innovation, which, in my opinion, also influenced Schumpeter.
10Another very useful chapter is Chapter 4 on the connection between Ramsey, de Finetti, and Savage on the theory of decision-making under uncertainty. Zappia shows us the points of continuity but also the important discontinuities between Ramsey’s view of probability and de Finetti’s logic of the probable. Zappia also shows us Ramsey’s legacy in Savage’s reformulation of probability.
11Other interesting issues addressed in the book, particularly in Chapters 3 and 5, include the discussion of “measurement without theory” in economics, initiated by Koopmans (1947), which involved the decision theory axiomatized by von Neumann and Morgenstern (Chapter 3), which Savage had transformed into an equally precise but more realistic model (Chapter 5). Koopmans’s approach, in his essay on “measurement without theory” in economics, contrasted with Friedman’s better-known 1953 approach (Friedman, 1953), according to which theoretical economists need not worry about using unrealistic axioms if they lead to correct predictions. In these two chapters, Zappia also reconstructs the historical and theoretical steps of the application of Bayesian philosophy in the theoretical construction of subjective expected utility, up to the discovery of the choice paradoxes by Allais and Ellsberg. Several paragraphs also clarify the connection between uncertainty and the notion of ambiguity. As you will see, Zappia’s book is a useful book for understanding that uncertainty has deep roots—historical and theoretical—in probability and utility.