In his 1922 review for Cambridge Magazine of Keynes's A Treatise on Probability, and again in his 1926 review "Truth and Probability" (published in 1931 and republished in Kyburg and Smokler's 1980 edition), Ramsey provided examples critiquing Keynes's logical theory of probability. However, these examples do not disprove Keynes's theory as all of them are flawed. The flaws arise because all the pairs of propositions that Ramsey used to substantiate his criticisms are irrelevant to each other. Such irrelevant propositions are explicitly excluded from Keynes's theory in pages 4-6 of his A Treatise on Probability. This paper highlights that Ramsey's examples, which involve irrelevant propositions, do not disprove Keynes's Boolean, relational logic. The only other defense of Keynes's theory, put forth by Watt in 1989, was found to be deficient by Brady in 2022.

This study documents the relationship between economic freedom and unauthorized immigration to the U.S.A. and tries to answer a still-in-debate question, what motivates people to unauthorizedly migrate? Using the generated instrument variables methodology, and a data panel of 15 countries and 16 years, the endogenous variable is the gap in economic freedom between the country of origin and the U.S., and the dependent variable is the unauthorized immigrant’s growth rate. The results show that for each 10% improvement in economic freedom in the country-of-origin unauthorized immigration decreases around 7%. Estimations are robust even after using other covariates and external instruments. The main conclusion is that economic and social factors play a significant role in shaping migration patterns and that the difference in economic freedom between the country of origin and the U.S. plays a fundamental role in deciding to unauthorizedly migrate

Since the establishment of neoclassical economics in the nineteenth century, there has been a debate in the economics profession over the role played by mathematics. Mathematics can add precision to discussion of real-world empirical problems in economics, but care needs to be taken when formalizing a problem to ensure that errors of translation are not made. Formalism allows one to be sure that a chain of reasoning is correct but applying conclusions back to an empirical science problem is fraught if an error of translation has been made. We illustrate such a difficulty in the context of Arrow’s impossibility theorem, specifically the mistranslation of the non-dictatorship condition. The notion of dictatorship entails causality, but causality does not correspond to the usage of the implication sign in mathematics or logic. We use the rules of logic to illustrate that the way that dictatorship is rendered mathematically in the impossibility theorem makes the existence of a dictator (or dictators) not only reasonable but likely.