The origins of de Finetti's critique of countable additivity

TL;DR

This paper explores de Finetti's development of finitely additive probabilities, analyzing his early work and correspondence, and contextualizing his views within the scientific community's debates on probability foundations.

Contribution

It provides a detailed historical and philosophical analysis of de Finetti's critique of countable additivity and his subjectivist conception of probability.

Findings

De Finetti initially supported finitely additive probabilities.

His correspondence with Fréchet influenced his stance.

The paper situates de Finetti's views within early 20th-century probability debates.

Abstract

Bruno de Finetti was one of the most convinced advocates of finitely additive probabilities. The present work describes the intellectual pro- cess that led him to support that stance and provides a detailed account both of the first paper by de Finetti on the subject and of the ensuing correspondence with Maurice Fr\'echet. Moreover, the analysis is supplemented by a useful picture of de Finetti's interactions with the international scientific community at that time, when he elaborated his subjectivistic conception of probability.