The History of Moral Certainty as the Pre-History of Typicality

TL;DR

This paper explores the historical development of the concept of typicality, tracing its roots from moral certainty in medieval theology to its role in modern physics and probability theory.

Contribution

It uncovers the historical lineage of typicality, linking medieval moral certainty to its significance in statistical mechanics and quantum physics.

Findings

Typicality played a crucial role in Boltzmann's explanation of equilibrium.

Hugh Everett III first introduced typicality in quantum mechanics in 1957.

The concept of moral certainty predates modern scientific uses of typicality.

Abstract

This paper investigates the historical origin and ancestors of typicality, which is now a central concept in Boltzmannian Statistical Mechanics and Bohmian Mechanics. Although Ludwig Boltzmann did not use the word typicality, its main idea, namely, that something happens almost always or is valid for almost all cases, plays a crucial role for his explanation of how thermodynamic systems approach equilibrium. At the beginning of the 20th century, the focus on almost always or almost everywhere was fruitful for developing measure theory and probability theory. It was apparently Hugh Everett III who first mentioned typicality in physics in 1957 while searching for a justification of the Born rule in his interpretation of quantum mechanics. The historically closest concept before these developments is moral certainty, which was invented by the medieval French theologian Jean Gerson, and it became a standard concept at least until the Age of Enlightenment, when Jakob Bernoulli proved the Law of Large numbers.