Mathis Bertrand

Thesis Project

The Reason of Numbers: Social Optimism, Moral Statistics, and the Metaphysics of the Average in France and Germany (1849–1918)

A first form of this project has been presented under the joint supervision of Éric Brian^† and Laurent Mazliak.
Admissible to doctoral contracts of the "History and Civilizations" doctoral school of EHESS, June 2025. Funding not obtained.
Thesis project currently seeking funding (doctoral scholarship, ANR, ERC...) and under reconfiguration.

My research focuses on the fortune of a framework of thought partly developed by Adolphe Quetelet (1796-1874), in which the law of large numbers does not merely describe society, but reveals an underlying stable, positive and moral order. This optimism manifests itself in at least three ways: through epistemological confidence in the average, through the establishment of calculation institutions at the European level and, finally, through a certain moral optimism.

Contrary to traditional descriptions of ‘statistical fatalism’, I analyse the evolution of this legacy between 1849, when the logician Moritz Drobisch publishes one of the first reviews of Quetelet's works and 1918, through three major themes:

• First, I examine how Quetelet's social ontology merged astronomy and morality to establish the ‘average man’ as the measure of the general good. This project, rooted in a Leibnizian and rationalist heritage, spans the century through philosophy, statistics and probability theory, and sociological thought. It structures numerous debates on the status of numbers, on the conditions for applying calculation to human phenomena, and on morality itself. Hence one needs to understand what kind of optimism Quetelet invented in order to study its ulterior development.
• While Belgium institutionalised the model, France (through the Paris Statistical Society and the positivists) and Germany (e.g. Wilhelm Lexis and Moritz Drobisch in texts that have not yet been translated) ardently debated its validity. This section questions the persistence of this methodological optimism after the death of its founder. Including the mathematical field of the Saint Petersburg School will help to understand the notion of mathematical rigour claimed by mathematicians such as Chebyshev, Markov and Lyapunov. In most of these cases, the discussion of the epistemological foundations of statistics also makes it possible to clarify the contours of a moral and sociological doctrine.
• Lastly, the analysis focuses on the break made by Durkheim, Halbwachs, Simmel and other ‘neo-Kantian’ thinkers. Aware of advances in mathematics and, in particular, statistics at the time, they gradually detached the concept of norms from simple mathematical frequency in order to turn it into an external social constraint. In doing so, they also helped to redefine the very nature of chance and contingency.

The work concludes with the First World War, a turning point where the experience of industrial and military contingency shattered the original statistical enthusiasm and the Laplacian model that supported it.

Ultimately, I would like to describe this shift on an epistemological level and classify these various positions in a satisfactory way.

Publications

• October 2023 Review of Anthologie de la calculabilité : naissance et développements de la théorie de la calculabilité des années 1920 à 1970, Michel Bourdeau and Jean Mosconi (eds.), Cassini, 2022. In Revue de Synthèse, vol. 144, no. 3-4 (2023), p. 423–437. [PDF]

Translations & Sources

The analysis of intellectual transfers between France and Germany relies on the study of sources that often remain untranslated. This section provides original texts alongside French translation drafts produced as part of my doctoral research. Comments and suggestions on these working translations are welcome.

• Moritz Wilhelm Drobisch (1867), Moral Statistics and Human Free Will (Die moralische Statistik und die menschliche Willensfreiheit). Unpublished French translation, notes. Working version (January 2026).
  Current version
  Original text (1867). N.B. PDF file edited for improved screen readability.
• Moritz W. Drobisch (1849), "Review of Adolphe Quetelet’s On Moral Statistics and the Principles Which Should Form Its Basis (Brussels, 1848)", Leipziger Repertorium der deutschen und ausländischen Literatur, Vol. 25, 1849 (Year 7, Vol. 1). [PDF]

Communications & Talks

• January 30, 2026 « A logician in moral statistics: Moritz Wilhelm Drobisch’s Die moralische Statistik und die menschliche Willensfreiheit (1867) »
  Online Presentation at Pr. Ingolf Max’s Oberseminar, University of Leipzig.
• November 19, 2025 « The ‘Society of Mathematicians’ in Maurice Halbwachs: The Memory of Scientific Activity between Analysis and Synthesis »
  Talk at the 35th Novembertagung on the History & Philosophy of Mathematics, Nancy, France. [Slides]
• March 28, 2025 « Statistics as a tool of sociological invention in Maurice Halbwachs: from the critique of the average to a discourse on sociological method? »
  Talk at the Seminar on the History of Probability and Statistics (EHESS), Aubervilliers, France. [Slides revised and enriched for online reading]
• April 20, 2023 « Reason as calculation : from the Euclidian ratio to the ideal of a universal characteristic »
  Informal talk at the seminar of Giovanna Cifoletti (EHESS), Paris, France. [Material]

Research Identifiers