4 weeks! This blog has been online for 4 weeks, and we still have not written any article about Condorcet. A great feat since this mathematician’s voting system is of major importance for Open Agora.
This article will present Nicolas de Condorcet, starting with a short biography, and then performing an analysis of some of his scientific theories like social mathematics. In an upcoming article, we will focus on his political commitment during the French Revolution. Eventually, we will discuss the details of the Condorcet voting system.
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Nicolas de Condorcet was born in 1743 in the north-east of France, in an aristocratic family. After a religious education, he presents a thesis in mathematics and then he writes several mathematical books on topics like statistics or probabilities. In 1769, he is elected at Academy of Science. Later, he is kingdom administrator in the finance department of King Louis XVI. During this period, Condorcet gets interested into politics and writes a book on the American Revolution.
Condorcet has worked on public topics like the Constitution or the educational system. Eventually, during “The Terror” (a dark era of the French Revolution), he is arrested because he belongs to the political group “Girondins”. The mathematician dies two days after, in prison, the exact cause of his death still being unknown today.
A Talented Mathematician
Nicolas de Condorcet contributed to the redaction of several mathematical chapters of the famous Encyclopedie of two french philosophers: Diderot and d’Alembert. Great mathematician, he has investigated several topics, such as geometry, integral calculus, probabilities. He has written books on this theories, among which: Integral Calculus (1765), Of Three-Body Problems (1767), Dissertation on the Probability Calculus (1781).
Between 1770 and 1785, Condorcet worked intensely on political arithmetics ⇒ What is it? This expression designates the use of mathematics in public management, in areas such as demography or economical statistics. For example, Condorcet has investigated French population statistics, using new sampling methods, in Dissertation on Knowing Kingdom Population (1783-1788). He also took part in the writing of various legal texts, like property taxation.
The Social Mathematics
From political arithmetics, the scientist has created a new discipline: social mathematics. Condorcet wanted to apply to Human Sciences the scentific methodology of Natural Sciences: rigor and reasoning.
Nicolas de Condorcet lived during the Age of Enlightenment and was deeply influenced by the famous philosophers of this period. According to these philosophers, Science is the only reliable source of knowledge, as opposed to religious obscurantism. These philosophers highlighted the importance of human reasoning in the course of progress. This theory and these methods have lead to great progress in Natural Sciences, for example in Medicine, Physics, or Biology.
Condorcet met numerous philosophers of Enlightenment such as Voltaire and D’Alembert, and he used a lot of scientific techniques during his career as a mathematician. He observed that methodology in Human Sciences was not as rigorous as it should be, since it was influenced by rhetoric and unfounded judgments. Condorcet has lead researchers in Human Sciences to use these processes: facts observation and reasoning. He explains this discipline in a speech at the Academy Sciences in 1782:
“By meditating on the nature of moral sciences, we can say that they are like Physical Sciences, based on facts observation. They must follow similar methods, acquire an exact and precise language, the same degree of certainty.”
In a book of 1793, he described away to apply scientific calculus techniques to political and moral sciences. He defines the terms of social mathematics and enunciates 5 mathematical theories that should be applied before reaching judgment in Human Sciences.
This discipline, social mathematics, appears again 150 years later, in the work of French researchers G.-T. Guilbaud and G.-G. Granger (during the 1940’s and the 1950’s). In 1981, the Center for Analysis and Social Mathematic is created (across Paris and Marseille).
To go further on social mathematics, you may read an article of Feldman J. (Condorcet and social mathematics, Mathematics and Social Sciences, 2005) or the book Condorcet Social mathematics, by G.-G. Granger (1956).
The Condorcet voting system is part of his social mathematics theory.
What Comes Next
All his life, Nicolas de Condorcet has been a philosopher, an engineer, an administrator, and a politician. His political opponents have criticized him for these different activities, for example Robespierre who said about Condorcet:
“He was a great mathematician for philosophers, and a famous philosopher for mathematicians.”
However, we cannot ignore the importance of Condorcet during the French Revolution, especially his contributions to the Constitution. This topics will be adressed in another article.