Other Expressions of the Spirit
The opinions of Fontenelle are frequently trotted out in characterizations of the Englightenment. Fontenelle commended the esprit géométrique for its promise of certainty and rationality, which might improve polity, morality, literature, and oratory as it had enriched astronomy and mechanics. By the end of the 18th century, a wealth of treatises and textbooks had praised the merits of mathematics and the solidity of reasoning in Euclidean geometry, often in terms borrowed from the previous century. Recent scholarship has pointed to John Arbuthnot's arguments in favor of the utility of mathematics, the appeal of the axiomatic approach and the persistence of Cartesian methods as mixed with mathematics, and the wide-ranging
influence of what one author calls the mathematical method-model.
What was reasonable or certain in the 17th and 18th centuries was intimately bound up with questions of probability and risk, in contexts ranging from law to morality, economics to public health. The richness of the analysis and examples in recent studies on probability will warrant careful attention in subsequent exploration of the esprit géométrique and the quantifying spirit. As the 18th-century controversy over inoculation against smallpox makes clear, the stakes could be high in disputes over the validity of quantitative arguments.
Such arguments could still carry weight even when the numbers were soft or when measurement was out of the question, as in discussions of moral arithmetic, meandering rivers, or thermometers for female emotional response, as calibrated from modesty through impudence. Here it is necessary to attend to what quantification promised: useful comparisons whatever the scale, informative models without measurement, precision (clarity, distinctness, intelligibility) rather than a close fit with the real world.
Although moral barometers scarcely belong to the realm of exact science, comparisons of soft and hard quantification may prove instructive. In particular, it is worthwhile measuring the play of the quantifying spirit in the 18th century against conspicuous accomplishments in the mathematization of science in the 17th century and the successes of mathematical physics in the late 18th and early 19th centuries. The articles in Nature mathematized explore examples of 17th-century exact science that enlightened thinkers subsequently found so persuasive. A recent issue of Revue d'histoire des sciences investigates the "conquest of new territories" by mathematical science between 1780 and 1830. And Jean Dhombres links the achievements of mathématisation with the nature of the French scientific community in the half-century between 1775 and 1825 in another recent article.