Intellectual history still quite commonly distinguishes between the episode we know as the Scientific Revolution, and its successor era, the Enlightenment, in terms of the calculatory and quantifying zeal of the former—the age of mechanics—and the rather scientifically lackadaisical mood of the latter, more concerned with freedom, public space and aesthetics. It is possible to challenge this distinction in a variety of ways, but the approach I examine here, in which the focus on an emerging scientific field or cluster of (...) disciplines—the ‘life sciences’, particularly natural history, medicine, and physiology —is, not Romantically anti-scientific, but resolutely anti-mathematical. Diderot bluntly states, in his Thoughts on the interpretation of nature, that “We are on the verge of a great revolution in the sciences. Given the taste people seem to have for morals, belles-lettres, the history of nature and experimental physics, I dare say that before a hundred years, there will not be more than three great geometricians remaining in Europe. The science will stop short where the Bernoullis, the Eulers, the Maupertuis, the Clairauts, the Fontaines and the D’Alemberts will have left it.... We will not go beyond.” Similarly, Buffon in the first discourse of his Histoire naturelle speaks of the “over-reliance on mathematical sciences,” given that mathematical truths are merely “definitional” and “demonstrative,” and thereby “abstract, intellectual and arbitrary.” Earlier in the Thoughts, Diderot judges “the thing of the mathematician” to have “as little existence in nature as that of the gambler.” Significantly, this attitude—taken by great scientists who also translated Newton or wrote careful papers on probability theory, as well as by others such as Mandeville—participates in the effort to conceptualize what we might call a new ontology for the emerging life sciences, very different from both the ‘iatromechanism’ and the ‘animism’ of earlier generations, which either failed to account for specifically living, goal-directed features of organisms, or accounted for them in supernaturalistic terms by appealing to an ‘anima’ as explanatory principle. Anti-mathematicism here is then a key component of a naturalistic, open-ended project to give a successful reductionist model of explanation in ‘natural history’, a model which is no more vitalist than it is materialist—but which is fairly far removed from early modern mechanism. (shrink)

This article focuses on the Russian chemist Dmitri Ivanovich Mendeleev's assessment of certain representations of various aspects of the periodic system that employed more mathematical methodology. The equations of interest were created by E. J. Mills, B. N. Chicherin, and J. H. Vincent. The English chemist Mills tried to find a firmer numerical basis for the periodicity of the elements. The Russian lawyer and political philosopher Chicherin was convinced of the existence of a mathematical law underlying the periodic system. The (...) English physicist Vincent explored the connection between atomic weights and the elements' order in listings based on atomic weights—a project which he associated with the periodic system of elements. Although, for Mendeleev, the equations of Mills, Chicherin, and Vincent promised a more precise expression of the law of periodicity, he continued to invoke his earlier standards. In particular, Mendeleev wanted the equations to respect the individuality of the elements, and called for completeness in conveying the complexities of chemical phenomena. Thus, the very qualities that he had valued while developing his periodic system in 1869–1871 also characterised his evaluation of the new means of representing aspects of that system. (shrink)

The concept of extent of reaction was discussed many times in physical chemistry journals and books. This contribution strongly suggests the use of the extent of reaction as standard basic tool in teaching stoichiometry. The same idea was suggested several times in the past without success because the concept of extent of reaction is still not presented in the first-year general chemistry textbooks. It is also remarked that the concept of extent of reaction represents a simple example of the way (...) of attaining a mathematization of chemistry, that is chemistry thought and made with the mathematical way of thinking, i.e. using variables, symbols and functions. Presenting the concept of the extent of reaction within the general chemistry curriculum will support successive physical chemistry courses, as these courses make extensive use of this powerful concept when teaching thermodynamics and kinetics of chemical reactions. (shrink)