Concept and Form:
The Cahiers pour l'Analyse
and Contemporary French Thought

This project is funded by an Arts and Humanities Research Council (AHRC) research grant and is supported by the Centre for Research in Modern European Philosophy (CRMEP) and Kingston University's Faculty of Arts and Social Sciences.

Dmitri Mendeleev (1834-1907) was a Russian chemist most famous for his invention of what is universally recognized as the periodic table of elements. Widely renowned in his own day, his accomplishment was particularly impressive in that Mendeleev correctly predicted the existence and qualities of several as yet undiscovered elements.

This set of brief excerpts from the 1897 French translation of Mendeleev’s Principles of Chemistry, based on the fifth edition of this volume first composed between 1869 and 1871, begins with the following editorial notice: ‘What we have isolated in the last chapter of the principles of chemistry (in M.E. Achkinasi and M.H. Carrion’s French translation) is too fragmentary for a study of Mendeleev’s chemistry, but it is enough to understand the concept of the periodic system of elements’ (CpA 9.14:195). The rationale for the selections is further clarified by the subsequent article in this issue of the Cahiers, an excerpt from a book by Gaston Bachelard (CpA 9.15) that makes use of many of the reproduced passages.

As suggested by the editorial notice, these excerpts from Mendeleev’s work have a narrow and recurrent focus on the nature of periodicity as a function of the punctual repetition of quantitative form, in this case the quantitative form of ‘atomic weight’ (or ‘atomic mass’). Crucial to Mendeleev’s vision is the primacy of measure over and against the discernment of phenomenal quality. He presents as a scientific problem the analogy between certain elements, and in particular the fact that there can be countervailing analogies on a qualitative level (e.g., Lithium and Barium are similar to Sodium and Potassium in some respects; in others they are more like Magnesium and Calcium). ‘It is therefore obvious’, he writes, ‘that to resolve this question our basis must be not only qualitative chemical properties, but also their quantitative signs, which are susceptible to measurement’ (CpA 9.14:195).

With the ‘cause of analogy’ as the main concern, the investigation proceeds by seeking out the relation between analogical properties and atomic weight. Atomic weight is a precisely measurable property. It ‘expresses the relative mass of the atom, or, in terms abstracted from the notion of atom, this size [grandeur] shows the relation that exists between the constituent masses of independent chemical unities, i.e. elements’ (CpA 9.14:196). With this ‘abstraction’ quantitatively determined, one can then correlate this number to recurrent properties. Whence ‘the periodic law’: ‘the properties of simple bodies, like the forms and properties of combinations, are a periodic function of the size of their atomic weight’ (CpA 9.14:196). [N.B. This ‘law’ is most familiar today in the short form: ‘the physical and chemical properties of elements are periodic functions of their atomic mass’.]

The remaining extracts from Mendeleev’s work confirm the predictive aspect of his insight. They reflect as well on the success of his predictions in one instance, given that a predicted element was discovered in his lifetime. In a formulation that likely resonated with those members of the Cercle d’Épistémologie intrigued by Georg Cantor’s use of the Hebrew aleph to name the first transfinite cardinal, Mendeleev had named his first predicted element ékasilicon, ‘éka’ being the Sanskrit prefix meaning ‘one’ and silicon being the adjacent element in the group to the blank space in which the new element would one day be inscribed (CpA 9.14:198). Sure enough, when ‘Germanium’ was later discovered in 1886 it had the properties predicted by Mendeleev and occupied its position in place IV-5 (fourth group – i.e. column, today IV-A; fifth series – i.e. row or period).

Read in the context of the Cahiers pour l’Analyse it is not difficult to see the appeal of Mendeleev’s work. In effect, a preliminary abstraction – the one that allows determination of atomic weight or mass – makes it possible to determine in advance qualitative phenomena. This primacy of number, of the discrete and quantitative – predicated in turn upon a void, since it concerns only the relation of atomic constituents and no primordial substance – allows not only for the speculative thinking, but the theoretical determination, of qualitative form. Finally, Mendeleev’s movement from a question concerning ‘cause’ to an emphasis on the formal and determinative category of ‘law’ resonates with the distinction between cause and law one finds elsewhere in the Cahiers, not least in Thomas Herbert’s inquiry into ideology in the same issue (CpA 9.5). The insight procured in Herbert’s analysis is that any transformation of the political field will not result not from mere knowledge of the ‘causal mechanism’, but in a transformative confrontation with the law that makes a given causal chain or set of relations operative in the first place.