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.

Although this excerpt on Mendeleev is the only reproduction of his work in the Cahiers pour l’Analyse, Gaston Bachelard (1884-1962) exerted a profound influence on the journal. Generally recognized as the single most influential thinker at the source of recent French epistemology and philosophy of science (notwithstanding precursors in the nineteenth century such as Pierre Duhem), Bachelard wrote a series of studies in the 1930s and 40s that would be foundational for the Cercle d’Épistémologie’s efforts in the Cahiers.

Two elements of Bachelard’s thinking were of especial importance, both discernable in this discussion of Mendeleev’s discovery of the periodic law. First is the conception of the ‘epistemological rupture’, the idea that the development of science out of ideology proceeds by way of epistemological breaks. In his books The New Scientific Spirit (1934) and The Formation of the Scientific Mind (1938), Bachelard developed the notion that in each instance scientific thinking begins through a rupture with immediate experience. In contrast to phenomenology, which sought to ground scientific knowledge in the pre-predicative experience of a lifeworld anterior to rational thought, for Bachelard scientific knowledge was the result of a confrontation between rational thought and a hitherto inchoate real. The peculiar kind of negation involved in this confrontation, which valorised the capacity of formal thought to supervene on the ‘real’, constitutes the second main element of Bachelard’s influence on the Cahiers. Bachelard’s more general anti-Hegelianism on this score is evident in his conviction that rational thought is not a retrospective manoeuvre or sublimation but itself an anticipatory and determining form: ‘Realisation prevails over reality. [...] Theory is a mathematical truth that has not yet found its complete realisation. The scientist must seek out this complete realisation. It is necessary to force nature to go as far as our minds.’¹ This passage comes from Bachelard’s The Philosophy of No, and the epigraph reproduced in each volume of the Cahiers comes from Georges Canguilhem’s review of this book: ‘To work a concept is to vary its extension and comprehension, to generalise it through the incorporation of exceptional traits, to export it out of its original region, to take it as a model or, inversely, to search out a model for it. In short, it is to confer progressively upon it, through regulated transformations, the function of a form’. As Bachelard’s text makes clear, Dmitri Mendeleev’s formulation of the periodic law is a perfect exemplar of this injunction.

‘The Classification of Elements according to Mendeleev’ comes from a book Bachelard published in 1932 titled Le Pluralisme cohérent de la chimie moderne [The Coherent Pluralism of Modern Chemistry]. The reconstruction of Mendeleev’s approach contained therein is intended to demonstrate its scientific rationality and above all the anteriority, and theoretical priority, of rational ordering over empirical findings. It is not simply that a coherent rational order allows the scientist to spot inconsistencies in empirical data, but that the rational order itself can determine the contours of future empirical developments and discoveries.

Bachelard begins by distinguishing Mendeleev’s principle of classification from a purely empirical classification by similarity. The latter tends toward metaphysics as it moves from function to substance, ultimately relying on a metaphysical essence that grounds phenomena in an independent and primordial variable (something along the lines of the classical ‘elements’ jettisoned in Lavoisier’s signal contribution to modern chemistry (CpA 9.12; cf. CpA 9.9:145). Mendeleev seeks the ‘well-specified, unique property’ (CpA 9.15:200) that accounts for the similarity among elements, but he also wants to avoid a merely pragmatic conception that is tethered to the changing behaviour of elements in different environments while remaining unable to explain it.

The solution lies in Mendeleev’s attempt to classify the elements according to their atomic weight alone, that is, by a quantitative variable that bears no immediate, or obvious, connection to qualitative manifestation. Through this comparison, he arrives at the conclusion that, indeed, all the properties of a substance are determined by its weight. In 1869 Mendeleev postulates his law of periodicity: ‘The properties of simple bodies, like the forms and properties of combinations, are a periodical function of the size of atomic weight’.

Mendeleev finds that if he combines different elements R with a monovalent element X (an element that can form only one bond) he encounters eight types of combinations. In his work on oxidation he encounters this figure again in eight types of oxidation. Mendeleev then discovers that the complementary presence of oxygen and hydrogen components confirms his thesis that no matter how many elements are involved in a chemical bond, it always obeys the same general quantifiable law. Bachelard calls this the ‘experimental birth of the notion of octave’ (202). What is noteworthy about this notion – what makes it neither pragmatic, nor phenomenological, nor merely ‘mnemotechnical’ – is that it ultimately has no intuitive base. ‘In Mendeleev’s work, no intuition will support or explain the fact that the sum of the equivalences between oxygen and hydrogen in different bodies is equal to eight’ (202).

In other words, Mendeleev’s realism – and Bachelard maintains that this is indeed a form of realism – is predicated precisely upon an abandonment of a quest for an intuitive base to his experimental findings. Here mathematics plays the decisive role. Mendeleev’s ‘audacity’, the certainty with which he relies on the weight of atoms as a determining factor, arises from the conviction that what he is ultimately dealing with is a finite number of possible combinations. What he needs is a mathematics that articulates or models periodicity, and this he finds in trigonometry, which charts functions in waves, that is to say, in periods. ‘Moreover, as Mendeleev notes, it is trigonometric functions “that provide the most rational way to seek to express the dependence between the properties of simple bodies and their atomic weight because this dependence is periodic like the functions of trigonometric lines”’ (204). Even so, however, trigonometric functions will, like the geometric representation of curves, be found inadequate for Mendeleev since neither can account for the ‘discontinuous character of stoichiometry, and this is the most important aspect of the question’. (‘Stoichiometry’ refers to the calculation of the quantitative aspects of a chemical reaction or process). It is this primacy of discontinuity that precisely allows for the categorization of the periodic table into discrete elements.

Ultimately, Bachelard’s account of Mendeleev’s work emphasises its realism and the primacy of rational initiative over phenomenological or empirical evidence. He criticises Friedrich Ostwald’s assessment of Mendeleev, which neglects the prescriptive power of the periodic law and instead sees it, in the light of its uncertain empirical proof, as a mere general rule on a par with early classifications in natural history. According to Bachelard, Ostwald mistakes the uncertainty of the empirical proof for the apparent indeterminacy of the law itself. Mendeleev himself, on the contrary, relied with such confidence on the validity of this law that he was able to predict the existence of chemical elements and their properties well before their actual, empirical discovery (CpA 9.14). Among Mendeleev’s contemporaries and fellow contenders for establishing something like the periodic table, it occurred to no one else to leave spaces in their table for elements that had a rational justification, but were yet to be discovered, nor to modify adopted atomic weights – apparently empirically justified – ‘to make them fit the system [pour les plier au système]’ (206), and not the reverse.

Notes

1. Bachelard, Philosophie du non, 36. ↵