To work on a concept is to vary its extension and comprehension, to generalise it through the incorporation of exceptional traits, to export it beyond its region of origin, to take it as a model or inversely, to search for a model for it - in short, to progressively confer upon it, through regulated transformations, the function of a form.1
The Cahiers pour l’Analyse - literally ‘Notebooks for Analysis’ - set out to ‘work’ on concepts in this sense. The Cahiers can be read as a series of extensions and transformations of specific concepts inherited from the works of Bachelard (epistemological break and rupture, ideological mutation), Althusser (theory, practice, ideology) and Lacan (suture, foreclosure, objet petit a, signifier, subject of science, vacillation).
Although philosophical considerations of the concept in German Idealism were certainly germane to the efforts of the authors of the Cahiers, the primary sources of influence on the journal were the ‘philosophy of the concept’ first proposed by Jean Cavaillès and central to French epistemology and the rethinking of the concept’s role in mathematics and logic initiated by Gottlob Frege.
In the idealist tradition, concepts were most fundamentally representational. Concepts in thought ‘represent’ something extrinsic to thought. The major revolution in Frege’s logic was to overturn this representationalist model and the grammar it was predicated upon. In traditional logic, the attribution of a concept was a matter of coordinating conceptual referents. For example, the truth status of the proposition ‘Socrates is a philosopher’ was a question of whether or not the conceptual contents of ‘Socrates’ and ‘a philosopher’ were appropriately aligned via the copula ‘is’. With Frege, the concept ceases to be a univocal category of representation and is instead reconceived as a function. ‘Socrates’ is not a concept; rather, ‘Socrates’ names an object. Inversely, ‘is a philosopher’ is not an object; ‘is a philosopher’ names a concept. What is important here is that the attribution of a concept to a given entity is no longer a matter of the coordination between two independent concepts, but a question of whether or not an entity falls within a category demarcated by a given concept and the function it describes. In other words, concepts are a question primarily of membership rather than representation. The question is not: Is Socrates a philosopher, i.e., is the idea of Socrates I have adequately represented by the concept I have of ‘philosopher’? It is: does the entity ‘Socrates’ belong in the set described by the property, or concept, ‘being a philosopher’?
The difference here may appear subtle, but the implications are profound. In Frege’s view, concepts are themselves ‘abstract objects’ which perform functions and accomplish mental tasks. Yet they are no less real for being artefacts of thought irreducible to a psychological substrate. Frege’s project was foundational for mathematical set theory and for the development of mathematical logic. As for French epistemology, the pertinence of Frege’s thinking to Canguilhem’s formulation cited above is clear. ‘Working’ concepts is not a matter of one-to-one coordination between ideas or entities and their conceptual correlates. ‘Working’ concepts means working with ‘their domain of extension’, i.e., determining how concepts modify, describe, or create.
Indeed, what distinguishes the ‘philosophy of the concept’ sketched by Cavaillès from idealist models is that it makes no recourse to a transcendental domain (be it Kantian consciousness or Hegelian ‘History’ ) wherein the movement of the concept ‘takes place’. Rather, concepts themselves are functional and determinant in a given theoretically demarcated domain. This notion of conceptual work will itself be modified and transformed in Althusser’s rethinking of Marxism. For Althusser, Marx’s key concepts (e.g., mode of production, class struggle, etc.) function in something like the Fregean sense. They intervene in a field to transform the material of that field and its formal arrangement. Concepts are no longer a reflective medium of thought but are instead the mechanism by which ‘theoretical practice’ – a core concept of Althusser’s own – operates.
In Althusser’s materialist epistemology, the raw material of a science is itself conceptual:
At its moment of constitution, as for physics with Galileo and for the science of the evolution of social formations (historical materialism) with Marx, a science always works on existing concepts, ‘Vorstellungen’, that is, a preliminary Generality I of an ideological nature. It does not ‘work’ on a purely objective ‘given’, that of pure and absolute ‘facts’. On the contrary, its particular labour consists of elaborating its own scientific facts through a critique of the ideological ‘facts’ elaborated by an earlier ideological theoretical practice.2
In the language of ‘On the Materialist Dialectic’, the raw material of a science is composed of ‘still ideological concepts, or of scientific “facts”, or of already scientifically elaborated concepts which belong nevertheless to an earlier phase of the science’. A second level of generality, theory, works on concepts of a lower level generality in order to produce ‘Generality III’, knowledge.
The ‘philosophy of the concept’ called for at the end of Cavaillès’s Sur la logique et la théorie de la science was an inchoate concept itself, but one that nonetheless proved remarkably fecund for thinkers operating in the Althusserian tradition. Cavaillès’s three-pronged critique of neo-Kantian historicism, ahistorical logicism, and Husserlian phenomenology anticipates many of the guiding concerns of the Cercle d’Épistémologie. For Cavaillès, science operates by a ‘perpetual revision of contents through deepening and erasure’. Moreover, Cavaillès specified that the ‘generative necessity’ at the core of scientific ‘progress’ was not that of an activity, but of a dialectic. Cavaillès’s refusal either to link the dialectic of concepts to the ‘activity’ of an agent extrinsic to conceptual play, or to a fixed set of contents (themselves undergoing perpetual revision and erasure), was developed within the Cahiers pour l’Analyse through its own conceptual labour, even as it was subjected to a kind of immanent critique in the pages of the journal itself (cf. François Regnault’s ‘Dialectique d’épistémologies’, CpA 9.4).
The Cahiers’ commitment to a ‘philosophy of the concept’ should not be mistaken for a programmatic uniformity, so much as a common allegiance to a set of distinct but open (and expanding) problems. In the Cahiers several unresolved debates around the nature of the concept develop from their immediate origins in Frege, Canguilhem, Althusser, and so on, ranging from disputes about the extent to which the development of concepts is conditioned by social formations (cf. Thomas Herbert’s articles, CpA 2.6 and 9.5, and the exchange with Michel Foucault, CpA 9.1-3) to disagreements about the nature of conceptual development within science and its relation to formal and intuitive modes of thought (cf. the whole of CpA 10).
In the Cahiers pour l’Analyse
Aside from work on particular concepts in the Cahiers, the first volume contains an extensive discussion of the nature of concepts as such, with specific reference to Frege’s philosophy. In CpA 1.2 and CpA 1.3. Yves Duroux and Jacques-Alain Miller engage Gottlob Frege’s theory of concepts as a basis for a logic of the signifier. According to Duroux, Frege takes up and modifies the concept of Vorstellung (representation), inherited from the German philosophical tradition, making a division between merely subjective representations, and properly ‘objective’ representations, which can be treated purely according to logical laws. Objective representations must themselves be divided into a concept on the one hand, and an object on the other. The ‘objects’ that are correlative to concepts are not necessarily empirically real objects, but may be entirely ideal; what is important is that they obey a logical structure and contain what Frege called ‘judgeable content’. Duroux shows how for Frege, number is first of all something that is ‘assigned’ to concepts (CpA 1.2:33).
At the outset of ‘La Suture: Éléments de la logique du signifiant’ (CpA 1.3), Miller says that the objective of his paper is to ‘articulate the concept of suture which, if it is not named explicitly as such by Jacques Lacan, is constantly present in his system’. His extension and transformation of Lacan’s ‘concept’ of suture proceeds by way of Frege’s theory of concepts, as laid out by Duroux. Miller elaborates that Frege’s discourse starts from a ‘fundamental system’ comprising the three concepts of Concept, Object and Number, and two relations, that of the concept to the object (subsumption), and that of the concept to the number (assignation). ‘What is specifically logical about this system’, Miller says, ‘is that each concept is only defined and exists solely through the relation which it maintains as subsumer with that which it subsumes. Similarly, an object only has existence in so far as it falls under a concept, there being no other determination involved in its logical existence’ (CpA 1.3:41). Nevertheless, according to Miller’s argument, Frege’s logicism rests on an implicit logic of the signifier. ‘It is clear that the concept which operates in the system, formed solely through the determination of subsumption, is a redoubled concept: the concept of identity to a concept’ (CpA 1.3:42). This presupposition of numerical identity in the object undermines Frege’s claim to ground the concept of number in purely logical terms.
In ‘L’Analyste à sa place?’ (CpA 1.4), Serge Leclaire takes up Freud’s use of the term ‘unconscious concept’ ‘to connote the unity of things that are small or indifferent, but which are capable of being separated from the body’ (SE 17: 131). Leclaire says that this concept (which connects infantile representations of the faeces, the penis, and babies) ‘certainly involves a unity, but one that covers things that are non-identical to themselves’. Responding to Miller’s ‘Suture’, he suggests that ‘perhaps we have here the concept, the reality of a thing that is non-identical to itself’ (CpA 1.4:52; cf. also ‘Compter avec la psychanalyse’, (CpA 1.5:67-68).
In the final issue of the Cahiers, on the theme of formalisation, Cantor’s ‘Foundations of a General Theory of Sets’ begins with the remark that further progress in set theory ‘depends on extending the concept of real integer beyond the previous boundaries; this extension lies in a direction which, so far as I know, nobody has yet attempted to explore’ (CpA 10.3:35; trans. 882). Cantor was a primary source of inspiration for Cavaillès’s thinking, much as he would be for Alain Badiou, who explores the nature of conceptual change in mathematical theory in his contributions to the Cahiers (CpA 9.8, 10.8). Other contributors will dispute whether or not conceptual thought can, in fact, in the last instance proceed without reference to a ground – be it lack or presence – extrinsic to the thinking itself (cf. Jean Ladrière ‘Le Théorème de Löwenheim-Skolem’ CpA 10.6). The fact that both Badiou and Ladrière could effectively call upon Cavaillès’s ‘philosophy of the concept’ for support itself testifies to the ongoing fecundity of this problematic.
- Althusser, Louis. ‘Sur la Dialectique matérialiste’. La Pensée 110 (August 1963): 5-46. Reprinted in Pour Marx. Paris: Maspero, 1965. ‘On the Materialist Dialectic’. In For Marx, trans. Ben Brewster. London: New Left Books, 1969. Online at http://www.marx2mao.com/Other/FM65NB.html.
- Canguilhem, Georges. ‘Dialectique et philosophie du non chez Gaston Bachelard’. Revue Internationale de Philosophie, 1963.
- Cavaillès, Jean. Sur la logique et la théorie de la science , prefaces by Gaston Bachelard, Georges Canguilhem and Charles Ehresmann. 2nd edition. Paris: Vrin, 2008.
- Foucault, Michel. ‘La Vie: Expérience et science’, Revue de métaphysique et de morale, 90: 1, 1985. ‘Life: Experience and Science’, trans. Robert Hurley. In Foucault, The Essential Works, vol. 1: Aesthetics, Method, and Epistemology, ed. James D. Faubion. London: Penguin, 1998.
- Frege, Gottlob. The Foundations of Arithmetic , trans. J.L. Austin. Evanston, Illinois: Northwestern University Press, 1980.
- ---. ‘Concept Writing’, in Conceptual Notation and Related Articles, trans. Terrell Ward Bynum. Oxford: Oxford University Press, 1972.
- Freud, Sigmund. ‘History of an Infantile Neurosis’ (‘The Wolf Man’). In Standard Edition of the Complete Psychological Works of Sigmund Freud, ed. James Strachey et al. London: Hogarth Press, 1953-1974. Vol. 17.
- Van Heijenoort, Jean. From Frege to Gödel: A Source Book in Mathematical Logic. Cambridge, MA: Harvard University Press, 1967.