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

Linguists describe as ‘metalanguage’ any form of language that refers to the properties and operations of language itself. Rather than denote an object or communicate a meaning, for example, metalinguistic discourse refers to the process through which language denotes or communicates; rather than communicate a meaning, it aims to explain how such communication proceeds, or helps to ensure that it is successful. Familiar metalinguistic expressions include phrases like ‘in other words’, ‘so to speak’, ‘I mean’, ‘do you know what I mean?’, etc. Roman Jakobson included the metalinguistic as one of five general functions of language, along with the referential, emotive, conative, phatic, and poetic. The metalinguistic function is concerned with the status of the ‘linguistic code’ itself, rather than the use of that code to refer to an object, issue a command, etc.¹

In modern logic, a metalanguage is typically contrasted with an ‘object language’. The distinction was developed by the Polish mathematician, logician, and philosopher Alfred Tarski in a 1933 article titled ‘The Concept of Truth in Formalized Languages’. Tarski’s goal was to provide a way for logicians to think through those instances wherein language is being used to talk about language itself and standard models of external reference do not apply. By applying the distinction between object language and a hierarchy of metalanguages, Tarski believed that formalised logic could avoid paradoxes of self-reference and serve as a reliable framework for the physical sciences. The basic distinction between object- and meta-language is nevertheless readily expressed in natural languages. In the sentence, ‘In French, you say bonjour to say hello to someone’, English is the metalanguage and French is the ‘object language’. Or consider the following two sentences: ‘Paris is the capital of France’, and ‘“Paris” is the name of the capital of France’. In this example, the distinction between metalanguage and ‘object language’ is not between two different tongues, it is instead internal to the grammar itself: in this first sentence, there is no metalanguage/‘object-language’ distinction, whereas in the second, we are effectively using language to talk about language. In general, we use metalanguage in Tarski’s sense whenever we put scare quotes around something we say.

Tarski’s distinction would be of crucial importance to Bertrand Russell, who used it in his own effort to defend his hierarchical ‘theory of types’ (Cf. CpA 10.4) and in his introduction to Ludwig Wittgenstein’s Tractatus Logico-Philosophicus. For Russell, Tarski’s theory provided a possible escape from Wittgenstein’s claim that syntax itself can only ever be ‘shown’ and never expressed in words.² Russell added a twist to the sense of ‘object language’ in his 1940 William James lectures (later published as An Inquiry into Meaning and Truth) when he used the expression to refer to a kind of ‘primary language’ that served as a lower limit for language as such. For Russell, it was self-evident that an ascending hierarchy of languages had no upper limit. By contrast, the hierarchy could not extend indefinitely ‘downward, since, if it did, language could never get started.’³ Later on, Russell defined this ‘primary’ or ‘object language’ as ‘a language consisting wholly of “object-words”, where “object-words” are defined, logically, as words having meaning in isolation, and, psychologically, as words which have been learnt without its being necessary to have previously learnt any other words.’ ⁴

According to Dylan Evans, ‘Lacan’s first reference to metalanguage comes in 1956, when he echoes Jakobson’s view on the metalinguistic function of all language: “All language implies a metalanguage, it’s already a metalanguage of its own register”’.⁵ By 1960, however, Lacan had come round to what would remain his subsequent view when he argued, referring to ‘the conception of the Other as the locus of the signifier’, that ‘no authoritative statement has any other guarantee here than its very enunciation, since it would be pointless for the statement to seek it in another signifier, which could in no way appear outside that locus. I formulate this by saying that there is no metalanguage that can be spoken, or, more aphoristically, that there is no Other of the Other. And when the Legislator (he who claims to lay down the Law) comes forward to make up for this, he does so as an impostor.’⁶ A few years later, in 1964, Lacan considered the question again, precisely in the light of Russell’s approach to logic. In the second session of his Seminar XII (9 December 1964), attended by many of the normaliens who were later to contribute to the Cahiers, Lacan directly referenced Russell’s An Inquiry into Meaning and Truth:

You will see there that by questioning things from the angle of this pure logic, Bertrand Russell conceives of language as a superimposition, a scaffolding, an indeterminate number of metalanguages. Each propositional level is subordinated to the control or to the correction of a higher-order proposition, where it is put in question as a first proposition […]. I think that this work, like any other by Bertrand Russell, is exemplary, in the fact that taking to its final term what I would call the very possibility of a metalanguage, he shows its absurdity precisely in the following: that the fundamental affirmation from which we begin here, and without which there would not be, in effect, any problem about the relationships between language and thought, between language and the subject, is the fact that there is no metalanguage. Every approach including structural linguistics is secondary, at a loss, compared to the first and pure use of language. Every logical development, whatever it may be, presumes at the origin the language from which it is detached […]. Mr. Bertrand Russell, to compose his language, made up of the scaffolding, of the Babel-like edifice of metalanguages, one on top of the other, thought that there must be a foundation; so he invented object-language. There must be a level, unfortunately nobody is able to grasp it, where language is in itself pure object. I defy you to put forward a single conjunction of signifiers which could have that function (2nd session, 9 December 1964, 13).

Lacan’s criticism of Russell posed a problem for the thinkers of the Cahiers pour l’Analyse, who were in search of principles for a general theory of discourse. Jacques-Alain Miller approaches the problem of metalanguage most directly in his key essay ‘Action de la structure’ (CpA 9.6), and he takes up the issue in other essays also written during the Cahiers period, but not published until the 1970s. Questions related to the possibility of metalanguage and its viability as a concept arguably inform many of the debates about formalisation and the relation between science and ideology in the Cahiers.

In the Cahiers pour l’Analyse

In the first text of the first issue, ‘La Science et la vérité’ (CpA 1.1), Lacan condenses and restates the critique of metalanguage in Seminar XII in the context of his ideas about the nature of truth. For Lacan, truth is not something spoken ‘of’ in a derivative or ‘meta-’ way; rather, it functions as the ‘cause’ of speech. In speech, regardless of intention or conscious will, it is truth itself that speaks; truth cannot be ‘spoken of’ in a metalanguage, but is rather ‘spoken’ through the symptoms that punctuate speech. Lacan is emphatic in his judgment: ‘there is no such thing as metalanguage (an assertion made so as to situate all of logical positivism), no language able to say the truth about truth, since truth is grounded in the fact that truth speaks, and that it has no other means by which to become grounded’ (CpA 1.1:18). Lacan then attributes the ‘traps of metalanguage, as sham and logic’ to ‘a lack of truth about truth’, that is, a ‘primal repression’ of this truth itself that allows for the ascending hierarchy of illusory metalanguages (CpA 1.1:19).

Jacques-Alain Miller refers to Lacan’s criticism of the concept of metalanguage in his ‘La Suture: Éléments d’un logique du signifiant’ (CpA 1.3:46n). Miller’s suggestion that Frege generates the sequence of whole numbers out of a ‘primal repression’ of lack that attributes to the concept of ‘non-identical to itself’ the mark of zero recalls Lacan’s critique of metalanguage in ‘La Science et la vérité’; both Lacan and Miller identify a covering over of an originary lack that allows for the possibility, and proliferation, of ‘science’ itself as a discourse. However, Miller’s commitment to the project of a general theory of discourse (as evidenced in ‘Action de la structure’ (CpA 9.6) oblige him to reject the sceptical implications of Lacan’s position and to find some means to defend a contemporary doctrine of science.

The term ‘metalanguage’ will resurface in François Regnault’s ‘Dialectique d’épistémologies’ (CpA 9.4) wherein the problematic of science’s relation to epistemology is expressed in such terms. ‘Were it to be objected that […] we prejudge the nature of epistemology by defining it as discourse on science’, Regnault writes, ‘we would repeat that, if the model is well made and considers the cases of science’s existence as well as non-existence, its unity as well as multiplicity, we will have effectively neutralised the danger of presupposition: if science disappears, as being and as one, there certainly remains this subordination to this Unding of the discourse that says it, but at the same time the relation is reduced to the minimum, i.e. to indetermination. […] This is to limit the presuppositions to nothing, except to the relation of a metalanguage to a language, whence the following sole postulate: every statement on science (or the sciences) belongs to what we will call epistemology, a domain defined by these statements’ (CpA 9.4:52).

In his comments in ‘Action de la structure’ (CpA 9.6) on the possibility of a doctrine of science, Jacques-Alain Miller attempts to provide a consistent theory of discourse that can both account for the possibility of closure in scientific theories while still attributing some form of lack to science. Miller proposes an anonymous ‘doctrine of science’ that can take account of the foreclosive character of science, as well as the sutures of ideological discourse. In the 1968 Appendix to the piece, Miller turns to the work of J.G. Fichte for an account of the fundamental properties of such a doctrine or Wissenschaftslehre. The key to the doctrine of science, Miller contends, is the notion of ‘auto-reflexivity’, which ‘by prohibiting the division of its own enunciation, makes the metalanguage indistinguishable in its field from the object language’ (CpA 9.6:104).⁷ Miller concludes that a doctrine of science is impossible, but that the attempt to grasp this impossibility is necessary both to desire and discourse.

The final issue of the Cahiers, on ‘Formalisation’, contains several texts that, although they do not address metalanguage directly, remain engaged with its problematic. Jean Ladrière’s assessment of the Löwenheim-Skolem theorem (CpA 10.6) argues that each instance of establishing a ‘metatheorem’ which describes another theorem involves an element of intuition that at once spurs formalisation and resists being incorporated into the formalised result. Alain Badiou’s ‘Marque et manque’ (CpA 10.8) argues for an image of logic as stratified rather than sutured. Badiou effectively treats the relation of increasing higher-order stratification (something akin to metalanguage) as unproblematic in its relation to ‘the absolutely primary raw material of the logical process [… ,] the stock of graphic marks [… ,] that we will call: alphabet’ (CpA 10.8:151-2) (something akin to ‘object language’). Finally, in the last article of the journal, Jacques Bouveresse enumerates Wittgenstein’s critique of efforts to ground mathematics in logical form, a critique which takes the form of a critique of the logic of the ‘meta-’ as such. For Wittgenstein, there is nothing essentially hierarchical, in the sense of ascendancy, in the establishment of new theorems based on old ones. ‘Metamathematics’ is not a higher-order ‘theory’ of mathematics by virtue of being ‘meta-’; it remains nonetheless a demonstration, like mathematics itself (CpA 10.9:195). As Wittgenstein says, referring to a game and its rules, ‘I can also invent a game in which I play with the rules themselves […, and] in that case I have yet another game and not a metagame’.⁸

A postscript to the Cahiers debates over metalanguage can be found in Jacques-Alain Miller’s ‘U ou “Il n’y a pas de méta-langage”’, written in 1967, but only published in 1975/76 in the journal Ornicar?.⁹ Developing Lacan’s critique of Russell further, as well as his own claims in ‘Suture’, Miller indicates how ‘metalanguage’ and ‘object language’ share the same characteristic that neither can be spoken or made present in itself. Just as one can never reach an ‘absolute’ metalanguage that would be the upper-limit, the lower limit ‘object language’ in Russell’s sense can also never be ‘reached’. Miller adopts the concept of ‘U-language’ from the logician Haskell B. Curry to describe the ineliminable ‘language being used’ in each instance as the absolute baseline, lower limit of language, subtending even Russell’s lowest ‘primary’ or ‘object language’, but also providing the domain in which any metalanguistic stratification takes place. ‘If U-language can be spoken, it is because it speaks of itself. It is itself metalanguage and object-language.’¹⁰ Miller describes this ‘U-language’ as ‘ultimate’ and ‘unique’ language. It is without exterior and cannot be transcended; it cannot be learned or spoken in the way an ordinary language can, precisely because ‘it speaks all by itself’. Miller contends the ‘Freudian rule’ is nothing other than introducing the subject to this dimension. In its status as a kind of absolute that can neither be totalized, appropriated nor spoken (by a conscious subject), the ‘U-language’ of this essay resembles the self-speaking truth described by Lacan in ‘La Science et la vérité’ (CpA 1.1:18; E, 867).

Select bibliography

• Curry, Haskell B. Foundations of Mathematical Logic. New York: McGraw-Hill, 1963.
• Evans, Dylan. An Introductory Dictionary of Lacanian Psychoanalysis. London: Routledge, 1996.
• Lacan, Jacques. Seminar XII: Crucial Problems for Psychoanalysis (1964-1965), trans. Cormac Gallagher, unpublished manuscript.
• Miller, Jacques-Alain. Un début dans la vie. Paris: Gallimard, 2002.
• Russell, Bertrand. An Inquiry into Meaning and Truth [1950]. London: Routledge, 1995.
• Tarski, Alfred. ‘The Concept of Truth in Formalized Languages’. In Logic, Semantics, Metamathematics, ed. John Corcoran. Indianapolis: Hackett, 1993.
• Wittgenstein, Ludwig. Remarks on the Foundations of Mathematics, ed. G.H. von Wright et al., trans. G.E.M. Anscombe. Cambridge: MIT Press 1978.