1 Philippe De Brabanter 1. I

Logique & Analyse 248 (2019), 351-378

WHAT DO WE MEAN WHEN WE TALK OF OBJECT-LANGUAGE AND METALANGUAGE IN THE THEORY OF NATURAL LANGUAGES?1

Philippe De Brabanter

Abstract In this paper I raise the issue whether it is legitimate to talk about metalanguage and object-language in the context of natural language, as linguists often do. I show that whereas the study of formalised languages allows a clear distinction between metalanguage and object-language, that distinction is muddied by a number of factors when it comes to natural language use. I also show that in the latter context, talk of metalanguage and object-language requires making a further distinction, between object-language and natural language, and that none of the features displayed by metalanguage and object-language in logical theory has a perfect counterpart in the realm of natural languages. In particular a natural ‘object-language’ proves not to be a language after all, while a natural ‘metalanguage’ should arguably be regarded as a use of a language instead of as a language in its own right. Keywords: metalanguage, object-language, formalised language, colloquial language, natural language, quotation, meta-word, metalexicon

1. Introduction

Linguists make frequent use of the term metalinguistic, and more occa- sional use of metalanguage, and object-language in discussions of natural- language phenomena.2 In what senses exactly? Do those terms borrowed

1 I would like to thank the audience at the conference Language and metalanguage, logic and meta-logic. Revisiting Tarski’s hierarchy, UCLouvain, May 19, 2016, for useful com- ments and challenges. I am indebted to an anonymous reviewer and to Raf Salkie for pointing out flaws in an earlier version of this paper, and to Mikhail Kissine for helpful suggestions. Finally, I gratefully acknowledge the financial support of the F.R.S.-FNRS research project T.0184.16, 2016-2020. 2 A note on the quoting conventions used in the body of this paper: – single quotes for the introduction of terminology, and for scare quoting – italics for metalinguistic citations, and for emphasis – double quotes for citations of other authors, and for direct discourse more generally – French angle quotation marks for meanings/contents – boldface for parts of examples that deserve special attention (mostly, quotations) These conventions are not necessarily followed in the examples when these are borrowed from external sources (various writers stick to various rules). doi: 10.2143/LEA.248.0.3287321 © 2019 by Peeters Publishers. All rights reserved. 352 PHILIPPE DE BRABANTER from the theory of formalised languages make sense when applied to the theory of natural languages? These are the questions I seek to answer in the present paper. My starting-point is a very conservative picture of the relations between object-language and metalanguage as defined for formalised languages. In particular, I am not concerned with the following issues: – the reasons logicians/philosophers had for making the distinction between object-language and metalanguage; – logicians’/philosophers’ views on the defective design features of natural languages; – the different kinds of metalanguage that can be distinguished in the theory of formalised languages (e.g. syntactic vs. semantic); – more recent proposals in logic for doing away with the (need for a) distinction between object-language and metalanguage.

The paper is organised as follows: after this short introduction, I devote Section 2 to a brief outline of the core design features of the metalanguages used in the theory of formalised languages, and how they relate to their object-languages. In 3, I examine at length what happens to these features and relations in the natural-language context. In Section 4, I offer diagrams of the relations between metalanguage, object-language, and natural language. This is followed by a brief conclusion in Section 5.

2. Object-language and metalanguage in the theory of formalised languages: a brief sketch

In the 1930s, Alfred Tarski put forward the idea that the truth-predicate of a language L — the semantic predicate par excellence — could not be defined in that very language, on pain of generating semantic paradoxes of self-reference such as the ‘Liar paradox’. His solution was to develop a view according to which there exists a hierarchy of languages, and truth in a language of level n (an object-language, LO) is to be defined in a richer, higher-order language of level n+1 (its metalanguage, LM) (e.g. Tarski 1944: 350).

In Tarski’s framework, an LM is always the metalanguage of a particular LO. Such an LM must contain at least the following building blocks:

– names of, and variables for, the well-formed formulas of the LO whose semantics is at stake (Tarski 1983:3 172-173; also Carnap 1947: 4; Church 1956: 60). In the cases that will be of greatest interest to us, those

3 This is the translation of a paper originally published in Polish in 1933. OBJECT-LANGUAGE AND METALANGUAGE 353

names are quotations, typically formed by enclosing LO formulas in quotation marks. – semantic predicates, such as true (sentence-in-L), satisfy, denote, designate, etc. (Tarski 1983 passim; 1944: 345; also Carnap 1947: 4; Gupta 1998: 266).

– all the LO symbols and formulas, or translations of these (Tarski 1944: 350; also Reichenbach 1947: 10-11; Church 1956: 63; Prior 1967: 230; Simmons 2009: 545).

Those various building blocks are illustrated below in two instances of Tar- ski’s T-sentences. The first one concerns a formalised language; the second one concerns what Tarski called a ‘colloquial language’, and is only provided because it permits me to exemplify a quotation-as-name. Note, however, that Tarski was highly skeptical of the possibility of giving a definition of truth for colloquial languages, owing to what he called their ‘universality’, i.e. the notion that “if we can speak meaningfully about anything at all, we can also speak about it in colloquial language” (Tarski 1983: 164).

(1) 1 2(ı1,2 + ı2,1) is a true sentence (in the language of the calculus of classes, or LCC) if and only if for any classes a and b we have a b or⋂ ⋂b a. (2) ‘Der Schnee ist weiss’ is a true-sentence-in-German if and only if snow⊆ is white.⊆

In (1), true-sentence-in-LCC is a semantic predicate. The expression 4 “ 1 2(ı1,2+ı2,1)” is the name, in the metalanguage, of a sentence of LCC. Here, the metalanguage is a suitably enriched variant of English (cf. also Carnap⋂ ⋂ 1947: 4; Church 1956: 47). Following if and only if, one finds a translation into the metalanguage of the LCC sentence (cf. Tarski 1983: 187). Note that the LCC sentence named and translated in (1) could also have been quoted. This would have been another way of naming it. To see how a sentence can be named by means of a quotation of it, see example (2), where the subject is a quotation-name of a German sentence, true-sentence- in-German is a semantic predicate, and snow is white is an extensionally 5 equivalent translation in EnglishM of a GermanO sentence. Note that if the

4 Exceptionally, for clarity, I use double quotation marks for metalinguistic citation, instead of italics. 5 Where suitable, I use subscripts to specify whether some linguistic object is to be regarded as a metalanguage or an object-language. A caveat is in order, though: in the context of natural languages, as we will see, the subscripts are not equivalent in meaning: GermanO means “the German language, considered as an object of description”; EnglishM means “the set of sentences in English that are metalinguistic”, not “the English language, considered as a metalanguage”. 354 PHILIPPE DE BRABANTER metalanguage had been enriched German, an LO sentence itself rather than its translation would have been used in the metalanguage.

LO’s and LM’s are constructed by logicians. The features that these languages should display are therefore stipulated. LO’s are formalised languages. LM’s are assembled in order to construct these formalised languages 6 and/or describe their semantics. Each particular LM is so designed as to be expressively richer than its LO. Since it is prohibited to name an LO element within LO itself, any sentence that contains a quotation-name of an LO expression is unambiguously a sentence of an LM of that LO. Likewise with sentences including a semantic predicate. This means that sentences of LO and LM can easily be told apart. Some writers think that it is important that LM include translations of all LO expressions instead of these expressions themselves (Carnap 1947: 4; Church 1956: 63; Simmons 2009: 545. For an extended discussion of what Tarski meant by translation, see Mou 2001; Raatikainen 2003).

Others do not seem to care much whether LM includes LO as such or translations (Tarski 1944: 350; Prior 1967: 230). If LM includes translations (and not expressions) of LO, there is no inclusion relation between LM and LO. If (or when) LM includes LO expressions themselves (and not translations), then LM LO (e.g. Tarksi 1944: 350). In the latter case, some sentences are “ambiguous as to level of language”, as Reichenbach (1947: 10) 7 put it. What all ⊃logicians agree on, however, is that LM is of a higher order than LO. Below is a recap of the main properties of the LO-LM relation in the theory of formal languages:

(i) LM is set up to describe/construct a particular LO; (ii) Both LM and LO are languages in their own right; (iii) LM has its own lexicon (set of building blocks). (iv) It is always possible to determine if a building block of a sentence

belongs to LO or LM; (v) It is always possible to determine if a sentence belongs to LO or LM. (vi) LM and LO occur at distinct levels in a hierarchy of languages; (vii) LM is expressively richer than LO. (Under certain conditions, LM LO); ⊃

6 An LM can also be used to formulate the formation and transformation rules (the syntax) of the expressions of an LO, as in Carnap (1934) or Church (1956, chapter 8). In this context, recourse to a metalanguage is a convenience, not a move necessary to avoid paradoxes of self-reference. 7 This ambiguity as to level of language hardly poses a problem for the hierarchy of languages. There is never any point for the logician to produce an object-level sentence, i.e. one containing no quotation-names or semantic predicates, while simultaneously intending it to be understood as a sentence of LM. OBJECT-LANGUAGE AND METALANGUAGE 355

3. Object-language and metalanguage in the theory of natural languages: a detailed discussion

In this central section of the paper, I discuss, in turn, the seven main features identified at the end of Section 2. I start with the question whether ML is used to describe/construct one LO (3.1); I then assess whether LM and LO are languages in their own right (3.2); ask if LM has its own lexicon (3.3); examine in turn the questions whether it is always possible to determine if a component of a sentence belongs to LM or LO (3.4) and if a sentence belongs to LO or LM (3.5); further assess if LO and LM can be said to occur at different levels in a hierarchy of languages (3.6); and close with consid- erations on the expressive power of LM and LO (3.7).

3.1. Is Lm used to describe/construct one LO? The properties of colloquial languages do not result from postulations. Lin- guists seek to account for empirical facts. It is one such empirical fact that, to talk about some particular colloquial language — choosing, say, English as LO (EnglishO) — ordinary speakers/writers can use any language as their metalanguage: (3)-(4). Likewise, a single language — say English, via its LM component (EnglishM) — can be used to talk about expressions and features of any colloquial language (5). These possibilities directly result from the universality of colloquial language. (3) Alice is a philosopher est une proposition principale en anglais. (4) Alice is a philosopher is een hoofdzin in het Engels. (5) Eppur si muove is a sentence in Italian.

Hence, unlike what was observed in the domain of formalised languages, there is no special connection between a particular LO and a particular LM. Now, consider (6), a sentence which makes a general claim about human languages: (6) Across languages, verbs are typically used to denote actions, events and states.

It seems to me obvious that (6) is an English metalinguistic sentence, hence part of EnglishM, although it is not about any particular LO. This further emphasises that there are no one-to-one relations between LO’s and particular LM’s in the context of colloquial languages.

3.2. Are LM and LO languages in their own right?

In the theory of formalised languages, both LM and LO are languages. Is that the case too in the context of colloquial languages? I will consider LM and 356 PHILIPPE DE BRABANTER

LO in turn. In the discussion, I will assume that a language is a (potentially infinite) set of sentences built from a finite lexicon using a finite number of formation (i.e. morphological and syntactic) rules.

3.2.1. LM

In this section, I focus on one LM, namely EnglishM. For EnglishM to count as a language, it must have its own lexicon — which, following Rey-Debove (1978), I will call ‘metalexicon’ — and set of formation rules capable of generating all and only EnglishM sentences, i.e. metalinguistic sentences in English. We want EnglishM to contain sentences like (7), where all the components are English, but also (2) and (5), where the quotations refer to a German and an Italian sentence respectively. (7) With is a preposition.

Regarding the formation rules, we can conservatively assume that they must be essentially the same as those that generate English sentences. The main problems arise in connection with the metalexicon. Two questions, in particular, must be addressed. The first concerns the status of the quotations in the examples seen so far: if they are names, what consequences does this have on the finiteness of the metalexicon? The second is about the colloquial-language counterparts of the semantic predicates: can these be defined as precisely as in the theory of formalised languages? I tackle these questions in Sections 3.3.1 and 3.3.2. I then address questions about meta linguistic sentences in Sections 3.4 and 3.5. Only when all that has been done, can I return to the question whether EnglishM is a language in its own right (Section 3.5.3).

3.2.2. LO

In this section, I consider whatever LO items can be ‘the object’ of EnglishM sentences. We saw above — examples (2) and (5) — that the LO of EnglishM or any other LM must contain at least the set of all colloquial languages. This already entails that the LO of EnglishM is not a language, since there is no single grammar that can generate all the languages of the world without simultaneously overgenerating a vast number of ungrammatical strings.

Maybe we can try saying instead that the LO of EnglishM is the set of colloquial languages: LO = {English, French, Lingala, Chinese, …}. But that will not do. As we shall see presently, it is not just the status of LO as a language that is threatened, but its status as ‘something linguistic’.

Remember that an LM designed to talk about a formalised language has, amongst its building blocks, the names of the well-formed formulas of LO. OBJECT-LANGUAGE AND METALANGUAGE 357

Likewise, in colloquial languages, you can talk about (and quote) words, phrases, sentences, but also other meaningful units such as morphemes (8). Besides, one also encounters quotations of things other than well-formed formulas: ungrammatical structures (9), arbitrary less-than-morphemic units (10), arbitrary non-constituents (11), pseudo-words (12), words in imaginary languages (13), non-words (14). (8) Vasectomy. It’s the -ectomy that puts me off. (Barnes 2001, 109) (9) Slept the a the is made up of English words but is not an English sentence. (cf. Harris 1991: 31) (10) Ever noticed that the -chine of machine is pronounced just like sheen? (11) In the sentence In some cultures being quiet and reserved is seen as a sign of politeness, the string quiet and reserved is seen is not a syntactic constituent. (12) Wug was a pseudoword used by Jean Berko Gleason in her 1958 experiments. (13) In Brobdingnagian, splacknuck is the name given to a very finely shaped animal about six foot long. (14) Wbnjnmrtk is not a word in any known language. (cf. Droste 1983: 687)

The quotations in examples (9) to (14) refer to things that have some of the trappings of genuine linguistic entities but not all. This means that the LO of EnglishM goes beyond the set of colloquial languages and includes elements whose status as linguistic entities is at least disputable. Pseudo-words (12) are special in the sense that they are only ‘pseudo’ with respect to some particular language: wug is pseudo-English as it respects the phono- tactic rules of English. As such, given an expansion of the English lexicon, it could become an English word.8 Hence, pseudo-words are poised on the edge of the English lexicon, and therefore less clearly outside of it than the referents of the quotations in (9), (10), (11), (13) and (14).

How, then, should we best conceive of the LO of EnglishM, or for that matter of any colloquial language? Here I draw inspiration from Droste’s proposal that LO is a “list of referents for the LM proper names” (1983: 690), which I take one step further by arguing that, as soon as one has given up the idea that LO is a language, it might just as well be regarded as a set of ‘quotables’, never mind whether the quotation strictly quotes linguistic objects or not. This move effectively severs the connection between each specific ML and some putative LO that would be its object. But, as we have seen, such a connection is hardly relevant in natural languages, and is therefore not worth preserving.

8 For a detailed discussion of pseudo-words and non-words in this context, see De Bra- banter (2018). Here, I provide only very brief sketches. 358 PHILIPPE DE BRABANTER

Now consider examples like (15), in which words attributed to Galileo are reported directly: (15) Galileo once famously said, “The earth moves”. (15) contains a direct speech report (or direct discourse, henceforth DD). DD standardly takes the form of a quotation. Now, it may be that (15) is not strictly speaking a metalinguistic sentence: although (15) contains a quotation that uses English words, it is not about English. It is about a person who is alleged to have made a particular statement. Besides, what Galileo is supposed to have literally said is Eppur si muove, which further confirms that a DD report is not (usually) intended to make a point about a particular language. Some would therefore argue that (15) should more properly be termed ‘metadiscursive’ than ‘metalinguistic’. This being said, (15) resorts to the same mechanism as, say, examples (2) to (5): it uses a quotation of a linguistic object to talk about a linguistic object. The only notable difference is that it refers to that object as a particular speech act, whereas the previous examples had quotations that referred to linguistic objects ‘out of context’ as it were.9 Note that the metadiscursive and metalinguistic orientations need not be mutually exclusive, witness (16), where the quotation refers both to an utterance ascribed to Tavan and to linguistic evidence for a feature of bare names in Lao: (16) As with reference to persons (see previous example), the use of the bare name in first mention presupposes recognizability or identifiability. This identifiability [of the place mentioned by a previous speaker] is immediately confirmed by Tavan’s reply of“Yeah, there’s no shortage (of that herb) there.” (Enfield 2013: 203) This example suggests that the boundary between metadiscourse and metalanguage may not be clear-cut. Endorsing the admittedly controversial view that instances of DD are relevant for the determination of the contents of LO, one is drawn, step by step, to examples that are more and more remote from the linguistic realm. In (17), the complement of went refers to a specific utterance-token; in (18), it refers to a noise; in (19), the complement of like refers to a person’s attitude. (17) The guy goes, “How much have y’all had to drink?” (Ferrara and Bell 1995: 267)

9 Readers might want to say that there is another difference, between the use of italics and of quotation marks. That, however, is merely a consequence of the typographical conventions I adopted. Note, for example, that a large number of the writers I have referenced so far use quotation marks for metalinguistic citation. OBJECT-LANGUAGE AND METALANGUAGE 359

(18) The door went EEEEEEEAAAAAAAW as he pushed it open. (Davies, BNC) (19) so then she tells me the baby’s by herself, and I’m like [facial expression of shock]. (Fleischmann & Yaguello 2004: 137)

I see no principled way of establishing a cut-off point between ‘narrowly linguistic’ DD and ‘extended’ DD. Simultaneously, I think it is clear that DD, as it resorts to the same mechanism as narrowly defined metalinguistic quotation, is relevant to the determination of LO. Therefore, I find any conservative delimitation of LO unwarranted. I conclude that LO is indeed a set of quotables, not all of which are linguistic in nature. Hence, LO in the context of natural languages is not a language at all.

3.2.3. The need for a third term: LN

In this section so far, I have spelled out the conditions on which LM can be considered a language, deferring until Section 3.5.3 the discussion of whether these conditions are satisfied. I have also shown that LO is not a language, nor even a set of languages, and argued that it was legitimate to view LO as the set of all the items that can be quoted. That set, regardless of whether its extension is treated liberally (as I advocate) or conservatively, is not associated with any particular LM. Furthermore, each of, say, EnglishO, LingalaO or ChineseO — i.e. the colloquial languages English, Lingala and Chinese considered as object-languages — is no more than a very small subset of LO. This means that terms like EnglishO, LingalaO or ChineseO have very limited explanatory use when it comes to the study of metalanguage in colloquial languages.

The lack of a strong connection between LM and LO suggests that a third term is needed if we are to be able to define ML , or, more accurately, the various LM’s. This term is simply ‘natural language’, or LN for short. Whereas in the theory of formalised languages any particular LM is defined as the language that is used to construct/describe this particular formalised language — its LO —, in the theory of natural languages, EnglishM, for instance, cannot be defined as that language (if it is a language) that is used to talk about EnglishO. EnglishM can talk about any of EnglishO, LingalaO or ChineseO. And so can LingalaM or ChineseM. What sets EnglishM apart from LingalaM or ChineseM is the fact that the sentences that constitute it are sentences of EnglishN, i.e. sentences of English ordinarily understood: the building blocks of EnglishM are English lexical items, and the structures 10 of EnglishM sentences are structures of English.

10 The introduction of ‘natural language’ as a term of art means that I will henceforth have little use for the term ‘colloquial language’. 360 PHILIPPE DE BRABANTER

I now turn to the third of the seven main features identified at the end of

Section 2. This will already take us some way towards determining if LM is a language or not.

3.3. Does LM have its own ‘lexicon’? This very complex question requires an extensive discussion. I start with the question whether natural languages contain names of LO elements in the form of quotations. After that, I look at the natural-language counterparts of the semantic predicates mentioned in Section 2 — what, for convenience, I will call ‘meta-words’.

3.3.1. Quotation-names? In the context of formalised languages, quotations are taken to be names of

LO elements (Tarski 1983; Carnap 1934; Quine 1940). When applied to natural languages, that ‘Name Theory’ of quotation has come under heavy criticism (e.g. Davidson 1979; Saka 1998; Recanati 2001), but some philosophers still defend a variant of it (Gómez-Torrente 2001).11 This is not the place to review the many aspects of the debate. Note, however, that in natural languages, there are many quotations which cannot be names: all those that, syntactically, do not occur as complements of a head, and hence, semantically, do not function as singular terms. One subset of these have been labelled ‘mixed’ (Cappelen & Lepore 1997) or ‘hybrid’ (Recanati 2001; De Brabanter, 2010, 2017) and are illustrated by (20) below. It is easy to see that if you replace the quotation with a name in a sentence like (20), you generate an ungrammatical string (21). This point was made by Searle as early as (1983: 185). (20) Gerald said he would “consider running for the Presidency”. (21) *Gerald said he would Henry.

One possible way out of that is to argue, as does Gómez-Torrente (2005), that quotation marks are ambiguous, with only one of their meanings generating quotation-names. But even granting that the Name Theory can in principle be rescued, there is a further reason to discard it. Lepore (1999) voices a concern about any attempt to enumerate the class of the quotable items of English. If

11 Salkie (2016) also defends a variant of the Name Theory, but one that regards as central the fact that naming, and quoting as a subtype of naming, are particular speech acts (acts of ‘onymic reference’). The focus on acts performed by a quoter means that Salkie’s theory has more in common with the depictive theory adumbrated in 3.3.1.4. than with the traditional Quinean or Tarskian account, and, more importantly, is immune to the ‘inflationary lexicon’ argument outlined below. OBJECT-LANGUAGE AND METALANGUAGE 361 quotations are names for the quotables and there is an infinite number of the latter, then there must be an infinite number of quotation-names too. Hence, if names are part of the lexicon of a language, that lexicon is itself infinite. Most theories of language agree that languages are infinite sets of sentences built from a finite lexicon using a finite number of formation rules. Would an infinite number of quotations jeopardise this standard picture? There are several possible responses to this question. One is to deny that there is an infinite number of quotation-names (3.3.1.1). One is to argue that quotation-names are not part of some particular lexicon but of a pool of words that is not language-specific (3.3.1.2). Another one is to argue that the set of quotation-names is infinite but recursively specifiable (3.3.1.3). A last possible response consists in making the more radical claim that quotations are not names and do not pose any infiniteness problem (3.3.1.4). I review these responses in turn.

3.3.1.1. Denying there is an infinite number of quotation-names.

We saw above that, even on a conservative view, LO is a heterogeneous set, linguistic and non-linguistic, to which there are no obvious limits. Now, even if only the linguistic component of LO is considered, the set of quotation-names must be infinitely large: given that sentences can be quoted or mentioned, and given that there is an infinite set of sentences in every natural language, the number of quotable linguistic objects is infinite, and so is the number of quotation-names. This is enough to conclude that the first response is untenable in the face of facts.

3.3.1.2. Quotation-names belong to a cross-linguistic ‘lexicon’ Several writers (e.g. Rey-Debove 1978: 138-39; Wreen 1989: 366) have made suggestions to this effect regarding proper names. If quotations are names, it follows on this view that they too are not language-specific: just as, say, the name Donald Trump does not belong to English or any other language, neither do the quotations “Donald Trump” or “Eppur si muove”. Quotations, then, are every bit as much part of Italian, Chinese and Lingala as they are of English. Rey-Debove defends a moderate variant of this position, arguing that the metalexicon of French contains only those quotations that are metahomonyms of French words, i.e. a finite number (Rey-Debove 1978, 29). Quotations that do not refer to French words — she makes no mention of French morphemes, phrases, sentences — fall outside the French metalexicon. This way, Rey-Debove avoids any runaway inflation of the French lexicon. The manoeu- vre of considering only metahomonyms of French words, however, strikes one as ad hoc. 362 PHILIPPE DE BRABANTER

If this ad hoc move is rejected and a radical view is adopted under which all names, including quotation-names, fall outside the lexicons of all natural languages, then the finiteness of LN lexicons is preserved. But one then needs to provide formation rules for LN sentences whose components are not all to be found in the LN lexicons. Pending proposals addressing this issue, I conclude that the second response cannot be endorsed at the present stage.

3.3.1.3. The set of quotation-names is infinite but recursively specifiable

Mark Richard (1986) attempts to show that the quotational component of the lexicon can be generated recursively using a finite set of primitives (letters, punctuation signs, spaces, mathematical symbols, plus a few more items) which are the input to two rules of concatenation that generate quotation- names: (A) For any expression e, lq followed by e followed by rq is a term. (B) For any expression e, lq followed by e followed by rq denotes e. (Richard 1986: 398)

In these formulas, e stands for any combination of primitive items, lq is the name for the left quote mark, and rq for the right quote mark. Note that (A) and (B) define two notions of specifiability, one for quotations as forms, the other for quotations as lexemes. If Richard’s two rules are sufficient to specify the whole class of, say, English quotations, then the fact that Eng- lish quotation-names are an infinite set is no longer a problem. Lepore (1999), however, believes that Richard’s attempt is unsuccessful. According to Lepore, this failure stems from the unrestricted nature of quot- ability, which cannot be systematically predicted by ‘alphabets’, however numerous (e.g. Greek, Cyrillic, Zapf Dingbats, etc.). Consider the following example: (22) Gillian marks up the newspaper every morning. She has a red pen and puts ✩s by stories she thinks I might find interesting or amusing. (Barnes 2001: 187)

One could nevertheless retort that more items could still be added to the set of primitive terms without it becoming infinite. But, very much in the spirit of what was argued at the end of Section 3.2.2, Lepore remarks that any squiggle, whatever its shape, is quotable, suggesting that no finite number of primitives will ever suffice to generate all quotation-names. A last-ditch effort to rescue Richard’s solution might consist in arguing that sentences that contain ‘quotations’ of squiggles, noises, gestures are not properly metalinguistic sentences. Strictly speaking, then, the referents of OBJECT-LANGUAGE AND METALANGUAGE 363 these quotations are not in LO understood narrowly. If we adopt a conservative attitude and concern ourselves exclusively with quotations that mention linguistic objects and non-linguistic objects that can be represented using orthographic means and linguistic sounds, it is perhaps reasonable to assume that recursive specifiability can be achieved along the lines pro- posed by Richard — provided one also identifies a set of primitives that can handle spoken quotations. Still, I have argued against such a conservative standpoint in 3.2.2, and besides I would argue that there is no need for this restrictive approach. There are other theories of quotation around, with a better claim to achieving theoretical economy and empirical coverage. This point is developed in the next section.

3.3.1.4. Quotations are not names Lepore (1999) defends a theory according to which only a demonstrative morpheme, contributed by the quotation marks, occurs in a quotational sentence. The quoted material itself is located in the context of utterance, not in the sentence. This, in essence, is the theory of quotation advocated by Donald Davidson (1979), one of whose popular variants was developed by Cappelen & Lepore (1997). On such an account, there is no risk of a runaway lexicon: nothing other than the quotation marks need be added to the lexicon. I agree with the Davidsonians that individual quotations themselves are not syntactically and semantically part of quotational sentences. Yet, I believe the ‘Demonstrative’ account suffers from irredeemable flaws (see Saka 1998; Recanati 2001). A different account is to be preferred, one which takes the essence of quotation to be ‘pictorial’ or ‘depictive’: a quotation is an act of iconic communication which context-sensitively depicts certain aspects of a target that is usually linguistic but can also be non- linguistic. The seminal papers are Clark & Gerrig (1990) and Recanati (2001); for a recent plea, see De Brabanter (2017). This family of theories views quotation as essentially not a linguistic phenomenon. Understanding a quotation, as opposed to an ordinary word, phrase or sentence, is not a matter of knowing a convention between a form and a meaning. Quotations belong to a mode of communication that is intrinsically different from that of natural languages. On the depictive account advocated by Recanati (2001), which I endorse, quotations can, but need not, function as constituents of a sentence. When they do, the iconic act is ‘recruited’ as a syntactic subject, direct object, modifier, etc. Recruitment can be understood as a function that turns any iconic input into a linguistic constituent. It is this recruitment function that is added to the language system (rather than the lexicon proper), an opera- tion that has no more inflationary implications than the Demonstrative 364 PHILIPPE DE BRABANTER theory. Example (23) illustrates the most frequent output of recruitment, i.e. NPs (For some details on other outputs, see De Brabanter, 2018): (23) In Received Pronunciation, ‘Chicago’ rhymes with ‘cargo’. Each individual quotation, qua non-linguistic communicative act, remains outside the lexicon. This way, any worries about an inflationary lexicon dis- solve. Note some similarity with the Rey-Debove/Wreen suggestion reviewed in 3.3.1.2. A crucial difference, however, lies in the justification of the recruitment mechanism. On the present proposal, this mechanism is grounded in the empirical fact that utterances are often ‘multimodal’, i.e. are made up of more than just their linguistic material. It is only a short step to accepting that some act produced in a non-conventional, non-linguistic, modality can sometimes occupy a slot that would otherwise be filled by a genuinely linguistic element. Proponents of the Rey-Debove/Wreen view, by contrast, face the task of justifying a mechanism like recruitment that concerns not just quotations but every name.

3.3.1.5. How hybrid quotation weighs in on the debate Hybrid quotations were introduced in Section 3.3.1, example (20). To my knowledge, Rey-Debove (1978) is the only author to have investigated ways in which the existence of hybrid quotation can affect metalinguistic sentences.12 I call ‘hybrids’ strings of words that are both used ordinarily and quoted at the same time. The quotation involved in the hybrid can derivatively be called a hybrid quotation (see De Brabanter, 2017 for details). Thus, in (24), the hybrids imperialist and Our borders are untouchable make their normal contribution to the syntax and the semantics of the sentence, while also being quoted. (24) One prominent poster shows a Soviet rocket striking an “imperialist” in the face and declares that “Our borders are untouchable.” (The Economist, 19/12/2015)

In Rey-Debove’s view, metalinguisticity is a gradable property. She talks of ‘metalinguistic density’: if a sentence contains a metalinguistic predicate and/or a quotation, it is to some degree metalinguistic. Example (24) includes instances of both scare quoting (“imperialist”) and the restricted category that Cappelen & Lepore (1997) called mixed quotation, i.e. a quoted string of words occurring within an indirect discourse report (“Our borders are untouchable”). In mixed quotation, some

12 Rey-Debove did not use the term hybrid. Hybrids correspond to a subset of what Rey- Debove subsumed under the label of ‘autonymous connotation’. OBJECT-LANGUAGE AND METALANGUAGE 365 extra metalinguistic density is always contributed by the presence of a report- ing verb. Therefore, ceteris paribus, mixed quotation makes for more meta- linguistically dense sentences than scare quoting. However, metalinguistic density is weaker than in a sentence that contains a pure quotation or DD report, e.g. (25), because the latter are exclusively about language (discourse), and not simultaneously about ‘the world’ (Rey-Debove 1978: 254). (25) The poster reads: “Our borders are untouchable”. Rey-Debove does not distinguish between sentences and utterances of these sentences. On the theory of quotation sketched in 3.3.1.4, an act of quoting is not linguistic, hence it cannot have an impact on the sentence level, unless the quotation has been syntactically recruited. Therefore, on the view I advocate, hybrid quotation cannot increase the degree of metalinguisticity of a sentence. By contrast, it can affect the metalinguistic density of the utterance that hosts it. At that level, it can be said that an utterance that contains a mixed quotation is more metalinguistic than one that contains an instance of scare quoting. Now, metalinguistic density is assumed to depend not just on quotations but also on meta-words. The next section continues the discussion.

3.3.2. Meta-words In what, to this day, remains the most detailed analysis available, Rey-Debove begins by dividing the lexicon of any language into three main subsets: (i) ‘mundane’ words, i.e. items which never signify anything linguistic (e.g. water, whitewashed, to vacuum); (ii) ‘neutral’ words, i.e. items which may or may not signify language, depending on the context in which they occur (e.g. bound, to raise, but also that, in, long); (iii) the metalexicon (Rey-Debove 1978: 26-27), which itself splits into two main classes: first, lexicalised metalinguistic items, like word or say (my ‘meta-words’); second those that are created on the fly, namely quotations. Since I have just argued, against Rey- Debove, that quotations (or any subset of them) should not be taken to be part of the lexicon, I will have nothing further to say about them in this section. Meta-words display varying degrees of metalinguistic density. This, according to Rey-Debove, can be shown by subjecting them to a componential analysis. Any word that contains a meaning component [+ language] is a candidate for membership of the metalexicon. The further left the component [+ language] occurs, the more metalinguistic the lexeme; the further right, the less metalinguistic (Rey-Debove 1978: 31): parole: simple element of language that makes communication possible parler: to utter simple elements of language which make communication possible 366 PHILIPPE DE BRABANTER parleur: one who utters simple elements of language which make communication possible.

Based on the paraphrases, we see that parole is more metalinguistic than parler, which in turn is more metalinguistic than parleur. This way, some general trends are revealed, notably the fact that meta-nouns (such as names of linguistic units: verb, preposition, subordinate clause, etc.) are more met- alinguistically dense than meta-verbs. One, however, quickly encounters borderline cases with items such as parloir (“parlour”). Is it still metalinguistic? Rey-Debove considers two responses. Either the presence of [+ language] anywhere in the definition is enough for the word to count as metalinguistic. This guarantees a cut-off point between meta-words and others, with the meta-words themselves placed along a continuum of metalinguistic density. Or the component [+ language] is not a sufficient condition for metalinguisticity, and some (arbitrary) decision has to be made regarding the level of embedding of [+ language] beyond which the lexeme is no longer to be classified as metalinguistic. Rey-Debove appears to waver between these two possibilities, neither of which is very appealing. There is a further problem. Up to now, I have tacitly relied on the fiction that every word is monosemous. Had I taken polysemy into account, I could not have introduced the scale of metalinguistic density with any clarity: parler, for example, has at least two senses. In the sense “utter simple elements of language”, it is highly metalinguistic, certainly for a verb. But in the sense “appeal to”, as in Cette symphonie ne me parle pas, it is barely at all. It is not as if the lexicon was neatly partitioned into lexemes whose meaning contains the component [+ language] at whatever level of inclusion, and lexemes whose meaning does not at any level. Some polysemous lexemes have one or more metalinguistic senses, but also one or more that have nothing to do with language, for example coordination, passive, singular, transform, generate. It is unclear where Rey-Debove’s neutral sublexicon fits into this picture: isposition a monosemous neutral word that is compat- ible with a metalinguistic reading in the appropriate context of use, or is it a polysemous lexeme only one of whose senses is metalinguistic? I see little use for the neutral sublexicon. I will assume that senses of lexemes, not lexemes themselves, are metalinguistic (or not).

3.3.3. Some conclusions about the metalexicon

In trying to answer the question whether natural languages have their own metalinguistic lexicon, we have had to recognise that the picture is much messier than in the context of formalised languages. There, the answer was a definite yes. Here, due to variable degrees of metalinguistic density and to polysemy, the answer can at most be a very tentative yes. OBJECT-LANGUAGE AND METALANGUAGE 367

Note also that the content of the ill-defined natural metalexicon is very dissimilar to the set of building blocks constituting the lexicon of the metalanguage of a formalised language. First, whereas the metalinguistic terms of logic belong exclusively to a metalexicon, any item that is part of the lexicon of, say, EnglishM also belongs to the lexicon of the natural language English. Second, real-life quotations should not be regarded as names, and therefore fall outside natural metalexicons. Third, not just semantic predicates are part of the natural metalexicon: predicates denoting phonetic, phono- logical, orthographic, etc. properties belong there too.

3.4. Is it always possible to determine if a component of a sentence belongs

to LM or LO?

We can now see that the question, as phrased, is otiose. Since any LM component there might be would also be quotable in some other utterance, anything that is in LM is automatically also in LO. A more relevant question is if it is always possible to determine if a component of a sentence belongs to some particular LM or to the complement of that set. As we have just seen, the answer to that question must be no. On the one hand, the move I have advocated of placing quotation outside of the metalexicon (and of language altogether) simplifies things consider- ably: only quotations that are recruited as constituents can be properly regarded as metalinguistic components of sentences. This, however, calls for two remarks. First, as mentioned above, a subset of these recruited quotations are DD reports: some writers, we saw, may be reluctant to call them metalinguistic, possibly preferring a label like metadiscursive instead. Second, nothing rules out the possibility that some non-recruited quotations, e.g. some hybrid ones, are metalinguistic in the narrow sense, rather than metadiscursive. As I have argued in 3.3.1.5, hybrid quotations cannot be metalinguistic components of a sentence, only of an utterance of a sentence. Arguably, example (26), from Recanati (2001: 682), is a case in point. Though fortnight is used ordinarily, it is simultaneously mentioned, as part of the process of providing a definition. This suggests that the hybrid quotation can be regarded as a metalinguistic element stricto sensu of an utterance of (26). (26) A ‘fortnight’ is a period of fourteen days. Turning now to meta-words, we have seen that, even if senses of words are taken to be criterial (instead of potentially polysemous words), metalinguistic density is an issue. Two solutions were envisaged. One is to assume that any sense whose componential analysis features the component [+ language] is part of the metalexicon. As a result, one sense of parlour (“a room in a monastery or convent that is set aside for conversation”) in my New Oxford 368 PHILIPPE DE BRABANTER

American Dictionary is part of the metalexicon, because the presence of conversation in the definition entails the component [+ language] at some deep level of embedding. Alternatively, one has to, quite arbitrarily, fix a level of embedding of [+ language] beyond which a word-sense is no longer metalinguistic. As I suggested above, neither option is attractive. But it needs to be pointed out that the lack of appeal of either solution reflects a fact about natural languages, not a particular flaw in Rey-Debove’s reflections.

3.5. Is it always possible to determine if a sentence belongs to LO or LM? As with the question in Section 3.4, the previous discussion makes it clear that the very phrasing of this question is infelicitous. A more meaningful question is if it is always possible to determine if a sentence belongs to some LM. We saw in Section 3.3.1.5 that sentences are not metalinguistic vs. non-metalinguistic simpliciter. Metalinguisticity comes in degrees. We also saw that in the context of natural languages, metalinguisticity (be it in the narrow sense or the broad sense which includes metadiscursiveness) may also concern the utterance level of analysis, not just the sentence level. Before we can answer the question that heads this section, however, it is necessary to consider how the logically prior differentiation between metalinguistic and non-metalinguistic sentences can be founded. Two proposals are encountered in the literature, only one of which is genuinely about sentences, the other being concerned with utterances. I examine them in turn.

3.5.1. Rey-Debove on metalinguistic sentences Rey-Debove proposes a simple formal criterion for a metalinguistic sentence: it must contain a meta-word and/or a quotation. This endows it with some degree of metalinguisticity (see 3.3.1.5). On the account of quotation that I advocate, only recruited quotations have an impact at the sentence level, so I will temporarily ignore non-recruited ones. According to Rey-Debove, the degree to which a sentence is metalinguistic is sensitive to two factors: (i) the metalinguistic density of the meta-words it contains (if any); (ii) the syntactic function of the meta-words and/or quotations it contains (if any). Factor (i) mobilises the continuum identified in Section 3.3.2. Considerthese examples: (27) Those words are fun. (28) That book is fun. (29) That writer is fun. (30) Your brother is fun. OBJECT-LANGUAGE AND METALANGUAGE 369

According to the level at which the component [+ language] is embedded in the definition of the heads of the Subject-NPs, words is more meta linguistically dense than book, which in turn is denser than writer. As for brother, it is a mundane word. As a consequence, (30) is not a metalinguistic sentence. By contrast, all of (27) to (29) are to some degree metalinguistic, and can be arranged on a scale from most metalinguistic (27) to least (29). One may find that the boundary between metalinguistic and non-metalinguistic sentences fails to match with intuitions about metalinguisticity (if such intuitions are conceivable at all). For instance, one might feel that (28) does not deserve the label ‘metalinguistic’, as it makes no point about words or utterances. As for (29), it is easy to imagine a world in which That writer in that example and Your brother in (30) refer to the same person, so why should the former clause be (somewhat) metalinguistic, while the latter is not? Rey-Debove is sensitive to these problems. She says about (31) that the presence of the component [+ language] in the meaning of book does not obviously turn it into a metalinguistic clause. (31) She was dusting the books with a feather duster. (Rey-Debove 1978: 165)

But then we are back to the second response envisaged in Section 3.3.2, an arbitrary decision on a threshold of metalinguisticity. Regarding factor (ii), let us consider three basic patterns in simple NP-VP clauses: (32) A linguistic sign has a meaning / Never has a meaning. (33) Language changes over time / Jolly is old-fashioned. (34) Albert is talking.

Both the subject and the predicate of (32) are highly metalinguistic. In (33), only the subjects are, while the predicates are neutral. In (34), only the predicate is metalinguistic. According to Rey-Debove, sentences like (32) exhibit a higher degree of metalinguisticity than the other two kinds. More importantly, perhaps, she stresses that the universe of discourse of the gram- matical subject is a decisive factor. Both (32) and (33) are about language in a way that (34) is not. This last point has interesting implications for the following pairs of sentences (see Rey-Debove 1978: 167): (35) A gardener wrote this poem. (36) This poem was written by a gardener (37) Certain kinds of seats are called armchairs (38) Armchair designates certain kinds of seats.

Although (35) and (36) entail each other, they are not metalinguistic to the same degree, with the second member of the pair being more metalinguistic 370 PHILIPPE DE BRABANTER as a result of the (somewhat) metalinguistic NP being in subject position. Likewise, (38), whose subject is a recruited quotation, is more metalinguistic than (37), which is primarily about items of furniture.13

3.5.2. Droste on metalinguisticity

Droste defines metalinguisticity in pragmatic terms. An utterance is metalinguistic if the speaker’s underlying communicative intention is to make a comment on (the use of) a particular language. Rather surprisingly, if a sentence includes meta-words but no quotation (example (6) above), it does not rate as metalinguistic. This seems misguided, though, as it is quite possible to talk about a specific linguistic object without quoting it. It suffices to resort to what Recanati (2000: 137) has called ‘heteronymous’ mention, i.e. mention by means of an NP that is not iconically related to its referent. Thus, the same meaning as “With is a preposition” (example (7)) can be expressed by means of (39): (39) The first word in the title of The Beatles’ second studio album is a preposition.

Whether or not Droste would be ready to revise his claim that the presence of quotation is a necessary condition for a sentence to be metalinguistic (Droste 1983: 682), it none the less remains that it is not a sufficient condition, as shown by these examples (from Droste 1983: 683): (40) ‘Your witness’, he said. (41) He said, ‘Your NitWess’. (42) He did not say, ‘Your witness’, he said, ‘Your NitWess’. For Rey-Debove, all three sentences are metalinguistic. For Droste, only (42) is clearly so, because what is at stake in uttering it is an aspect of phonetic structure (1983: 683). (41) is ambiguous between a pure DD report — in which case it is not metalinguistic — and a comment on somebody’s pronunciation — in which case it is. Although Droste says nothing about (40), we can guess that he does not regard it as metalinguistic. As Cornulier (1978: 82) pointed out, parenthetical clauses like he said around a quotation always attest that the quotation is presented as an imitation of a previous utterance. This would make it metadiscurive rather than metalinguistic in the strict sense.

13 For more reflections on the (probably unpreventable) inadequacy of Rey-Debove’s various criteria, see De Brabanter (2018). OBJECT-LANGUAGE AND METALANGUAGE 371

3.5.3. Back to the initial question It has now become plain that, short of making unappealing arbitrary decisions, it is not possible to give a definite answer to the question asked in 3.5.There are too many sources of variablity for a definite yes or an unequivocal no. Besides, as we have just seen with Droste’s proposal in 3.5.2, natural languages force the linguist to consider not just sentences (syntax and semantics) but also utterances (pragmatics), thus contributing an additional layer of complexity. We are, however, in a position to answer the question left pending in

Section 3.2 — whether LM’s are languages in their own right. It seems most sensible to answer in the negative. We have just seen that there are many difficulties in deciding if any given sentence belongs to EnglishM, making it an ill-defined set. Beyond a core of unambiguous metalinguistic sentences (e.g. (2), (5), (23)), there is a very large set of borderline cases, and this for a variety of reasons, amongst which the variable density of meta-words, discourse about pseudo-words and non-words, the inability of quotation to provide a straightforward criterion, the significance of the syntactic position of meta-words or recruited quotations in the sentence. There are also pragmatic concerns, with the distinction between a metadiscursive intention and a metalinguistic one in the narrow sense, and the possibility that a string of words that has nothing metalinguistic at the sentence level may display some degree of metalinguisticity at the utterance level (26). Granted, it is theoretically possible to make a number of arbitrary decisions to clarify the picture, say, that genuine meta-words (more accurately, ‘meta-word-senses’) cannot have the [+ language] feature beyond the second level of embedding, and that the only type of quotation that can make a sentence metalinguistic is recruited metalinguistic citation. But that is still not enough. We would have to make further pragmatic decisions, notably on whether recruited instances of DD (underlying most of which there is a metadiscursive intention) should be included or not. That pragmatic concerns should interfere with the determination of a language understood as a set of sentences is awkward, to say the least. This awkwardness is reinforced by the arbitrariness of the decisions alluded to above. In the end, it seems that, in natural languages, there is not enough that sets the putative set of metalinguistic sentences apart from the rest. In particular, as we have seen, quotation, even its recruitment, does not prove to be a criterion for metalinguisticity. In other words, the set of metalinguistic sentences is divorced from any genuinely interesting phenomenon that could found it, such as quotation, the sort of phenomenon that is truly of interest to the linguist.

The upshot is that it seems sensible to view EnglishM not as a language proper, but as a special use or function of English. In other words, I advocate 372 PHILIPPE DE BRABANTER making a pragmatic move not unlike Droste’s, one that is also endorsed by others (e.g. Jakobson 1985: 117; Gamut 1991: 27; even Rey-Debove 1978: 7, 9). This way, metalinguistic use is one use amongst others. It is a use that proves especially interesting when it is associated with quotation, just as metadiscursive use is too. Uses may overlap and cannot usually be delim- ited rigidly. Overlaps and fuzziness are an issue when one is concerned with determining the boundaries of languages; but they are not when one is concerned with uses.

3.6. Do LO and LM occur at different levels in a hierarchy of languages? Whereas a neat hierarchy of language-levels is a requisite in the case of formalised languages, it is an aspect of the versatility of natural languages that they are able to generate semantic paradoxes (Tarski 1983: 164). If, say, EnglishM is used to describe the semantics of English, the very semantic predicates used in EnglishM sentences are also automatically English predicates. This means that natural metalanguages and object-language(s) are not organised in a strict hierarchy. That is unsurprising, as natural LO is not a language and natural LM’s are best regarded as special uses of their respective LN. As we saw in Section 2, in the theory of formal languages it is always n possible, should the logician wish to formalise an LM of level n (LM), to n+1 construct an LM for the description of the semantics (and/or the syntax) of n 14 that LO. Interestingly, something resembling this hierarchy can be identified in the theory of natural languages, provided one focuses on sentences whose high degree of metalinguisticity is indisputable. A ready illustration of this is the fact that recruited quotation is iterable, as has been pointed out by e.g Rey-Debove (1978: 42-45, 114), Droste (1989: 931), or Saka (1998: 119-20): (43) Mary is a butcher is a sentence. (44) “Mary is a butcher is a sentence” is a sentence. Whereas (43) is a sentence of something akin to a first-order metalanguage 1 LM — it is uttered to state something about the basic-level sentence Mary is a butcher — (44) is a sentence of something akin to a second-order 2 1 1 metalanguage LM — it can be uttered to state a property of the LM /LO item “Mary is a butcher is a sentence”. This could be repeated ad infinitum. The iterability of quotation is not the only symptom of a semblance of a hierarchy in natural languages. Meta-words offer another illustration

14 n n n–1 LM and LO are the same language, viewed once as a metalanguage (of some LO ), n+1 once as an object-language (of some LM ). OBJECT-LANGUAGE AND METALANGUAGE 373

(Rey-Debove 1978: 44). Prototypical meta-nouns (noun, verb, preposition) 1 belong to something like a first-order metalanguage ML . A few meta-words 2 are words of a putative LM , such as autonym, metalanguage, metalinguistic, or quotation (in a narrow ordinary sense which I reject). These words 1 1 denote elements of LM /LO. Meta-words above that level are few and far 3 between, but the noun meta-metalanguage would be part of LM. To conclude this short section, the question asked must be answered in the negative: natural LO and LM(’s) do not form part of a neat hierarchy of languages. However, some hierarchical structuring can be discerned locally.

3.7. Is LM expressively richer than LO? We have seen that in logic the metalanguage of a formalised language is expressively richer than the formalised language. In other words, all that can be said in the LO can be said in the LM, either because the LM contains the LO, or because the LM contains translations of all the well-formed formulas of LO. In the context of natural languages, it makes little sense to talk about the expressive power of LO, which is not a language, so the question as formu- lated in the heading to this section is strictly speaking unanswerable. One can, however, raise a somewhat similar question by substituting some relevant

LN for LO, e.g. English if one is looking at EnglishM. If that is done, it appears clearly that EnglishM is not expressively richer than English. We saw that EnglishM was best defined as a special use of English. Hence, everything that is expressed in EnglishM is expressed in English, and English can express a lot more besides. The obvious conclusion is that EnglishM is expressively poorer than English.

4. The relations between LM, LO and LN

The long discussion in Section 3 has allowed us to gain valuable insights into the main features of LM and LO in the context of natural languages. One striking result is that, strictly, they exhibit none of the features of LM and LO in logic. The most that can be granted is that they display a loose and more complex version of some features. Still, it is possible to propose what I hope are helpful Venn diagrams of the relations between LM and LO and LN, provided some decisions are made that reduce the scope of what is shown and some necessary idealisations are tolerated. In Figure 1, the relations are shown for an idealised first-order 1 EnglishM (= EnglishM) and a subset of LO from which are excluded all 0 metalexical items and metalinguistic sentences (= LO). 374 PHILIPPE DE BRABANTER

n n–1 Figure 1. Relations between EnglishN, EnglishM and LO , for n = 1

A different diagram would be obtained if these parameters were changed. 2 Let me consider two such modifications in turn. First, for the pair EnglishM 1 and LO , first-order metalinguistic sentences like (2), (5) or (7), which in Figure 1 are found in EnglishN EnglishM, would migrate to EnglishN LO 2 in a diagram representing the relations between EnglishN, EnglishM and 1 LO (See the simplified Figure ⋂2). The same would be true of all the recruited⋂ quotations that refer to linguistic objects. The reason is that meta-metalinguistic sentences refer to (first-level) metalinguistic sentences, (first-level) meta-words, and (linguistic) quotations, as in (45) and (46): (45) In sentence (7), “With” is a quotation of the preposition with. (46) You find the following statement in many grammar books:“Nouns are typically used to denote objects and people”.

1 In Figure 1, sentences like (45) and (46) are placed not in EnglishM, but in EnglishN, since they are incontrovertibly English sentences. In Figure 2, by 2 contrast, they are located within EnglishM (which of course is included in EnglishN). The other modification of the parameters that I will consider here is one on which no restrictions are placed on LO. On such a picture, there is not much of interest that can be shown about LM’s, a natural consequence of OBJECT-LANGUAGE AND METALANGUAGE 375

n n–1 Figure 2. Relations between EnglishN, EnglishM and LO , for n = 2

Figure 3. Relations between LO and four natural languages. 376 PHILIPPE DE BRABANTER the severance of any privileged connection between LM’s and LO in natural language. The only relations worth displaying are those between LO and various LN’s (see Figure 3). Since any morpheme, word, phrase, sentence of any language is quotable, LO simply contains LN’s as particular subsets. Where would LM’s fit in such a diagram? Since ML ’s are mere (fuzzy) subsets of their respective LN’s, they would occur within the sets for these natural languages.

5. Conclusions

The results of the present inquiry do not come as a surprise. Some of the logicians who elaborated the relations between formalised object-languages and their metalanguages were very much aware that these relations cannot be replicated exactly when it comes to natural languages. Pointing out flaws of natural languages, such as vagueness, ambiguity, and irregularities (Carnap 1934: 2; Tarksi 1944: 347; Reichenbach 1947: 6; Church 1956: 47), they questioned the existence, in natural language, of a clear boundary between object-language and metalanguage (Reichenbach 1947: 16), sometimes readily assuming that, contrary to the situation in formalised languages, the natural object-language contains its metalanguage (Grelling 1936: 486). As we saw, they were also aware that the universality of natural languages prevents them from being organised along a hierarchy of languages (Tarski 1983: 164). However, apart from Rey-Debove and Droste, whose work has been widely referred to in this paper, no one had looked in detail into the exact features of ‘natural metalanguage’ and ‘natural object-language’ and into their relations. I hope the present study has improved on the insights of these predecessors, notably by pointing up the many intricacies involved in this undertaking, some of which, I believe, had never been considered before.

References

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