Is Metalinguistic Usage a Conversational Implicature?

I argue against the view that metalinguistic usage is a form of conversational implicature. That view, suggested by Thomasson (Anal Philos 57(4):1-28, 2016) and Belleri (Philos Stud 174(9):2211–2226, 2017), has been most recently fleshed out by Mankowitz (Synthese 199:5603–5622, 2021). I provide two types of criticism to the implicature view. From an empirical point of view, metalinguistic usage differs in key respects from standard cases of conversational implicature. From a conceptual standpoint, I argue that the calculation algorithm provided by the implicature view makes undesirable predictions. Although my main objective is negative, I end the paper by sketching an alternative neo-Stalnakerian view of metalinguistic usage, that can be gathered from work by Barker (Linguist Philos 25(1):1–36, 2002; Inquiry 56(2–3):240–257, 2013) and others.


Introduction
The purpose of this paper is to argue against the view that metalinguistic usage (and consequently, metalinguistic negotiation) arises due to conversational implicature.A speaker makes a metalinguistic usage of an expression e when they use (importantly: not mention) e with the intention to fix, or modify, some aspect of e's meaning.The conversational implicature view of metalinguistic usage purports to explain how this comes about.The view claims, roughly, that metalinguistic usage of e arises in contexts where an utterance u containing e would seem to flout or violate a Gricean maxim.For this reason, the audience is invited to infer that the point of u is to convey a metalinguistic proposition to the effect that e ought to be used in the way exemplified by u.
The implicature view has been sketched by Thomasson  (2016), Belleri (2017), and Plunkett and Sundell (2019,  p. 12).More recently, it has been defended at length by Mankowitz (2021).I present the implicature view in Sect. 2 and provide two types of criticism in Sect.3. First, I rely on guistic negotiation occurs when a speaker disputes a certain metalinguistic usage (via metalinguistic usage).These phenomena are best illustrated by example, so here are a couple of standard cases from the literature: (1) Tall: Feynman's height is known; someone asks: What counts as tall around here?1 a. Feynman is tall.b.No, Feynman is not tall.
(2) Athlete: Secretariat has been included in the list of best athletes of the twentieth century. 2 a. Secretariat is an athlete.b.No, Secretariat is not an athlete.
Take the dialogue in Tall.Normally, speakers use sentences like (1a) to inform about the heights of people.But if Feynman's height is known, a sentence like (1a) can be used to inform about the threshold for calling someone 'tall', instead of informing about Feynman's height.This is to make a metalinguistic usage of the word 'tall'.When metalinguistic usage is disputed, as in (1b), a metalinguistic dispute arises.Metalinguistic disputes can be divided in two types: descriptive metalinguistic disputes concern how a term is actually used (e.g., in a certain linguistic community).Normative metalinguistic disputes, also known as metalinguistic negotiations, concern how a term ought to be used.
In the context envisaged by Barker, the metalinguistic dispute in Tall is descriptive, since it concerns the actual threshold for 'tall' in the context of use (i.e.'around here').By contrast, in the context of Athlete originally described by Ludlow, the question is, not what 'athlete' actually means, but what it should mean: Speaker a claims that 'athlete' should be used in a way that includes horses; speaker b advocates for a horse-exclusionary usage.This is a normative metalinguistic dispute, or metalinguistic negotiation.
Metalinguistic negotiation has played an important role in various philosophical debates during the last decade.It was initially put forward by Plunkett and Sundell to resist the socalled argument from disagreement in meta-ethics (2013a) and legal philosophy (2013b).From there on, the notion has seen fruitful applications in various subfields.In philosophy of language, the notion has been used to characterize disagreements involving subjective and evaluative expressions (Sundell 2011, 2016, 2017; Umbach 2016; Bolinger 2020;  Barker 2013).In metaontology, metalinguistic negotiation has been thought useful to account for protracted metaphysical disagreements (Thomasson 2016; Belleri 2017, 2020).It has also been deployed in philosophy of science (Sambrotta 2019) and philosophy of logic (Kouri Kissel 2021).

Metalinguistic Usage as Conversational Implicature
In a metalinguistic usage, a simple, declarative sentence appears to have a different communicative function from its usual one.First, consider (1a).As noted above, to an utterance of (1a) we would normally assign the proposition that Feynman's height meets some contextually salient threshold.But in the context described above, (1a) is more sensibly interpreted as conveying the descriptive metalinguistic proposition that around here, 'tall' is used in a way that applies to Feynman.Next, take (2a).Normally, to an utterance of (2a) we would assign the standard proposition P: Secretariat is an athlete.In the context described above however, an utterance of (2a) turns out to communicate the normative metalinguistic proposition M: 'athlete' should be used in a way that applies to Secretariat. 3How?Plunkett and Sundell have been 'content to remain neutral' (Plunkett and Sundell 2019, p. 12; see also Plunkett  and Sundell 2023) regarding the exact linguistic mechanism underlying metalinguistic usage, even if they seem to favour a broadly pragmatic account.Others have been more specific: Thomasson (2016, pp.20-23) critically considers a conversational implicature account, but eventually opts for an alternative view.Belleri (2017) declares a preference for an implicature view, but does not spell it out.It is not until Mankowitz (2021) that we find a full-fledged account of metalinguistic usage and negotiation as conversational implicature.
Mankowitz purports to situate metalinguistic negotiation within a mainstream theory of communication (Mankowitz  2021, p. 5606, see also Plunkett and Sundell 2023, fn.11), and thus aims to reconstruct metalinguistic usage as the result of a Gricean reasoning process.This process is triggered by the fact that metalinguistic usage of an expression e arises in contexts where an utterance u containing e would seem to flout or violate a Gricean maxim.For this reason, the audience is invited to infer that the speaker's intention in uttering u is to convey a metalinguistic proposition to the effect that e ought to be used in the non-standard way exemplified by u.
Let's look at this reasoning process in more detail.Mankowitz (2021, Sect.3) helpfully divides it in three steps, 4 which I illustrate with the Secretariat example.Consider a context where it is common ground that Secretariat was a very successful racehorse.In that context, speaker a utters (2a).Upon hearing (2a), speaker b might reason as follows (note that step 1 is divided, depending on whether speakers start off from a shared interpretation of 'athlete' or not.The rest of the reasoning process is the same in both cases): This reasoning accounts for a metalinguistic interpretation of (2a).But metalinguistic negotiation also involves a disagreeing party, so something needs to be said about (2b).Mankowitz proposes that b's answer (2b) results from a similar Gricean process.
Here appear two crucial differences with the procedure described above.First, if P is clearly false in the context envisaged, and (2b) standardly expresses not-P, then an utterance of (2b) would not flout Quality.Rather, it would flout Quantity, in virtue of being trivially true.Alternatively, if 'athlete' has no settled meaning at that context, an utterance of (2b) would also flout Quantity.Hence, in contrast to steps 1a/b in the previous reasoning, here we have a threat to Quantity regardless of whether 'athlete' has its traditional, exclusionary meaning or no settled meaning.Secondly, we naturally take (2b) to convey the negation of M. But, as Mankowitz highlights, this is ambiguous between not-M ('athlete' should not be used in a way that applies to Secretariat) and not-M ('athlete' should be used in a way that does not apply to Secretariat).So an additional inferential step is needed to disambiguate between these two interpre-4 Actually, Mankowitz distinguishes four steps, but her step (iii) only applies to sentences embedded under sentential operators.Since we are considering the bare sentence 'Secretariat is an athlete', I skip this step.But step (iii) resurfaces in the account of (2b) just below.
tations.The inferential process, this time from a's point of view, is as follows: In sum: in this view, metalinguistic usage results from a Gricean reasoning process that takes the hearer from the expression of a standard proposition, which would violate a Gricean maxim, to the expression of a metalinguistic proposition, which would not.

Arguments Against the Implicature View
In this section, I put pressure on the implicature account of metalinguistic usage and negotiation.In Sect.3.1, I offer linguistic data showing that metalinguistic usage is markedly different from standard cases of conversational implicature.In Sect.3.2, I turn to theoretical considerations to the effect that the calculation algorithm described above is problematic.

Cancellability and Embeddability
Conversational implicatures are cancellable and do not interact with operators such as negation, conditionals, and propositional attitudes in the way that semantic content does.By contrast, metalinguistic usage is non-cancellable and metalinguistic propositions behave like semantic content in interaction with said operators.

Cancellability
Conversational implicatures are cancellable.To illustrate this phenomenon, consider the following example (Davis 2019):  In this context, b's reply semantically entails that she is not going to the party, while c's conversationally implicates so.This is shown by the fact that b cannot felicitously cancel that inference, whereas c can (I mark infelicity with #): (4) a. Are you going to Paul's party?b. # No, I am not going, but I will go.c.I have to work, but I will go.
Cancellability is a hallmark of conversational implicature.More specifically, it is considered a necessary, but not sufficient property of conversational implicatures-potentially many other inferences are cancellable as well (Blome-Tillmann 2013; Zakkou 2018).Insofar as it is a necessary property, it follows that if an inference is not cancellable, it is not a conversational implicature.
The metalinguistic inferences triggered by, e.g., Athlete cannot be canceled (Odrowa ˛ż-Sypniewska 2023 observes this as well).The metalinguistic proposition M purportedly implicated by an utterance of (2a) in the context above cannot be canceled; and the negation of M cannot be canceled following an utterance of (2b) either.This suggests that it is not a conversational implicature. 5) a. # Secretariat is an athlete, but 'athlete' should not be used in a way that applies to Secretariat.b. # No, Secretariat is not an athlete, but 'athlete' should be used in a way that applies to Secretariat.
Before moving on, various counterexamples have been offered to the cancellability test (see Zakkou 2018 for an overview).It could be argued that metalinguistic usage pertains to some class of non-cancellable conversational implicatures.
There are two salient categories of non-cancellable conversational implicatures.First, it has been observed that some implicatures are semantically entailed by the sentences that trigger them, which makes them non-cancellable (Blome-Tillmann 2013; Davis 1998): (6) a. Are you or your spouse 65 or older or blind?b.I am 67.
b's answer implicates an affirmative answer to a's question, since it does not answer it directly.But b's reply also entails such an answer.Might metalinguistic usage be seen as this type of entailed conversational implicature?Perhaps, although this would seem to defeat the purpose of offering a pragmatic theory of metalinguistic usage, as the relevant metalinguistic propositions would be semantically entailed as well.
Secondly, figurative uses of language, such as irony, sarcasm, or metaphor, arguably arise due to conversational implicature and yet they are usually non-cancellable.Here is an example (Åkerman 2015): (7) a. Stephen King will win the Nobel Prize for literature.
In this case, b's ironic answer implicates that Stephen King will not win the Nobel.But it would be infelicitous to cancel the implicature (# 'Yeah, and 2 + 2 = 5.But I don't mean to imply that Stephen King will not win the Nobel').
It seems implausible that metalinguistic usage is figurative, however.After all, the speaker of (2a) does really think that Secretariat is an athlete (in virtue of their preferred usage of 'athlete').The defender of such a view would have to say that the speaker of (2a) is using 'athlete' with its standard (horse-exclusionary) meaning figuratively, in order to implicate their preferred, non-standard usage.I return to this issue in Sect.3.2.

Embeddability
Generally speaking, conversational implicatures do not interact with sentential operators in the way that semantic content does.Rather, an implicature-carrying sentence tends to lose its implicatures when embedded in certain environments. 6o see this, consider the following answers to a: As we saw, b's answer conversationally implicates that b is not going the party.But this does not apply to the other constructions: none of them implicate that the speaker is not going to the party, and the implicature does not embed under the relevant operators either: c's answer does not implicate that c is going to the party (at most it implicates that they might consider it); d's answer does not implicate that, if d is not going to the party, then d will arrive too late; and e's answer does not implicate that Mary thinks that e is not going to the party.By contrast, the metalinguistic propositions associated with the utterances in Athlete interact with operators in just this way: (9) a. No, Secretariat is not an athlete.
b.If Secretariat is an athlete, then Lassie was an actor.
c. Mary thinks that Secretariat is an athlete.
In the context described above, each of these constructions can easily be interpreted as conveying an (embedded) standard or metalinguistic proposition. 7And more importantly, those metalinguistic propositions interact with operators in the same way that standard content does.We already saw that this is the case for (9a): A speaker can utter (9a) to disagree with someone else's metalinguistic statement, meaning Secretariat should not be used in a way that applies to Secretariat.The same is true of ( 9b) and ( 9c): (9b) can be naturally interpreted as conveying that, if 'athlete' should be used in a way that applies to Secretariat, then 'actor' should be used in a way that applies to Lassie.Similarly, (9c) can be used to convey that Mary thinks that 'athlete' should be used in a way that applies to Secretariat. 8When we discussed (9a), we saw that the implicaturist has a potential account of why it implicates not-M [not-M ], namely that it violates the maxim of Quantity.But what can the implicaturist say about (9b), or (9c)?Assuming that 'athlete' is interpreted standardly, those sentences do not seem to violate any Gricean maxim, at least not obviously. 97 As a reviewer points out, this is not that surprising, given that metalinguistic and standard (descriptive) interpretations are very close to each other: whenever a competent speaker (of a language that includes 'ϕ') thinks a is ϕ, they will usually also think that 'ϕ' applies to a. 8 Here is a context: Imagine that Mary is the president of the International Olympic Committee.In the midst of a metalinguistic disagreement about whether horses can be athletes, (9c) can be interpreted as reporting Mary's metalinguistic views in support of a liberal concept of 'athlete'. 9One might say the following about (9b): In a context where it is common ground that Lassie does not fall under the standard concept of 'actor', (9b) might seem to violate Relevance or Quality, which would allow Gricean reasoning to kick in, resulting in an interpretation of (9b) as conversationally implicating (9a).(9b) would then be similar to examples like 'if I owe you $1000, the moon is made of green cheese'.This is a possible interpretation of (9b).However, the resulting implicature is not the purported metalinguistic interpretation of (9b), namely that if 'athlete' should apply to Secretariat, then 'actor' should apply to Lassie.That is, this pragmatic process would not generate the reading that we're after.Moreover, (9b) can also be used in contexts where there is no settled concept of 'athlete' nor of 'actor'.In such context, (9b) intuitively conveys that, if we should adopt a liberal concept of 'athlete', then we should also adopt a liberal concept of 'actor'.Thus, a metalinguistic interpretation of (9b) may arise in the absence of any More generally, the problem is not so much that the implicaturist owes an account of these other cases.The issue is, rather, that this systematic pattern of embedding is exactly what one expects to find if the metalinguistic proposition M associated with (2a) belongs to the semantic content of that sentence, and not to its implicatures. 10,11

Calculability
I turn now to considerations about the calculation algorithm proposed by Mankowitz (2021, Sect.3, starting on p. 5613).My criticism is two-fold.First, the algorithm over-generates metalinguistic interpretations, as it predicts metalinguistic usage in contexts where it does not appear, and allows for deriving other metalinguistic propositions beyond the metalinguistic proposition(s) at play in metalinguistic negotiation.Secondly, the implicature view also under-generates metalinguistic interpretations, as it fails to predict a class of metalinguistic usages which seem to involve no clear maxim violation.

Over-generation
Mankowitz's algorithm over-generates metalinguistic interpretations in the following two senses: First, recall that, in Athlete, the calculation of M on the basis of an utterance of (2a) starts off with the observation that (2a) flouts either the maxim of Quality (if 'athlete' was interpreted standardly, see step 1a), or Quantity (if 'athlete' has no antecedently settled meaning, see step 1b).In the latter case, the generalization would seem to be that whenever speakers use sentences containing expressions whose meaning isn't antecedently settled and thus express no mutually discernible proposition, a pro-Footnote 9 continued obvious maxim violation.Mankowitz (2021, p. 5608) includes these embedding data, which she uses to argue against Thomasson's 2016 non-propositional account of metalinguistic usage (according to which metalinguistic content would be non-propositional).She notes that the embedding data might seem to push against her pragmatic view, and she replies by providing a general criticism against a semantic account. 11Two further, well-known tests for conversational implicatures are their non-detachability (Grice 1975/1989, p. 39) and their reinforceability (Sadock 1978).An inference i triggered by an utterance u is non-detachable iff one cannot say the same thing as u with different words without inviting the audience to infer i; and i is reinforceable iff i can be added explicitly to u without redundancy.The non-detachability test is used traditionally to distinguish conversational and conventional implicatures (only the latter are detachable); the reinforceability test was proposed to distinguish conversational implicatures and presuppositions (only the former are reinforceable).Given that we are not entertaining the hypotheses that metalinguistic usage arises due to conventional implicature or presupposition, I do not discuss these tests here.
123 cess of metalinguistic interpretation is set off.But that seems incorrect, as there are many contexts where a meaningless utterance is not interpreted metalinguistically.
Secondly, the algorithm allows for deriving many other metalinguistic propositions, over and above the metalinguistic proposition(s) presumably at play in metalinguistic negotiation.But many of those metalinguistic interpretations are unattested, and the implicaturist does not say why their preferred metalinguistic interpretation is generated.Let us look at this problem more closely.
The calculation algorithm relies on the observation that, whereas the standard proposition expressed by the speaker flouts a Gricean Maxim, the metalinguistic proposition does not.Let us illustrate this with (2a).Whereas the standard proposition P ('Secretariat is an athlete') expressed by (2a) flouts Quality, the metalinguistic proposition M ("athlete' should be used in a way that applies to Secretariat') does not.But we can think of many variations on M that would equally satisfy Quality: (10) a. M 1 : 'Athlete' may be used in a way that applies to Secretariat.
b. M 2 : 'Athlete' is probably used in a way that applies to Secretariat.
c. M 3 : 'Athlete' was used in a way that applies to Secretariat.
d. M 4 : In my linguistic community, 'athlete' is used in a way that applies to Secretariat. ...
The issue is that the calculation algorithm provides no way of guaranteeing that M should be implicated instead of any of these alternatives. 12In particular, M 1 -M 3 are just not available interpretations of (2a), even though the calculation algorithm could generate them just like M. So Mankowitz's account needs to be supplemented with an account of why M gets implicated as opposed to these alternatives.
However, note that this flexibility in Mankowitz's account could be wielded as advantageous.After all, some of those alternative metalinguistic propositions might be the right interpretation of (2a) in some contexts.E.g., descriptive metalinguistic propositions such as M 4 are sometimes conveyed with utterances like (2a) (a salient example is Barker's (1), prompted by the descriptive metalinguistic question What counts as 'tall' around here?).So an account that can generate an implicature of M 4 as well as of M would be welcome.That being said, the issue remains that Mankowitz's view offers no explanation for why the desirable metalinguistic propositions (say, M and also M 4 ) are implicated but not M 1 -M 3 . 13In the absence of a determinate calculation of M (or M 4 ) as opposed to the alternative metalinguistic propositions in (10), the implicature view cannot guarantee the right interpretation of (2a).

Under-generation
Mankowitz's algorithm also under-generates metalinguistic interpretations, in the following sense: In Mankowitz's view, metalinguistic interpretation results from a reasoning process set off by a perceived threat to a Gricean Maxim.However, there are many cases of metalinguistic usage and negotiation which seem to involve no such threat.Let us look at this more closely.
Consider (2a).As we saw, Mankowitz considers two routes from an utterance of (2a) to an implicature of the metalinguistic proposition M ('athlete' should be used in a way that applies to Secretariat).Either (2a) literally expresses P: Secretariat is an athlete (where athlete excludes nonhumans), or no discernible proposition at all (if the meaning of 'athlete' is not antecedently settled in context).In the former case, since P is obviously false, it flouts Quality; in the latter case, since (2a) expresses no discernible proposition, it flouts Quantity.Either way, the metalinguistic proposition M rescues the utterance.
The problem is that there is a substantial class of cases of metalinguistic usage and negotiation that don't seem to fit either description.Arguably, Athlete is one such case.In that context, it is implausible that speaker a intends to express either P or no discernible proposition at all.It is comparatively more sensible to think that a intends to use their preferred meaning of 'athlete', and thereby express the proposition P * : Secretariat is an athlete* (where athlete* includes non-humans).
Indeed, this coheres with the initial picture of metalinguistic negotiation (painted by Sundell, Plunkett, and others), which promised to reconcile the possibility that speakers express compatible propositions with their having a dispute (Plunkett and Sundell 2013a).According to this picture, the intuitive characterization of Athlete is such that (2a) expresses P * , whereas (2b) expresses not-P: Secretariat is not an athlete (where athlete excludes non-humans).
That being said, and even though Mankowitz's theory does not explicitly countenance the possibility that a expresses P * , her view could be supplemented in order to account for such cases, in the following way: Suppose that (2a) literally expresses P * .Since the merits of Secretariat are common ground, it is obviously true that Secretariat is an athlete*.Thus, (2a) would flout Quantity, and Gricean reasoning would be set off.This would indeed be an alternative way of reconstructing a pragmatic derivation of M that would not be subject to the objection just outlined.However, it is not obvious that it would work in a case such as Athlete.Note that this latter reconstruction requires that the hearer interprets the speaker of (2a) as being uninformative.But in a case such as Athlete, it is doubtful that the speaker aims to be uninformative, and it cannot be guaranteed either that the hearer will interpret them in that way.
Consider the speaker's point of view first.As noted above, the speaker of (2a) plausibly intends to express P * (rather than P or no discernible proposition).It is equally plausible that they intend to be informative.This may not be obvious when we consider a bare utterance of 'Secretariat is an athlete'.But it is easy to think of alternative ways of phrasing (2a) that stress its informativity: Speaker a could have said 'Hey, they forgot to include Secretariat.He was a great athlete!' or 'Secretariat should be on that list!(of best athletes of the 20th century)'.It is doubtful to see a in these cases as intending to utter a triviality.
From the hearer's point of view, it is also implausible to expect that they will perceive the speaker as intending to utter a trivial truth.Note that it would have to be common ground between speaker and hearer that 'athlete' means athlete*-otherwise the hearer could not sensibly reason their way from (2a) to P * .But in cases such as Athlete, that does not seem right.If it were common ground that 'athlete' meant athlete*, no dispute would arise.Therefore, it is unclear that this addition to Mankowitz's view can be made to work in cases like Athlete. 14n additional, related consideration concerns the type of implicature mechanism posited by Mankowitz.Following  Meibauer (2009), conversational implicature can be divided in two broad categories: additive and substitutional.Additive implicatures are such that the implicated content is added to literal content.E.g., in (3) (repeated here), the implicature that c is not going to the party is added to the proposition that c has to work.By contrast, substitutional implicatures are such that the implicated content substitutes the literal content.E.g., in an ironic remark such as (7), the implicature that Stephen King is an unlikely candidate substitutes the proposition that 2 +2 = 5.
(7) a. Stephen King will win the Nobel Prize for literature.
b. Yeah, and 2 + 2 = 5. (≈ Stephen King will not win the Nobel Prize for literature) Metalinguistic usage, according to Mankowitz's calculation algorithm, would count as a substitutional implicature (although she does not classify it as such herself): In Athlete, a sentence like (2a) does not end up conveying its literal meaning (the proposition P or no discernible proposition) + the metalinguistic proposition M (' 'athlete' should be used in a way that applies to Secretariat').Rather, the result of the inferential process is that (2a) communicates M only (this holds as well of our additional reconstruction, starting from P * ).
But this substitutional implicature construal of metalinguistic usage would not be entirely satisfactory, for the following reason: Speakers who convey extra-semantic content via substitutional implicature should be ready to admit that the literal meaning of their utterances is not what they intended to communicate.If one asks the speaker of (7b) whether they really meant that 2 + 2 = 5, they will of course say no (similarly with other types of substitutional implicatures, such as hyperbole or metaphor).By contrast, the speaker of (2a) may well insist that they mean exactly what they said, namely that Secretariat is an athlete.This marks a strong contrast between metalinguistic usage and substitutional implicatures.
In closing this section, I shall stress that the previous points are not so much arguments against Mankowitz's view as an observation that her account is underspecified in important ways.It is up to the implicaturist to fine-tune their proposal in a way that circumvents these issues.

The Neo-Stalnakerian Alternative
In contrast with the Gricean approach reviewed above, it is possible to see metalinguistic usage as the result of the interaction between context and content along broadly Stalnakerian lines. 15This type of view has been put forward by Barker (2002) and Barker (2002, 2013) in order to account for metalinguistic use of vague predicates, and has been applied to other forms of metalinguistic usage and disagreement more recently by Kocurek et al. (2020). 16I present the view in four stages: I discuss some preliminaries (Sect.4.1); I present the view informally (Sect.4.2); I lay out (one possible version of) the formal model (Sect.4.3); and finally, I show that this view overcomes the difficulties of the implicature view discussed in Sect. 3 (Sect.4.4).

Preliminaries
Any view of metalinguistic usage and negotiation has to start by tackling two questions: first, what expressions in the lexicon can be used metalinguistically?Second, how can we determine which expression(s) in a given sentence are the target of metalinguistic usage?
First, it is safe to assume that many words are "marked" for possible metalinguistic readings, insofar as there is some possible variation in their meaning.So e.g., most nouns and adjectives ('athlete', 'tall'), but also quantifiers ('every') and verbs are such that they might be interpreted differently in different contexts, allowing for metalinguistic usage and negotiation.It's perhaps harder to say what expressions, if any, cannot be used metalinguistically at all.Intuitive candidates might include logical connectives (but see Kouri Kissel  2021, which contributes to a long tradition of logical pluralism dating back to Carnap 1937), mathematical expressions ('prime', 'odd'), and some adjectives in comparative form ('taller', 'older').
Second, within a given sentence there may be multiple expressions that could be interpreted metalinguistically.Thus, there ought to be a procedure for determining what expression(s) are the locus of any given metalinguistic dispute.Following Mankowitz (2021), we may rely on a combination of contextual cues, grammatical structure, and prosody.(Mankowitz (2021) focuses on the latter aspect, see her Sect.2.2.) 17 Perhaps the safest criterion is occupying predicate position.Consider another well-known example of metalinguistic negotiation: a United Nations hearing discussing whether waterboarding is torture (Plunkett and  Sundell 2013a, p. 19).In principle, both expressions 'waterboarding' and 'torture' can be used metalinguistically, which would lead to different metalinguistic disputes.But if the dispute features the sentence 'waterboarding is (not) torture', it would be difficult to interpret it as a metalinguistic dispute about 'waterboarding'.To have a metalinguistic dispute about 'waterboarding', it seems that the expression should be in predicate position. 1817 In later work, Mankowitz has stressed the role of QUD identification for metalinguistic usage (Mankowitz and Shaw 2022, p. 705).I thank Poppy Mankowitz (p.c.) for drawing my attention to this. 18Further cues might help fix other aspects of the dispute, such as what interpretations of the relevant term are at issue.Plunkett and  Sundell (2013a, p. 19) construct the waterboarding example as a case where one speaker advocates for the US Justice Department definition of torture-where waterboarding is not torture-while the other defends the UN definition-according to which waterboarding is torture.Similarly, Ludlow (2008) presents Athlete as a conflict regarding a "horse-inclusive" and a "horse-exclusive" definition of 'athlete'.This is clearly determined by contextual factors, and other interpretations might be at play in other contexts.

The View, Informally
The view is, at core, a Stalnakerian view, according to which context is conceived as a set of live possibilities, and assertions are proposals to rule out some of those possibilities (see Stalnaker 1978/2002).In the standard Stalnakerian picture, those possibilities are purely factual; that is, they concern what the world is like.Barker and others enrich this picture by proposing that contexts not only track factual possibilities, but also interpretative possibilities (regarding how to use language).Interpretative possibilities determine how to use vague terms as well as other imprecise expressions, such as (some) quantifiers, adjectives, and nouns-the expressions "marked" for metalinguistic usage.
This suggests a natural distinction between metalinguistic and descriptive usage of an expression.Most standardly, speakers hold fixed the relevant interpretative possibilities and use declarative sentences to inform about the world.In those situations, they make descriptive use of an expression.Such is often the case with 'tall': we assume a threshold for 'tall', and by applying 'tall' to individuals, we rule out worlds where their height does not meet the threshold.Similarly, many uses of nouns such as 'athlete' work like this: speakers hold fixed a certain interpretation of 'athlete' (e.g., a horse-exclusionary one) and when they predicate 'athlete' of an individual they inform their audience that the individual has the properties associated with 'athlete' according to that fixed interpretation.
In a metalinguistic usage, things work the other way around: there, all the relevant factual information is held fixed, and the same sentences have the communicative purpose of ruling out interpretative possibilities.Such is the case with 'tall' in the context described in (1).There, Feynman's height is known, and the purpose of uttering (1a) is to rule out interpretations according to which 'tall' does not apply to Feynman.Similarly, in the context envisaged by Ludlow (2008), the factual properties of Secretariat are taken for granted, and the discussion turns on different interpretative possibilities for 'athlete'.Let us spell out this distinction more formally.

The View, Semi-formally
The account works formally by building factual and interpretative information (possible worlds and interpretations, respectively) into the semantic value of declarative sentences, as world-interpretation pairs. 19tart from the familiar view of the common ground of a conversation at a given time as a set of possibilities representing the information that interlocutors accept, and think that everyone else accepts, for the purpose of the conversation at that time.The common ground is standardly taken to contain as a parameter a set of possible worlds, those compatible with what speakers take the world to be like.We take the possible world parameter to represent factual information.Next, in order to model metalinguistic usage, we postulate a second parameter or component in the common ground: a set of possible interpretations (of expressions that allow metalinguistic usage).This second component represents the way in which speakers interpret language, that is, they model metalinguistic information.If speakers agree on, say, a horse-exclusive interpretation of 'athlete', every interpretation in the common ground will be such that 'athlete' is assigned a horse-exclusionary intension.Combining these two parameters, we may model the common ground as a set of world-interpretation pairs.
Next, sentences are assigned, as their semantic values, sets of ordered pairs of possible worlds and interpretations.To a sentence like (2a) we would assign pairs w, i according to which the properties of Secretariat at the world w fall under the denotation of 'athlete' relative to the interpretation i.We can write this as follows: 20 (11) [[Secretariat is an athlete]] = { w, i : athlete(S)(w)(i)} A natural correlate of this picture is a notion of truth relative to an index of evaluation, which is a world-interpretation pair.We say that a sentence like (2a) is true at a w, i just in case w, i belongs in its denotation: Note that, in this framework, one can still characterize a classic notion of truth-at-a-possible world, so long as we hold fixed the interpretation parameter (conversely, if we hold fixed the worldly parameter, we obtain a notion of truth-at-aninterpretation).In principle, the natural language predicate 'is true' may pick out any of these notions.
Relatedly, the denotation of 'athlete' is not a classical intension (a function from worlds to extensions), but a function from pairs of worlds and interpretations to extensions.a common ground.See Stalnaker (1978/2002) for a classic presentation of this view, and Rothschild and Yalcin (2016, 2017) for the relationship between static and dynamic semantics. 20On notation: In what follows, I use underlined text for complex metalinguistic-classical intensions, bolded for classical intensions and italics for metalinguistic intensions.I distinguish these concepts in what follows.
However, we can characterize classical intensions based on this semantic value: For each interpretation i, 'athlete' picks out a classical intension, namely, the intension of 'athlete' according to i. E.g., if i is an exclusionary interpretation of 'athlete', 'athlete' will pick out some sporty properties of humans (call this property athlete E ) relative to i.If i is an inclusive interpretation, 'athlete' will pick out sporty features non-humans can have (call them athlete I ).Thus, where i E and i I are these two interpretations, (2a) will be truth-conditionally equivalent to two different classical propositions relative to each interpretation: Conversely, if we hold fixed the world component, then 'athlete' will pick out (what we may call) a metalinguistic intension: a function from interpretations to extensions.At any world w, the metalinguistic intension of 'athlete' is the set of interpretations of 'athlete' that are compatible with the (relevant) properties of Secretariat at w.So e.g., if w is a world where Secretariat is the fastest racehorse in history, then 'athlete' at w will pick out interpretations according to which the fastest racehorse in history counts as an 'athlete' (let 'athlete F ' stand for such metalinguistic intension).Relative to a world where Secretariat is a not-so-great racehorse, 'athlete' will pick out interpretations according to which not-so-great racehorses count as 'athletes' (call that metalinguistic intension 'athlete G ').Where w F and w G are each of those worlds, (2a) will be truth-conditionally equivalent to the following two metalinguistic propositions at each world: These metalinguistic propositions may correspond to the metalinguistic propositions that Mankowitz features in her account ('athlete' should be used in a way that applies to Secretariat).Importantly however, in Sect.3.2.1,we saw that there are many other metalinguistic propositions that could be pragmatically derived thanks to her algorithm, some of which are intuitive interpretations of (2a) and some of which are not (cf.( 10)).What we've said so far does not obviously guarantee that the metalinguistic propositions in (14) correspond to the attested metalinguistic propositions as opposed to the non-attested.I return to this issue on Sect.4.4.
Next, to assert a declarative sentence in this framework is to propose to add its content to the common ground.Standardly, this is represented as set intersection.Where the common ground is a set CG = { w 1 , i 1 , ..., w n , i n }: We can now illustrate how metalinguistic and descriptive usage works.Start with descriptive usage.Suppose, first, that we are in a context where speakers have settled on the traditional, "exclusionary" interpretation of 'athlete'.By contrast, suppose speakers are unsure whether Usain Bolt is a sportsperson or a politician.The common ground of this conversation is such that (i) all the admissible interpretations are such that the interpretation for 'athlete' only applies to humans (call these i E ), and (ii) at some worlds w P in CG, Usain Bolt is a politician; and at some other worlds w S , he is a sportsperson.Simplifying, the common ground contains only two world-interpretation pairs: CG = { w P , i E , w S , i E }.
When we add a sentence like 'Usain Bolt is an athlete' to this CG, the result is as follows: (16) Usain Bolt is an athlete According to the only available interpretation for 'athlete' in this common ground, i E , the only world where Usain Bolt qualifies as an athlete is w S , and so the pair that survives the update is w S , i E .Note that, since the interpretation of 'athlete' remains constant, the result of adding ( 16) to this common ground is tantamount to adding the classical proposition that Usain Bolt is an athlete E to the worldly component.This follows from our previous observation that factual-metalinguistic propositions are truth-conditionally equivalent to classical propositions relative to a fixed interpretation.Applied to ( 16): (18) ∀w : [[( 16)]] w,i E = 1 iff w ∈ {w : athlete E (U )(w)} Now consider metalinguistic usage.In Ludlow's sports context, it is common ground that Secretariat is the fastest racehorse ever, but it is unclear whether 'athlete' should include non-humans or not.We can represent this as a common ground containing only w F worlds, but including both i E and i I interpretations: Adding (2a) to this common ground results in the following update: Given the properties of Secretariat, the only interpretation according to which Secretariat qualifies as an athlete is i I , and so the pair that survives the update is w F , i I .Since the properties of Secretariat remain constant, the result of adding (2a) to this common ground is tantamount to adding the metalinguistic proposition that Secretariat falls under 'athlete' to the interpretation parameter of the common ground (as shown in (14a) above).

Predictions vis-á-vis the Implicature View
Setting aside the formal details, the crucial aspect of this view is that it does not treat metalinguistic usage as the result of Gricean reasoning.Thus, this view can accommodate all the empirical observations of Sect.3.1, which were not predicted by the implicature view: First, metalinguistic usage is not predicted to be cancellable.This is to be expected, for the following reason: in the neo-Stalnakerian view, uttering a declarative sentence in a metalinguistic context (a context where the relevant facts are fixed, but where the relevant interpretations are not) amounts to adding a metalinguistic proposition to the common ground.Thus, it is to be expected that explicitly denying that metalinguistic proposition is felt to be contradictory.Secondly, the kind of semantic values proposed by this view are predicted to interact with operators in just the same way as standard semantic values do.For example: in standard Stalnakerian possible world semantics, the negation of a proposition p is the complement of the set of possible worlds at which p is true.In this neo-Stalnakerian view, the negation of p is the complement of the set of world-interpretation pairs at which p is true.Other operators are characterized in a similar fashion.
Since metalinguistic usage is not calculated pragmatically, the view does not incur the calculability issues raised in Sect.3.2: First, this view does not predict that, if a sentence fails to express a identifiable proposition, that sentence will be interpreted metalinguistically.All that is required is that the relevant facts (e.g., the properties of Secretariat) are common ground.Thus, the neo-Stalnakerian avoids the first over-generation worry.
Secondly, as we noted in Sect.4.3, the neo-Stalnakerian can provide a notion of metalinguistic proposition-cf.( 14)-and they can say that, when speakers use declarative sentences in the appropriate common ground, they express those metalinguistic propositions.However, in Sect.3.2.1 we observed that there are multiple alternative metalinguistic propositions that could in principle be conveyed by (2a) (cf.( 10)), and the Gricean could not guarantee that only some of these metalinguistic propositions are implicated.Can the neo-Stalnakerian do better?I think so.
The attested metalinguistic propositions are normative propositions about how to use language, such as M, and descriptive metalinguistic propositions about how some linguistic community uses language, such as M 4 .The neo-Stalnakerian can say, on the one hand, that metalinguistic propositions such as those in ( 14) are normative because the common ground has a normative status in virtue of representing what speakers should accept, given the current state of the conversation.On the other hand, the neo-Stalnakerian can characterize descriptive metalinguistic propositions as classical (possible-world) propositions about particular lin-guistic communities.To assert these propositions is not to update the interpretation component of the common ground.Rather, they update the factual component with information about actual language use.So the neo-Stalnakerian has an advantage over the Gricean insofar as they can at least provide a principled distinction between the two types of metalinguistic propositions that bare declarative sentences seem capable of expressing.
Thirdly, the neo-Stalnakerian view does not require any maxim violation in order to trigger a metalinguistic interpretation, and thus does not under-generate metalinguistic interpretations in the way that the Gricean view does.Moreover, the neo-Stalnakerian view treats metalinguistic usage as neither additive nor substitutional implicature.Sentences are sets of world-interpretation pairs, which implies that they always carry metalinguistic information.Whether a proposition's metalinguistic information is expressed at a context boils down to features of the context of use.In a context where there is uncertainty about the world and not about the discourse, a declarative sentence s will be used descriptively to reduce factual uncertainty.In a context where there is uncertainty about the discourse and not about the world, s will be used (normatively) metalinguistically to reduce interpretative uncertainty.But crucially, in the latter case, we do not start by interpreting a standard proposition P and then deriving a metalinguistic proposition M which may supplement or substitute P-metalinguistic content is part of the meaning of s from the very start.
Finally, as noted in Sect.3.2.2,part of the original motivation for putting forward the notion of metalinguistic negotiation was to preserve the intuition that speakers discussing, e.g., whether Secretariat is an athlete could be expressing different propositions and still disagree with each other.And we saw that the implicature theory did not quite deliver this result, as the Gricean process resulted in a sentence like (2a) communicating a metalinguistic proposition instead of the sentence's literal content.The neo-Stalnakerian view has an advantage here as well.For they can say that, in a metalinguistic dispute, speakers convey different (and compatible) classical propositions.Let us illustrate this with (2).
Suppose, first, that negation is just set complementation.So, where W is the total set of worlds and I is the total set of interpretations, [[( 2b)]] = W × I \ [[(2a)]] (that is, the denotation of (2b) is the complement set of (2a)).Next, if adding (2a) to the common ground of Ludlow's context results in the pair w F , i I (see ( 19)), then adding (2b) should result in the other pair in the original common ground, w F , i E .The situation looks like this: Given (13) above, the worldly component in each of these updated common grounds is compatible with different clas-sical propositions: (2a) is true relative to w F , i I just in case the classical proposition that Secretariat is an athlete I is true at w F ; and (2b) is true relative to w F , i E just in case the classical proposition that Secretariat is an athlete E is false at w F .Thus, relative to each speaker's preferred interpretation of 'athlete', each of their utterances expresses a different, classical proposition, as expected.This feature of the view preserves the intuition that speakers in a metalinguistic dispute are expressing compatible propositions.More can be said to characterize and defend the neo-Stalnakerian view of metalinguistic negotiation.But hopefully, these brief remarks suffice to show that it is a viable alternative to the implicature view, and that it is well suited to evade some of the latter's obstacles.

Conclusion
In this paper, I have argued against the view of metalinguistic usage as conversational implicature.I have put forward two types of criticism of that view.First, I have observed that there is linguistic data against the implicature view: metalinguistic usage is non-cancellable and interacts with operators such as negation, conditionals and propositional attitudes in the same way that semantic content does.Secondly, I have argued that the calculation algorithm put forward by defenders of the implicature view is problematic, since it both overand under-generates metalinguistic interpretations.Moreover, the view seems forced to classify metalinguistic usage as a substitutional implicature, which is at odds with some of the central properties of the phenomenon.In contrast to the implicature view, I have briefly presented a neo-Stalnakerian account of metalinguistic usage, a view that can largely evade the problems that beset the implicature view.Overall, I believe that the available evidence leans in favor of the neo-Stalnakerian view, even if that requires a slightly more sophisticated semantic theory than classical, possible-worlds semantics.But it is of course open to the implicaturist to build a more elaborate version of their view that can overcome the worries that I have laid out here.

( 3 )
a. Are you going to Paul's party?b.No, I am not going.
c.I have to work.

( 8
) a. Are you going to Paul's party?b.I have to work.c.I don't have to work.d.If I have to work, then I will arrive too late.e. Mary thinks that I have to work.

( 3 )
a. Are you going to Paul's party?c.I have to work.(≈ I have to work + I am not going to the party) (19) CG + [[2a]] = { w F , i I } (20) CG + [[2a]] = { w F , i E } 1a If the context is such that 'athlete' (following standard usage) excludes non-human animals: If a's utterance (2a) expressed the standard proposition P (Secretariat is an athlete), it would flout the Maxim of Quality ('Do not say what you believe to be false').1b If the context is such that it is not antecedently set- tled whether 'athlete' excludes non-human animals: a's utterance (2a) does not express any (mutually) discernible proposition, therefore it flouts the Maxim of Quantity ('Make your contribution as informative as you can (for the current purposes of the exchange)').2 If a's utterance (2a) purported to communicate the metalinguistic proposition M instead, it would not flout the Maxim of Quality/Quantity. 3 a's utterance (2a) communicates M.