There’s the door: The paradigm of the Gricean theory of implicature and its criticisms.

Introduction

Since Grice introduced the concept of implicature, its study has become an important part of the philosophy of language. And for good reason, since implicature explains many otherwise puzzling phenomena and seems integral to how we use and understand language.fnv:{ c::LycanIntro;; 157} Grice’s theory of implicature, further developed or modified by other philosophers (‘Griceans’) has been by far the most popular theory of implicature. Yet, it has also come under critique, most exhaustingly by c::DavisImpl;;. Reviewing these criticisms, one must ask: How far-reaching are they? To understand if developing the Gricean theory further, rather than developing truly independent theories of implicature, is probable to yield an understanding of implicature, answering this question is of paramount importance. For this reason, and to enable the reader to engage more deeply with the criticisms raised by Davis, I will begin with an explanation of Gricean theory. For this purpose, I will explain what implicature is, how Grice attempted to explain it and how Davis then interprets Grice. In preparation for Davis’ criticism, I explain how Gricean theory derives three common implicatures. Finally, I develop three lines of argument from c::DavisImpl;;. I conclude that Davis’ critique is convincing, and sufficient to recommend the development of competing theories.

What is implicature?

Sentences can say things. For our purposes, let us say they say that, i.e. they express a proposition (One could also say they perform the illocutionary act of saying that). fn:{c::DavisImpl;; 5} Sentences can also imply things one has not, strictly speaking, said. One way a sentence can imply another is to entail it. Another way one can imply something is to implicate something. Implicature is a technical term introduced by Grice, and described by him so:

Implicature (Grice): […] whatever [a person] implied, suggested, meant […], is distinct from what [that person] said […] fn:{c::GriceWay;; 24}

Saying here is meant as saying that, as defined above. Davis reads Grice’s definition as follows:

Implicature (Davis): the act of meaning or implying something by saying something else. fn:{c::DavisImpl;; 5}

For example, if I say ‘There’s the door’, but I mean ‘Leave now.’, I haven’t said that you have to leave. But I have certainly meant it, and said it by saying ‘There’s the door’. Therefore, I have implicated it.fnv:{ c::LycanIntro;; 157}

Grice distinguishes two types of implicature: conventional, which follows from the conventional meaning of words. The conventional meaning of a sentence is what a sentence would mean, assuming basic things, like the speaker speaking a standard version of English. (e.g. The conventional meaning of ‘The die is green and heavy.’ is that the die is both green and heavy, a conventional implicature that the die is green.) fnv:{ c::DavisImpl;; 4}

The counterpart to conventional implicature is nonconventional implicature, which doesn’t arise simply from the conventional meanings of words. How, then, do they arise? Grice’s theory of conversational implicature attempts to explain this phenomenon for one type of nonconventional implicature: conversational implicature, which is what we will limit our exploration to. fnv:{ c::GriceWay;; 25f} Grice does not define conversational implicature, but simply says it is essentially connected with certain general features of discourse.fn:{c::GriceWay;; 26} Let us then examine what these features are, and how these features give rise to implicature.

Grice’s theory of conversational implicature, according to Grice

The Cooperative Principle and its maxims

Grice starts with the assumption that our conversations are cooperative efforts. Based on this, he sketches a rule which participants in a conversation would, since they are cooperative efforts, be expected to follow:fnv:{ c::GriceWay;;}

Cooperative Principle (henceforth CP): Make your conversational contribution such as is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged. fn:{c::GriceWay;;}

How does one ‘make one’s conversational contribution such as is required’? How does one say something cooperative? For this, Grice proposes that there are certain maxims that, if followed, will (in general) result in cooperation with the CP. Put another way, these are rules that, taken together, will result in a conversational contribution that is cooperative. Grice divides these into four categories with certain supermaxims and submaxims:fnv:{ c::GriceWay;;}

• Quantity:
  • Make your contribution as informative as is required (for the
    current purpose of the exchange)
  • Do not make your contribution more informative than is required.fn:{That this maxim should be counted among the others is disputed by Davis, and Grice also only hesitantly postulates it. Therefore, it is often not included among the maxims. For Davis treatment of this maxim, see: c::DavisImpl;; 83. In a footnote on the same page, it is also stated ’Quantity-2’ is also affirmed by Berg (1991: 419) and Matsumoto (1995). I take this sentence to be implicating ‘No other important philosopher of language affirms it.’, using a quantity implicature}
• Quality: Try to make your contribution one that is true.
  • Do not say what you believe to be false.
  • Do not say that for which you lack adequate evidence.
• Relation: Be relevant.
• Manner: Be perspicuous.
  • Avoid obscurity of expression.
  • Avoid ambiguity.
  • Be brief.
  • Be orderly.fn:{All: cf. c::GriceWay;; 26 - 27}

Grice admits there might be other maxims that are at work in talk exchanges, but none as connected to the CP. fnv:{ c::GriceWay;; 28}

The theoretical backbone

Our starting question was: ‘How do we say one thing, and mean another?’ We now know the rules of cooperatively contributing to a conversation. How are these connected? To answer that; to connect the CP and its maxims with conversational implicature, Grice offers the following definition:

Grice’s definition of conversational implicature (d1): A man […] may be said to have conversationally implicated that q, provided that [Or: A person has conversationally implicated q iff]

0. [he said p, and by saying (or making as if to say) that p he has implicated that q;]
1. he is to be presumed to be observing the conversational maxims, or at least the Cooperative Principle;
2. the supposition that he is aware that, or thinks that, q is required to make his saying or making as if to say p […] consistent with this presumption;
3. and the speaker thinks (and would expect the hearer to think that the speaker thinks) that it is within the competences of the hearer to work out, or grasp intuitively, that the supposition mentioned in (2) is required.fn:{c::GriceWay;; 30f}

So, the fact that the speaker is presumed to be observing the Cooperative Principle, and the fact that the speaker thinks that the only way to observe the Cooperative Principle while saying what theyfn:{I use the singular they as a gender-neutral pronoun whenever possible, i.e. whenever I am not quoting or directly referring to a formulation of an author who used ‘he’ as a generic pronoun} have said is to implicate q, is what connects the CP and implicature. (To be precise, it only connects presumption of the observance of the CP with conversational implicature while presuming that there is an implicature.fn:{This explanation also leaves out (3), the mutual knowledge clause. We will work with Davis’ definition, though, so nothing is lost by simplifying for explanatory purposes for now})

Grice additionally believed that, for something to count as a conversational implicature, as opposed to a conventional implicature, one must be able to work out a conversational implicature, that is, give an argument for arriving at the implicature, using the definition, and therefore the CP and its maxims.fnv:{ c::GriceWay;; 31} So, how would one do that? Grice gives a pattern:

Grice’s working-out schema:

1. He has said that p;

2. there is no reason to suppose that he is not observing the maxims, or at least the Cooperative Principle; [this corresponds to d1 (1)]

3. he could not be doing this unless he thought that q; [this corresponds to d1 (2)]

4. he knows (and knows that I know that he knows) that I can see that the supposition that he thinks that q is required. [this corresponds to d1 (3)]

5. he has done nothing to stop me thinking that q; he intends me to think, or is at least willing to allow me to think, that q; and so he has implicated that q.”fn:{c::GriceWay;; 31}

While using this schema, the hearer will rely on different kinds of data: (1) the conventional meaning of the words used, together with the identity of any references that may be involved; (2) the Cooperative Principle and its maxims; (3) the context, linguistic or otherwise, of the utterance; (4) other items of background knowledge; and (5) the fact (or supposed fact) that all relevant items falling under the previous headings are available to both participants and both participants know or assume this to be the case.fn:{c::GriceWay;;}

Generating implicatures through the Cooperative Principle and its maxims

Implicatures are created by violating the CP at the level of what is said, since then the supposition that one has meant something different, and therefore implicated it, becomes necessary.fnv:{ c::GriceWay;; 32f} But there are two ways that violating the CP does not produce an implicature: One, opting out of the maxim and/or the cooperative principle, by indicating that one cannot or will not.fnv:{ c::GriceWay;; 30} This possibility of signaling that one is not following the CP is known as cancellability. Cancelling can be done explicitly or implicitly.fnv:{ c::GriceWay;; 39. That passage only talks about generalized conversational implicatures, but the reasoning in it also applies to particularized conversational implicatures} Two, violating a maxim quietly (e.g. saying something you know to be wrong, but pretending as if it were true): In this case, the speaker will often mislead. fnv:{ c::GriceWay;; 30}

So, how does one violate the CP, and therefore implicate something?

Implicatures where the supposition of an implicature explains the violation of a maxim

The speaker S says p, which violates a maxim, but is presumed to be following the CP. The supposition of the implicature q is necessary to conform to the CP. The reasoning process might be sketched as follows:

(1, 2, 3) He has said that p; there is no reason to suppose that he is not observing the maxims, or at least the Cooperative Principle; but p violates the CP, more specifically the maxim M. His statement p is only in accordance with the CP and M if he, in fact, thought q. (4) he knows […]fnv:{ c::GriceWay;; 32. The sketch of the reasoning process is derived from the example given there and the working-out schema given above}

Implicatures where the supposition of a clash between maxims explains the violation of a maxim

Shortly:

He has said that p; there is no reason to suppose that he is not observing the maxims, or at least the Cooperative Principle; but p violates the CP, more specifically the maxim M. The only reason for not observing M is that he would otherwise be violating another maxim M2, if he observed M. Therefore, he is implicating he cannot observe M.fnv:{ c::GriceWay;; 32f., sketch derived as above}

Implicatures in which a maxim is flouted and exploited

If S violates a maxim very obviously, and not out of necessity, how can he still be following the CP? In short, he can’t mean what he said, so he must mean something different.fnv:{ c::GriceWay;; 30} What is this something? Here the account faces major problems, as Davis will later show.

To find out, then, if Davis’ critique of Grice damns Gricean Theory, we must first find out how Davis reads Grice.

Davis’ interpretation of Grice’s theory of conversational implicature

Davis covers much of the same groundwork as Grice, although he does slightly alter the wordings. He considers the following to be the main tenets of Grice:fn:{c::DavisImpl;; 1}

The Cooperative Principle and its maxims

Cooperative Principle. Contribute what is required by the acceptedpurpose of the conversation.
Maxim of Quality. Make your contribution true; so do not convey what you believe false or unjustified.
Maxim of Quantity. Be as informative as required.
Maxim of Relation. Be relevant.
Maxim of Manner. Be perspicuous; so avoid obscurity and ambiguity, and strive for brevity and order.fn:{c::DavisImpl;; 11f}

The theoretical backbone

The theoretical definition: S conversationally implicates p iff

1. S implicates p;
2. S is presumed to be observing the Cooperative Principle. (cooperative presumption);
3. The supposition that S believes p is required to make S’s utterance consistent with the Cooperative Principle (determinacy); and
4. S believes (or knows), and expects H to believe that S believes, that H is able to determine that (iii) is true (mutual knowledge).fn:{c::DavisImpl;; 13}
   Calculability Assumption:Conversational implicatures must be capable of being worked out. fn:{c::DavisImpl;; 14}

The Generative Assumption

In the theoretical definition, the fact that ‘s implicates p’ is a premise to get to the conclusion that ‘s conversationally implicates p’. Davis argues that this isn’t actually the view Grice holds. Looking at the working-out schema from above, it is clear that Grice thinks that (ii) – (iv) actually generate the implicatures. Not just the conversationality, but the existence of the implicature itself depends on (ii) – (iv).fnv:{ c::DavisImpl;; 16} Therefore, he holds the view that:

Generative Assumption: Conversational implicatures exist because of the fact that the cooperative presumption, determinacy, and mutual knowledge conditions [(ii)- (iv)] hold. fn:{c::DavisImpl;; 17}

Therefore, one can simplify the definition above by removing (i) from the premises.fnv:{ c::DavisImpl;; 17f. This is also how c::SaulDavis;; 631 reads it}

Why implicate? Grice’s Razor

Why do we need all this complex theory, though? Take the sentence from the beginning: ‘There’s the door.’ Why don’t we just simply say: ‘Well, there’s one sense in which the sentence means that the door is there, and another in which it means ›leave now.‹ It just has two senses, and that’s that.’ Well, this is where Grice’s Razor comes into play:

Grice’s Razor: Other things equal, it is preferable to postulate conversational implicatures rather than senses, conventional implicatures, or semantic presuppositions because conversational implicatures can be derived from independently motivated psychosocial principles.fn:{c::DavisImpl;; 19}

That is, if we postulate two senses, then we need conventions for every word and every sentence, too many to ever write down. But with Gricean theory, we can just derive the implicatures from a short list of principles and some definitions! fnv:{ c::DavisImpl;;}

This additional, independent postulate brings with it an issue, though. Remember that the working-out schema would allow us to postulate conventions as background information.fn:{See p. 6} Since conversational implicatures can be inferred from and explained by the CP and its maxims (the aforementioned psychosocial principles), we cannot postulate linguistic conventions to explain away problems that will come up without giving up Grice’s Razor, and losing any reason to prefer implicatures over senses or other entities.fnv:{ c::SaulDavis;; 638f} With these tools in hand, let us now look at how Gricean theory explains common implicatures.

Common implicatures, and their explanation in Gricean theory

In this paper, we will examine three types of implicatures. The existence of these implicatures is not in doubt, rather, the Gricean explanation is. To explain these three types of implicatures, let ⊐ mean ‘implicates’, ⊐̸ mean ‘does not implicate’, ¬ mean ‘it is not the case that’, and ⊐⊐ mean ‘is predicted as an implicature by the CP and its maxims’.

Quantity implicatures

A quantity implicature is when a less informative statement implicates the denial of a more informative statement. fn:{c::DavisImpl;; 33} Consider:

1) ‘Some died.’ ⊐ ¬’All died.’

2) ‘The food is warm.’ ⊐ ¬’The food is hot.’fnv:{ c::DavisImpl;; 34}

Grice explains these with the Maxim of Quantity. (Be as informative as required.) If the speaker were in a position to make the more informative statement, they should have. Because they did not, they must believe that the more informative statement is not true. fnv:{ c::DavisImpl;;} This is an implicature of type 1. as discussed under 3c.

Tautology implicatures

A tautology implicature is when a tautology (a completely uninformative statement by itself) means something besides its guaranteed truth. Consider:

3) ‘War is war.’ ⊐ ‘It is the nature of war that terrible things happen.’

4) ‘A war’s a war.’ ⊐ ‘One war is as bad (or as good) as another.’fnv:{ c::DavisImpl;; 43}

Gricean theory explains that these completely uninformative statements could not possibly be obeying the Maxim of Quantity, and therefore are flouting it.fnv:{ c::DavisImpl;; 41} How we should get from the fact that they can’t mean their guaranteed truth and are therefore implicating something completely different to the specific implicature they are supposed to possess remains unanswered. fnv:{ c::DavisImpl;; 43}

Conjunction implicatures

Consider the conjunction ‘and’, as in ‘A and B’. In a basic sense, it just means ‘Both A and B are true’, e.g. ‘I got an A in math and a C in chemistry.’ But the sentence ‘Jane took off her trousers and went to bed.’ seems to implicate a temporal order of the conjuncts, which we will call temporal implicature of conjunctions.fnv:{ c::DavisImpl;; 46f. There is actually some debate if this is not just an ambiguous meaning of ‘and’, but we will assume (as Davis does) that it is an implicature} Therefore:

5) ‘Jane took off her trousers and went to bed.’ ⊐ ‘Jane first took off her trousers and then went to bed.’fnv:{ c::DavisImpl;; 46f}

Grice explains these implicatures via the Maxim of Manner (‘Be perspicuous’), specifically a submaxim ‘Be orderly. If engaged in a narrative, the best way to be orderly is to follow the temporal order, the order in which they took place.’fnv:{ c::DavisImpl;; 48}

The failure of Gricean theory

Let us now begin examining the criticisms of Gricean theory. Davis offers a whole host of distinct, but interrelated arguments for the failure of Gricean theory. I have here categorized them thuslyfn:{This is not Davis‘ categorization. Given that space does not permit including all of Davis’ arguments, I think this categorization is suited to give an overview of some of the problems Gricean theory faces. I also have only considered chapters 1 – 3 of c::DavisImpl;;}: First, I will discuss the arguments that pertain to the Gricean theory failing as a result of generating results that are contradictory to the theories premises, specifically the premise of determinacy. These fulfill the purpose of showing that the theory is not a self-consistent system. Second, I will discuss the ways in which Gricean theory generates implicatures that do not bear out in reality, therefore showing that the maxims at best are only approximations to the rules that govern cooperative talk exchanges. Third, I will discuss the criticisms that claim that the Gricean project is fundamentally flawed. This short sketch aims to impart an overview of the flaws that face the Gricean theory but does not aim at an exhaustive treatment, as space does not permit.

Gricean implicatures conflicts with the theory’s premises – failures of determinacy

One important part of Gricean theory is determinacy: The supposition that S believes p is required to make S’s utterance consistent with the Cooperative Principle. That is, there cannot be a competing supposition - that S believes q - that would make the utterance consistent with the CP. Relying on determinacy is the Calculability Assumption: Conversational implicatures must be capable of being worked out. Since we cannot work out an implicature if there are multiple possible implicata, if determinacy fails, so does the Calculability Assumption. fnv:{ c::DavisImpl;; 62}

How does determinacy then fail?

1. Because ignorance is a possibility

According to one reading of the Maxim of Quantity, one is to make the most informative statement possible.fnv:{ c::DavisImpl;; 34} Therefore, making a less informative statement implicates that one is not able to make a more informative statement. ‘All died.’ is considered more informative than ‘Some died.’, therefore uttering ‘Some died.’ is taken to mean that the speaker could not make a more informative statement, and therefore to implicate ¬’All died.’ But there is another possible reason that one is not able to make a more informative statement: Because one does not know if it is true. Therefore, ‘Some died.’ also implicates ‘I don’t know if all died.’ Therefore:

(6) ‘Some died.’ ⊐⊐ ¬’All died.’ ⊻fn:{The logical ‘exclusive or.’} ‘I don’t know if ‘All died.’’ fnv:{ c::DavisImpl;; 77}

Since there are two possible implicatures, determinacy fails. Therefore, all quantity implicatures cannot fulfill the determinacy condition. fnv:{ c::DavisImpl;; 77f}

2. Because more than one statement can be more informative

Consider the sentence (7) ‘Beyoncé and Tinashe moved the piano.’ If they had moved it together, the Maxim of Quality would have required the speaker to utter that (being a more informative statement), therefore: (7) implicates ‘Beyoncé and Tinashe moved the piano separately.’ But consider: If they had moved it separately, the Maxim of Quality would have required the speaker to utter that (being a more informative statement), therefore: (7) implicates ‘Beyoncé and Tinashe moved the piano together.’fnv:{ c::DavisImpl;; 38}

Therefore, (8) ‘Beyoncé and Tinashe moved the piano.’ ⊐⊐ ‘Beyoncé and Tinashe moved the piano separately.’ ⊻ ‘Beyoncé and Tinashe moved the piano together.’

This obviously violates determinacy.

So, how do we solve these problems? Well, Grice posited that if you can work out more than one implicature, the resulting conversational implicature will be a disjunction of such explanations.fnv:{ c::GriceWay;; 39f} It is actually unclear whether this means an inclusive or an exclusive disjunction.fn:{Davis (1991) 71f. presupposes an inclusive disjunction. Contrast c::SaulDavis;; 635, which presupposes an exclusive disjunction} In the case of both (6) and (8), an exclusive interpretation would result in a plausible implicature, the sentences seem to actually be implicating an ambiguous statement, interpreted inclusively, the implicature would be contradictory.fn:{I am not implicating the possibility both that ‘Not all died’, and that I don’t know if this is the case, nor am I implicating the possibility that Beyoncé and Tinashe moved the piano both separately and together} For now, we can consider the problem of determinacy ameliorated.

Gricean theory conflicts with reality - Failures of misgeneration

There exist many ways in which the implicatures generated by Gricean theory do not match up with our experiences of what sentences do actually implicate:

Disjunctions are predicted to be implicated, but not always actually implicated

Returning to disjunctions: Consider the following example: One writes a letter of recommendation for Claudette, writing ‘I cannot recommend Claudette highly enough.’ This sentence is violating the Maxim of Quantity, but there are two ways to make this sentence cooperative: Either I can say no more because I can’t find adequate words of praise or because she is so lacking I can’t give a sufficiently positive recommendation for the job. fnv:{ c::SaulDavis;; 634 f} If we don’t want determinacy to fail, I must mean the disjunction either Claudette is so wonderful that I cannot find adequate words of praise, or she is so lacking that I don’t feel I can give a sufficiently positive recommendation for the job.fn:{c::SaulDavis;; 635} Clearly, this isn’t what I mean, a completely false implicature is generated.fnv:{ c::SaulDavis;;} Therefore, positing disjunctions does not save determinacy in all cases, and the problem of 6.1 persists.

Many of the maxims fail when applied to other languages

If the Cooperative Principle and maxims are derived from general psychosocial principles, as Grice’s Razor claims, one would expect them to generalize to other languages.

Consider quantity implicatures. In English, the sentence ‘I see a person.’ ⊐ ¬’I see a person I know well.’, per the Maxim of Quantity. One would expect that this sentence, if translated into another language, would bear the same implicature. But in Malagasyfn:{A language from an ethnological report cited by c::DavisImpl;;, first mentioned on c::DavisImpl;; 8}, the sentence carries no such implicature. fnv:{ c::DavisImpl;; 37}

Or consider ‘War is war’, carrying the tautology implicature ‘It is the nature of war that terrible things happen.’ In French, ‘La guerre est la guerre’ (‘War is war’) carries no implicature, hardly even makes sense. To convey the same implicature, one would have to say ‘C’est la guerre’ (‘That’s war’).fnv:{ c::DavisImpl;; 44} So it seems, rather than being general psychosocial principles, the maxims are merely conventions. fnv:{ c::DavisImpl;; 37}

Many of the maxims fail when applied to specific English sentences

Even for English, there are many implicatures that are misgenerated.

Consider this list of implicatures, which are all false, but implicated by the Maxim of Quantity:

1. ‘Some died’ ⊐̸ ‘Some were murdered.’

2. ‘Some died’ ⊐̸ ¬’35.72% died’

3. ‘2 is an even number.’ ⊐̸ ¬’2 is necessarily an even number.’

Etc. The list can be extended endlessly.fnv:{ c::DavisImpl;; 35f. For a longer - but not endless - list see c::DavisImpl;;}

Or consider the parallel sentences:

1. ‘Jane entered a house’ ⊐ ¬’Jane entered her house’

2. ‘Jane lost a book’ ⊐ ‘Jane lost her book’

The Maxim of Quantity would have wrongly generated b. as ¬’Jane lost her book.’.fnv:{ c::DavisImpl;; 37}

For another example, remember that we specified earlier that the temporal reading of ‘and’ is, according to Grice, because the Maxim of Manner recommends a temporal reading of narratives according to the order in which they took place. According to this:

‘Jane set a record and cleared 15 feet.’ ⊐⊐ ‘Jane set a record, and then cleared 15 feet.’, which is obviously wrong, and not what is implicated.

In light of these issues, it seems that, far from being derived from general psychosocial principles, the maxims are at best simply first-order approximations.

Fundamental flaws in the Gricean theory

The Maxim of Quantity doesn’t generate any implicatures

Let’s take the question

6) H: ‘Did anyone die?’

And suppose S answers it with ‘Yes.’ ‘Yes’ is a fully cooperative answer, since it is as informative as required. But if ‘Yes’ is a fully cooperative answer, meaning (not implicating) ‘Some died.’, then ‘Some died.’ must also be fully cooperative, meaning that the implicature ¬’All died.’ was not required, but supererogatory. This simply means that determinacy fails, but points at a deeper misunderstanding.fnv:{ c::DavisImpl;; 81f}

Suppose one were to, as a rejoinder, reword the Maxim of Quantity as follows: ‘Be as informative as possible.’ Then imagine S is asked ‘Who won the game?’, and S answers truthfully ‘Real Madrid.’. From this, one could implicate that S does not know the final score, or even in which league Real Madrid plays in, or that Madrid is in Spain etc., because if they did, to comply with the reworded Maxim of Quantity, they would have said it.fnv:{ c::DavisImpl;; 82}

Observe that we claimed when examining failures of determinacy that Therefore, making a less informative statement implicates that one is not able to make a more informative statement.fn:{See p. 12} This is a statement only derivable from the reworded Maxim of Quantity, and yet, it is necessary to derive the implicature of ‘Some S are P.’ For the only way for ‘Some S are P.’ to always implicate ¬’All S are P.’ is to either assert the obviously false stronger Maxim of Quantity, or for it to be always true (true in every context) that implicating ¬’All S are P’ is required for the talk exchange. There exist many contexts where this isn’t true, for example, if one wants to establish the truth of a proposition z, and one has established that ‘If some S are P, then Q.’fnv:{ c::DavisImpl;; 85. A longer list of contexts can be found c::DavisImpl;;} Lacking context, the Maxim of Quantity cannot generate any implicatures.

Every statement could be flouting

Grice claims that one can flout a maxim (violate it obviously). Figurative speech pretty much always blatantly violates the Maxim of Quality (is not true), and therefore must be flouting.fnv:{ c::GriceWay;; 34}

But even allowing the possibility of flouting, and therefore speaking figuratively, dooms determinacy. For maybe, when S says ‘Some died.’, they are flouting the Maxim of Quality, engaging in understatement, and implicating ‘Most died.’ or ‘All died.’. And when S says (9) ‘It is a fine day!’, maybe they are engaging in literal speech, or maybe they are flouting the Maxim of Quality, engaging in Irony, and implicating ‘It is an awful day!’. Therefore, there is no belief required to make the utterance consistent with the Cooperative Principle. Cases like these can be found for every sentence, that is, S could be flouting the Maxim of Quality and speaking figuratively in every sentence. Therefore, determinacy fails for every case of literal speech.fnv:{ c::DavisImpl;; 66}

Now, there is the counterargument that, instead of determinacy requiring the belief that p, nothing would be lost if one softened it to ‘The supposition that S believes p is probable […]’. But take (9). There might be no circumstances in which irony is more likely than literal speech, and yet S might still have been speaking ironically. This is problematic because the CP would not predict that implicature, and so there would be no way to implicate irony in cases where it is unlikely.fnv:{ c::DavisImpl;; 67}

Alternatively, for these failures of determinacy, it may be argued, positing the implicature as a disjunction between all the alternatives would work quite well. As formulated by Grice, the disjunction cannot contain the literal meaning, but it would seem to be no big problem to rework Gricean theory to be able to accommodate that. One would then, however, have to accept that every case of literal speech implicates a disjunction of literal speech and all possible metaphoric meanings. It seems unlikely that speech is, in fact, this indeterminate, or that the Calculability Assumption would hold, since it seems unlikely that the hearer could or would work out the disjunction between all metaphoric meanings.

Conclusion

Every one of Davis’ criticisms by itself could be tolerated as part of a theory that is a work in progress. But the fact that one is stuck between positing very unlikely or contradictory implicatures or violating determinacy or calculability (6.1, 6.2.1, 6.3.2), that the worked-out implicatures are wrong in all sorts of cases (6.2), and that the mechanism for predicting one of the most common implicatures, quantity implicatures, is fundamentally broken (6.3.1) seems to me quite damning. Equally damning are some of the other objections mentioned by Davis, such as the lack of a positive stage in the explanation of flouting, especially in the case of tautology implicatures and metaphor, or the problems of defining ‘meaning’ as the definition of implicature refers to it. Reviewing these criticisms, it seems that the Gricean theory of implicature should not be seen as a monolith, to be modified somewhat, but otherwise accepted, but as a first step to developing an active and varied field.