2023-11-26

Implicatures, or how formal pragmatics help with subtext

Alright, buckle up bunnies, because today we’re talking implicatures.

What is that? Can you eat it? Unfortunately not, but stay with me anyway.

If you’ve ever wondered why, when you ask “Is Cyan good at their job?” and someone replies “Heh, they always come on time and haven’t ended up in jail yet”, you understand that the answer is “no” even though they didn’t actually say that… That’s ‘cause you just inferred an implicature.

Linguistics 101

Linguistics is this big field of technical studies about how language works. Within linguistics, we have various subfields, that analyze language phenomena from different perspectives.

• Phonology focuses on the sounds of language and how they evolve. If you’re looking at the use patterns of different [r] sounds across different families of languages, you’re doing phonology.
• Syntax is all about grammatical structures. If you’re looking at how the passive voice is constructed in different languages, you’re doing syntax.
• Semantics is about how language expressions relate to meanings. If you’re looking at how expressions like “Some”, “All”, “Not all”, “More than three” (=quantifiers), express different distributions of a property on a set of individuals, you’re doing semantics.¹
• Pragmatics is about how language can affect the world around us. If you’re looking at how, exactly, an imperative like “Close the door!” can lead to someone getting up and closing the door, you’re doing pragmatics. I adore pragmatics, and I will probably keep talking your ears off about it regularly, so it’d be nice if you could remember that.
• Logic is about how we reason, and what constitutes rules of reasoning and inferences. It’s not really a subfield of linguistics, more like its root, because it applies in mathematics, philosophy, computation, etc. If you’re looking at how ‘Both A and B are C’ gives you grounds to say ’therefore, A is C’, you’re doing logic. If you’re looking at “What makes a mathematical proof a valid proof?”, you’re doing logic - and also I like you.

Of course, these subfields communicate, and it’s rare to study one at the exception of all others. A semanticist will have to deal with syntax and logic eventually to figure out the impact of grammatical structures on meaning and reasoning. Pragmatics need some good semantics behind to understand the way words relate to meanings which affect the world. But this is the map of the park for today’s little hike.

Implicatures as pragmatic inferences

Our trail is firmly in the pragmatics area of the park. Implicatures, as a concept, were introduced by Herbert Paul Grice from 1957 onwards.²

They try to account for this phenomenon that, when something is said in a certain context, we recognize a specific subtext that is not said. However, these inferences do not happen by means of logical deductive reasoning. The best example to see that is the one of scalar implicatures - a specific category of implicatures that arise when speakers use words that are part of a scale.

Bell: “Ugh, I just posted the exam results.”

Avi: “So, how did they do on the exams?”

Bell (the teacher): “Well, some of them passed the test.”

Some is a quantifier expression that expresses at least one. But, in the above exchange, the fact that the teacher uses some makes us infer that not all students passed. This is not a logical inference: from at least one, you cannot always deduct not all. ‘Some men are mortal’ and all that.

Now I realize I probably have to make some explanation on the notion of valid inference. Why did I decide to write this thing again? Anyway. The notion of valid inference in logic is about rules of reasoning that structure a proof regardless of the type of statements it contains. A valid inference from A to B is one that is structured according to rules of reasoning, such that no matter what statement A and B stand for, if A is true, then B is true. Most of us suck at making valid inferences.

In the case that is relevant to us, can you always make a valid inference from ‘Some A is B’ to ‘Therefore not all A are B’? No, because we can make a bunch of counter-examples: that at least one element A is B gives you no evidence that there is an element A that is not B. Is it true that if ‘Some humans are mortal’ then ‘Not all humans are mortal’? I think the fuck not.³

Instead, the inference from some to not all has to do with the effect of the teacher’s speech in the context. As the teacher, they can be assumed to know how many of their students passed the test after results are out. Because the results are public, they can be assumed to be at liberty to share. So the inference from some to not all comes out because, if the teacher had been in the position to say ‘All students passed the test.’, they would have done so: it would be more informative!

What we’re dealing with when we deal with implicatures is a pragmatic inference: an inference that is made because of the words in a specific context. Because they’re inferred from context, implicatures are defeasible: in our example, it wouldn’t be weird, or contradictory, for the teacher to correct their utterance with “Oh, actually, all the students passed, they’re pretty smart cookies.”. When there’s a different context “Some of the students passed, but I haven’t finished grading”, the implicature also gets corrected, or amended. That’s what we mean by defeasible.

Conversely, take logical inferences: since not zero follows logically from at least one, there’s no way Bell can amend their statement with “Oh actually, none of my students passed” without contradicting themself. It’s much harder to undo a logical inference.⁴

The Maxims of Conversation

“But, Llwyn, implicatures are pragmatic, ok, but there must be some reason why some inferences are possible to make in a context (’not all the students passed’) and some are not so easily available (‘Exactly three students passed’)?” Quit whining, we’re right here.

Herbert Paul tells us:

Our talk exchanges do not normally consist of a succession of disconnected remarks, and would not be rational if they did. They are characteristically, to some degree at least, cooperative efforts; and each participant recognizes in them, to some extent, a purpose or set of purposes, or at least a mutually accepted direction.

Told you he was a fun guy. Of course, not all conversations are cooperative. We disagree, we have conflicts, and sometimes a conversation does not care so much about truth than about maximizing a number of sailing-related puns. However, what Grice points out is that there are some general principles that participants are expected to observe, at least in appearance. That’s… drumroll

The Cooperative Principle: 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.

Remember when we talked yesterday about how discourses have sets of rules that they follow, and a scientific discourse has different rules on proof and evidence as a political discourse? Yup, so here we have: when you’re in a conversation that has a certain set of rules, your contributions are perceived by other speakers in light of these rules. What about when you don’t know the rules?

Fear not, we have some maxims that, in general, will work.

Please remember: these are not prescriptions that one ought to follow in conversations! These are principles that describe the type of behaviour that is generally expected in conversations, and we reason from these - oft unstated - assumptions to understand other speakers’ contributions, because we’re not telepaths.⁵

• Quantity: Make a contribution that is as informative as required, and no more than required. In other words, say all you can, no more than you should.

  If I’m asking you about the best place to buy wool in the neighborhood, I am neither expecting a 30-min speech on the compared merits of peruvian wool vs. merino⁶, nor am I expecting a “Yes, there is a yarn shop” with complete refusal to elaborate.

• Quality: Make a sincere contribution that you believe to have adequate evidence for.

  If I’m asking you if you’d like pasta for dinner, I expect you to answer according to your needs and preference, not say “Yes to pasta” when you’re deadly allergic.

• Relation: Be relevant.

  That’s the one that connects your contribution to what was said before. If I say “Pasta for dinner?”, I sure don’t expect you to follow up with “There are seventeen bunnies outside” (but also, show me the bunnies).

• Manner: Politeness, brevity, avoiding ambiguity, and other bunnies.

  That’s the general expectation that a conversational partner will make their contribution clear, and perform it reasonably quick and without an unnecessary fuss.

You see why I insist that these are not prescriptive? People lie. It’s normal. But the reason why lying can even be a thing is that, when you engage in a conversation, it’s with an assumption that people are saying the truth. Call it a pretense, if you will. A pretty powerful set of conventions we generally think apply to our exchanges.

This is what we can call a normative approach to analyzing conversations. The idea behind it is that conversations have an unspoken set of rules, or norms, that participants are assumed to be following when they make contributions. Are they actually following the rules? Who knows. But do we interpret their contributions as if they were? Abso-fucking-lutely.

How we calculate implicatures, based on Maxims

The other piece of the puzzle, now. Once we have conversational norms that participants are generally expected to follow, then when someone overtly violates these norms, it is surprising. And it poses questions, and other participants make inferences. Tada!

Let’s find our examples again.

Bell: “Ugh, I just posted the exam results.”

Avi: “So, how did the students do on the exam?”

Bell (the teacher): “Well, some of them passed the test.”

When Bell says “some of the students passed the test.”, there’s a readily available alternative - “All of the students passed the test.”. This alternative would be more informative, if it were true. The process that makes one reason from some to not all is that, assuming Bell is a cooperative speaker, if they were in a position to say all, they would have to say all, to be as informative as possible. But Bell doesn’t say all. So, because we assume them to be a cooperative speaker, we think they have a good reason to prefer a less informative statement and break the maxim of Quantity. The closest available reason? They are not in a position to say all, because it’s not true.

Avi: “Is Cyan good at their job?”

Bell: “Heh, they always come on time and haven’t ended up in jail yet”

This one is less obvious in terms of reasoning, but what Bell is doing here violates the maxim of Relation. They answer with a statement that appears unconnected with the question - neither coming on time nor avoiding jail is connected with being particularly good at one’s job.⁷ Hence, the inference that the reason why Bell is answering this way is because they are not in a position to say that Cyan is good at their job.

Avi: “Did you just take my coffee mug?”

Bell (sipping from Avi’s mug right in front of them): “You know I would never.”

Bell is breaking the maxim of Quality in a very obvious manner. While they are expected to at least pretend to believe their contributions, they’re making it obvious that they do not. Situational humour ensues.

Conclusion

And there you have it! Implicatures are pragmatic inferences that we make, all the time, when we see speakers breaking norms of conversations, because we assume they have good reasons to do so.⁸

And they’re really fun, when you know about them! Something something on humour and the subversion of conversational expectations. Relevance might be my favourite to play with.

Enjoy your newfound way of making the world a weirder place!