Listen to part of a lecture in a linguistics class. 

Ok, the conventions or assumptions that govern conversation, these may vary from one culture to another, but basically, for people to communicate, there is a ... they have to follow certain rules. Like if I am talking with you and I start saying things that are not true, if you can't tell when I am lying and when I am telling the truth, well, we are not going to have a very satisfactory conversation, are we? Why? Because it violates one of the Gricean Maxims. That's a set of rules or maxims a philosopher name H.P.Grice came up with in 1970s. One of these Gricean Maxims is... well, I've already given you a hint.

Oh, you just can't go around telling lies. 

Right, or as Grice put it, "Do not say what you believe to be false." That's one of Grice's Maxims of Quality as he called it. So that's pretty obvious. But there are others just as important, like, eh... suppose you would ask me what time it was and I replied "my sister just got married", what would you think? 

You are not really answering my question. 

No, I am not, am I? There is no connection at all, which feels wrong because you generally expect to find one. So one important maxim is simply: be relevant. And using the so-called Maxim of Relevance we can infer things as well, or rather the speaker can imply things and the listener can make inferences. For instance, suppose you say you would really love to have a cup of coffee right now, and I say "there's a shop around the corner". Now, what can you infer from what I said? 

Well, the shop sells coffee for one thing. 

Right, and that I believe it is open now. Because if I won't implying those things, my response would not be relevant. It'd have no connection with what you said before. But according to the maxim, my response should be relevant to your statement, meaning, we should assume some connection between the statement and the response. And this maxim of relevance is quite efficient to use. Even if I don't spell out all the details, you can still make some useful logical inferences, namely, the shop is open and it sells coffee. If we actually have to explain all these details, conversations would move along pretty slowly, wouldn't they? 

OK, then there's the maxims of manner, including things like be clear, and avoid ambiguity. 

And another more interesting maxims is one of the so-called maxims of quantity, quantities of information, that is. It says, to give as much information as is required in the situation. So suppose you asked me what I did yesterday and I say "I went to the Art Museum." You would likely infer that I saw some works of art. Suppose, though, that I did not go inside the museum, I just walked up to it then left. Then I violated the quantity maxim by not giving enough information. So you can see how important implications are to our ability to carry on a conversation. 

But there are times when people will violate these maxims on purpose. Let's say a boss is asked to write a letter of recommendation for a former employee seeking an engineering job. The letter he writes is quite brief. Something like, uh, Mr . X is polite and always dresses quite neatly. So what does this really mean? 

Oh, I see. By not mentioning any important qualities related to the job, the boss is ... like, implying that this is best that can be said about Mr . X that he is really not qualified. 

Exactly. It's a written letter not a conversation, but the principle is the same. The boss is conveying a negative impression of Mr. X without actually saying negative about him. So, by violating the maxims, we ...eh... but ... it can be a way to be subtle or polite, or to convey humor through sarcasm or irony.  

Sometimes though people will violate maxims for another purpose: to deceive. Now, can you imagine who might do such a thing? 

Some politicians. 

Or advertisers.

Right. Anyone who may see an advantage in implying certain things that are untrue without explicitly saying something untrue. They think, hey, don't blame us if our audience happens to draw inferences that are simply not true. So next time you see an advertisement saying some product could be up to 20% more effective, think of these maxims of quantity and relevance, and ask yourself what inferences you are being led to draw. Think, more effective than what exactly? And why do they use those little phrases "could be" and "up to"? These claims give us a lot less information than they seem to.