Now that we've talked a lot about logical implication, let's take a second to talk about a perhaps more important phenomenon: conversational implicature.
If I go into the kitchen, find the main course missing from the counter, and ask "what happened to the roast?" You might, noticing that the dog looks satisfied and full, say "well, the dog certainly looks happy." Logically, you haven't answered the question. We can say a lot about the logical implications of what you've said, but that won't tell us what you've accomplished by saying what you said. Instead, we need the concept of a conversational implicature: a way we can communicate more than is logically implied by what we've said by relying on the rules of conversation.
In this example, there's a rule in conversations that says "don't say things that aren't relevant to the topic at hand." I'll therefore assume that you mean "the dog looks happy" to be a relevant piece of information to my question. So it seems like what you're implicating (even though you're not logically implying it) is that the dog ate the roast.
To highlight some of the awkwardness that can happen when we accidentally implicate things, here is a list of funny implicatures and the rules they violate which give them the unintended meaning:
- I have a brother, I also have another brother
- This is called "scalar implicature": it's where you say something and everyone assumes that you've said the most informative quantitative statement you could have. Here, it's assumed that you would have made the strongest claim available: I have two brothers
- Mitch Hedberg has a great one liner that's also a sort of scalar implicature: "I used to do drugs. I still do, but I used to, too."
- Another Mitch Hedberg gem (he's a master of implicatures): "I want to hang a map of the world in my house. Then I'm gonna put pins into all the locations I've traveled to, but first I'm gonna have to travel to the top two corners of the map, so it won't fall down."
- The rule is something like "don't say you're going to do something like hang something on your wall if you don't mean to say that you're going to do everything required to do it in a normal way." By ignoring this rule, Mitch makes us assume that he is going to hang the map normally and then plays with that assumption.
- More Mitch Hedberg: "I wrote a script and I gave it to a guy who reads scripts. And he read it and he said he really likes it, but he thinks I need to re-write it. I said "Screw that, I'll just make a copy.""
- Of course, we're assuming that the editor in question meant that the script needed serious revision because of a rule that says something like "don't say something needs to be rewritten when you just mean it needs to be copied." or more generally "make appropriate requests given the technology of the time." Mitch is playing on that assumption by acting like he interpreted the editor the opposite way from the way he intended.
- Mitch Hedberg again: This one commercial said "Forget everything you know about slip covers," so I did. And it was a load off my mind. Then the commercial tried to sell slip covers, but I didn't know what they were.
- We all know that when someone says "forget everything you know about x" they aren't intending the phrase literally and instead, by convention, mean something like "here's a paradigm-shattering new product," or "I'm about to show you something which defies your previous assumptions about slip covers." Mitch is instead interpreting it literally, which isn't what convention dictates, even if Logic might dictate that we do so (in this case, it's unclear what logic would tell us to do)
To take a more relevant and controversial example: If my friend says, "Black people matter," and I respond with, "All people matter", then I'm saying something which logically implies that "black people matter." But even though my statement has this logical implication, there's a rule of conversation that says something like "don't make a broader statement when you mean to communicate something more specific." In breaking this rule, the conversational implicature is that people shouldn't be claiming that "black people matter" and instead should be claiming that "all people matter." The implicature is that there's something somehow wrong with saying "Black people matter" and that they should be saying something more general—that the person affirming the worth of black people has made some sort of mistake. In saying "all people matter" in response to someone saying, "black people matter", therefore, I'm doing something equivalent to the following:
"I love Oak trees"
"Well, I love all trees"
The implicature is that there's something wrong with saying one loves oak trees. That there's something mistaken in making the more specific claim. Again, it's like the following:
"We need to cure cancer as soon as possible."
"We need to cure all diseases as soon as possible."
The second speaker, because they are "zooming out" to a less specific claim, is implicating that there's a mistake in the first claim—that it’s too specific. But presumably there’s no problem with saying we need to cure cancer as soon as possible. This is partially because cancer is a particularly widespread and deadly disease.
Conversely, some people read the saying "black lives matter" as having the implicature that "black lives matter and other lives do not," or "black lives matter more than other lives." The idea here, I take it, is that in making this claim we are singling out a specific group when what we mean to be doing is affirming the importance of all lives and so we are making a mistake: we're implicating that black lives exclusively or especially matter. I don’t think there is a mistake in saying “black lives matter,” but the goal here is to understand how confusions begin (apart, perhaps, from problematic racial attitudes).
Both of these examples show how communication—particularly about sensitive and important issues—breaks down easily. When we're not all in agreement on the rules of the conversation and the common ground stock of knowledge we share, we can easily make claims that get misinterpreted. We all need to be charitable, take care and take our time, and be humble in our verbal interactions with one another. As always, try to focus more on your own mistakes than those of others.