Entailments in Two Directions


We got a comment over on our video about implicatures, entailments, and presuppositions asking about the difference between upward and downward entailments, and I thought I’d bring the discussion of that point over to here, too. ^_^

So entailments are things that are 100% guaranteed to be true, assuming that the original statement is true. Like, take a sentence like “Joyce overheard her mom talking”. If that’s true, then it must also mean that Joyce overheard a person talking – after all, all moms are people.

But when we try to define groups, we often do it by referring to different sets. So let’s talk about kittens. Kittens are a kind of cat – arguably the most adorable kind – and so if we made a set of all the cats in the world, the whole set of kittens would be in it. But the set of kittens is also made up of smaller sets of kinds of kittens – Siamese kittens, Maine Coon kittens, Japanese bobtail kittens, and more. And the different kinds of entailment point us either up or down, to the larger set kittens are part of, or the smaller sets that make it up.

Let’s start with something simple: “I watched the kitten frolic”. If that sentence is true, then it entails that I watched a cat frolic; that just has to be true, too. Because the entailment goes up into the larger set of cats that frolicking kitten is part of, it’s an upward entailment. But the entailment doesn’t go down into the sets of different kinds of kittens; it could just as well have been an Abyssinian kitten or a tuxedo kitten. It’s not necessarily true about any of the smaller kitten sets.

And most sentences work like this – simple declaratives just point up. “The kitten attacked the girl’s foot”? “Adele admired the kitten”? Those just give you upward entailments. But you can find sentences that go the other way, down into the sets that make up the set you’re concerned with. Like, “The vet didn’t treat any kittens that day”. If that one’s true, then it must be true that the vet didn’t treat any tabby or Mau or Manx kittens, either – it has to hold for all the sets that make up the kitten set, and so it’s a downward entailment. But the vet could still have had adult cat patients; it doesn’t tell you anything about the larger set.

Entailments are useful from a logical perspective, but they also help solve syntactic questions, like about where we can use words like “any” or “ever”. Take a look at these sentences, where the * means it’s bad, as usual:

* The shelter has any kittens left.

The shelter does not have any kittens left.

* Many people ever frown at a kitten.

Few people ever frown at a kitten.

Words like not or few allow you to use things like “any” or “ever”, because when they show up in the right place, they give you a downward-entailing environment for your sentence. And those words are only really happy in those environments. So knowing about these entailments can help you work out whether your “any” or “ever” sentences should check out or not, and vice versa. It’s a cool point of connection between syntax and semantics. ^_^


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