So let’s talk about negativity. When we’re close to someone who’s feeling angry or
sad, it can make us feel bad, too. It’s like everyone around gets dragged down with
them. And the same’s true in language. When a word like “not” wanders into a sentence,
it affects everything around it. And there are even some words that are such
downers, they only get invited to the saddest language parties. So, how can we tell when
and where these woeful words will appear? I’m Moti Lieberman, and this is The Ling Space.
There are lots of different kinds of information that we can communicate with our sentences.
And as we’ve talked about in the past, one of the ways we can get something across to someone
is by what a sentence entails. For example, the sentence “Riley and her family moved
to San Francisco” tells you that Riley and her family must have travelled there, since
it’s pretty hard to move somewhere without actually going there, too!
This inference works because the first sentence — the one with “move” — entails the
second — the one with “travel.” To get specific, there’s no way that Riley and
her family moved to San Francisco could be true, while Riley and her family traveled
to San Francisco is false. The truth of the first sentence guarantees the truth of the second.
But just like how our lives can feel like they’ve been turned inside out when we relocate
to a new city, the relationships that hold between sentences can be put under a lot of
strain once we introduce a little bit of negativity. Take the sentence “Riley and her family
didn’t move to San Francisco.”
Suddenly, the connection is broken. We can’t say for sure, one way or the other, whether
Riley and her family travelled there. Maybe they did, just to visit or something; maybe
they’ve never been to San Francisco in their lives. All we know now is they didn’t move there.
But… so what? It isn’t a huge surprise to find out that negation changes the meaning
of a sentence. The thing is, when we go negative, something else happens, too. Now, we can stick
in some other words that we couldn’t before. Like, we could say “Riley and her family
didn’t move to San Francisco at all.” Or, “Riley and her family didn’t give
a hoot about moving to San Francisco.”
These expressions are known as negative polarity items, or NPIs. They’re called that because
they thrive in negative environments. When we try to put NPIs into a positive sentence. . .
well, they really put up a fight. “Riley and her family moved to San Francisco at all”
sounds about as good as broccoli on pizza. And “Riley and her family give a hoot about
moving to San Francisco” isn’t much better.
So it looks like negation’s entailment-destroying powers are what open up the gates and let
these gloomy little critters in. Except, we can actually find NPIs in other sentences, too.
Like, in the sentence “all of Riley’s memories that are at all sad will eventually
make her cry.” That “at all” is an NPI, since it doesn't fit very well into a sentence
like “Riley’s memories are sad at all,” but it’s perfectly comfortable in something
like “Riley’s memories aren’t sad at all.”
What’s even weirder, though, is that if we move the NPI over to the very end of that
first sentence, we get “all of Riley’s memories that are sad will eventually make
her cry at all,” which has gone back to being strange.
So, what’s going on here? To get a better grip on the behind-the-scenes action in charge
of all this NPI business, we need to go back to the beginning and focus in on something
that we skipped over the first time around.
When we stuck negation into that first sentence, we didn’t just break the relationship it
had with the second one; we reversed it! The negation of that second sentence actually
entails the negation of the first! So if Riley didn’t even travel to San Francisco, she
definitely couldn’t have moved there.
Now that we’re thinking about it this way, we have what we need to figure out what’s
happening inside the sentence “all of Riley’s memories that are at all sad will eventually
make her cry.” Let’s first look at a smaller version: “sad memories can make Riley
cry.” Notice that it entails the much more general sentence “memories can make Riley
cry.” If it’s true that sad memories can do it, then it’s true that memories can.
So, entailment runs in the direction from the specific to the general. But, when we stick
“all” at the beginnings of each of these sentences, suddenly something that should
be starting to get familiar happens; the direction of the entailment gets reversed! Now, if all of
Riley’s memories are able to make her cry, then it’s definitely true that all the sad ones can.
The word “all”, just like negation, turns entailment upside down. And just like negation,
it lets in NPIs like “ever” and “at all.” Hence, “all of Riley’s memories
that are at all sad will eventually make her cry.”
But if a word like “all” can do this, why can’t we just put an NPI at the end and say
“all of Riley’s sad memories will make her cry at all”? Well, to explain this,
we’re going to need to tweak our definition of entailment a little.
Up until now, we’ve been talking about entailment as a relationship that holds between sentences,
but we should really be thinking about it as a relationship that holds between sets.
So back when we talked about Generalized Quantifier Theory, we said that quantifiers like “some”
and “all” compare sets; “all” says that the first set it combines with is a subset
of the second, while “some” says that the intersection of the two sets it compares is non-empty.
Looking at a word like “all” from this angle, we can now consider each of the two
sets it combines with. Let’s go back to the sentence “sad memories can make Riley
cry.” If that’s true, then the more general sentence “memories can make Riley cry”
must also be true. And this is the default: entailment runs in an upward direction, moving
from a smaller set like “sad memories” up to a larger one, like just plain “memories”.
So that means that being in the smaller set entails being in the bigger one. And this
isn’t just true of noun phrases; it’s true of verb phrases, too! The more specific sentence
“sad memories make Riley cry loudly” entails the more general sentence “sad memories make Riley cry."
So, as sets get bigger, entailment runs up. But look at what “all” does to each of
the sets it combines with. When we put the quantifier back at the start of each sentence,
the direction of entailment in the first set now runs down, from bigger to smaller sets.
So, “all memories make Riley cry” entails “all sad memories make Riley cry.”
For this reason, the quantifier “all,” along with a word like “not,” is said
to be downward entailing. It turns the direction of entailment in the first part of the sentence on its head.
But "all" leaves the direction of entailment pointing up for the second half of the sentence,
because “all memories make Riley cry loudly” entails “all memories make Riley cry,”
where we’re still moving from a smaller to a larger set.
But we have a contrast in what "all" does to the different parts of the sentence. The
set represented by the noun phrase in the leftmost part of the sentence gets turned
upside down, but the rightmost set represented by the verb phrase stays pointing up. So from
there, we can get a bit more specific and say that “all” is left downward entailing
but right upward entailing.
Remarkably, this seems to account for why “all” lets NPIs into the beginnings of
sentences, but doesn’t allow them to appear at the end. The beginnings are downward entailing,
but the ends aren’t.
And every single one of the quantifiers we find in English, along with in other
languages, can be classified in this way. For example, “some” is both left and right
upward entailing, which means it doesn’t reverse entailments at the beginning or the
end, while “no” is both left and right downward entailing, so it reverses both. Meanwhile,
“every” and “all” are a mix!
And, so, “some” can’t combine with any NPIs, but “no” is more than happy to.
We can’t say “Someone ever liked that stupid gum commercial song,” but it’s
perfectly fine to say “no one ever liked that stupid gum commercial song.”
The downward entailing environments created by words like “not” and “no” and even
“all” spell out just where these sorts of words can show up. Even if we aren’t
consciously aware of the abstract relationships operating the controls of language, they play
a big part in how it works.
And when it comes to NPIs, it looks like a little negativity is a pretty positive thing!
So, we’ve reached the end of The Ling Space for this week. If you managed to keep your
entailments pointed in the right direction, you learned that some words, like “ever”
and “any,” are negative polarity items;
that these NPIs only show up in certain contexts, namely ones that reverse the direction of
entailment; and that we can categorize words based on whether they create downward entailing environments.
The Ling Space is produced by me, Moti Lieberman, and directed by Adèle-Elise Prévost. This
week’s episode was written by Stephan Hurtubise. Our editor is Georges Coulombe, our music
is by Shane Turner, and our graphics team is atelierMUSE.
We’re down in the comments below, or you can bring the discussion back over to our
website, where we’ll have some extra material on this topic.
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