So let’s talk about clarity. When you’re talking with someone, you want what they think
you mean to match what you really mean. It can be as innocuous as just asking for some cookies,
or it can be as dangerous as getting that tricky magic spell just right. But we always want our meaning
to be clear. Unfortunately, sometimes our words don’t allow us that clear path
to just one interpretation. I’m Moti Lieberman, and this is the Ling Space.
So whenever we run into a sentence, we have to quickly work out what that person was trying
to get across. We take their words, and we run them through our mental syntax to get
out a logical form. That logical form is our first stab at meaning – and in a
lot of cases, it’s all we really need. So for a sentence like, “Penny’s
hair is metallic green”, there’s pretty much only one interpretation we can get.
But with the whole variety of sentences out there, it doesn't take a lot
before things start getting more complicated. Ambiguity becomes a real problem real fast. Let’s
consider something like “All Quentin’s friends went to a fantasy land.” If you
think about it for a second, you’ll see that this sentence can mean
two different things. It could mean that every single one of his friends went to
the exact same fantasy land. Or it could mean that all of them went to some fantasy land, but
not necessarily to the same one. So the sentence would still be true if one person went to
Narnia, another to Oz, a third to Fillory, etc. As long as all of them made it to some
otherworldly destination, the sentence will still be true.
So… where do these meanings come from? How can the same exact sentence be true in two
totally different situations? It’s not that any of the nouns or verbs themselves have
separate meanings that are making this sentence all ambiguous. And it's not the way we're attaching those
nouns and verbs to each other that's causing the problem. The secret here is in those most
innocent-seeming of words: “all” and “a.”
Those little words might seem like they’re not that special, but they play a powerful
role in how we interpret a sentence. Remember, we have to get a logical form out of any given
sentence, right? That’s the sort of clear-cut, LogicBot 3000 way of looking at things. Well,
harmless-looking words like “all” and “a” actually help map out our possible logical
forms. We refer to them, and the other words like them, as quantifiers. Quantifiers tell
us what conditions the sentence has to meet in order for it to turn out to be true.
Okay, so for a concrete example, let’s look back at our sentence, “All Quentin’s friends
went to a fantasy land.” How can LogicBot map out all the ways the sentence is true?
First of all, that “all” there tells us that if even a single member of the group
stayed home, the sentence will be false. It’s got to be everyone. And then, the “a”,
that simple little vowel, it humbly tells us that there has to be a fantasy land out
there for our group to visit. Saying “a fantasy land” is logically equivalent to
saying “there is a fantasy land that exists”, even if it’s just, you know, in our imaginations.
But wait. So if that’s the only role “all” and “a” have, where do the multiple meanings
come from? It doesn’t look like that should be ambiguous at all. Everyone went out, and
everyone went to a fantasy land that exists. Awesome! End of story.
Well… yeah, not really. See, when you put multiple of these logic tools in the same
sentence, they start fighting for dominance. Each one wants to have influence over the
whole interpretation, each one wants to be the Big Quantifier On Campus. In semantics,
the influence a quantifier has, its logical power, is known as its scope.
So in our sentence, there are two of these logical operators battling it out. It’s a question
of whether “all” or “a” is more powerful. If “all” gets the upper hand, it has scope
over “a”. That means the fact that all the kids went out is more important than where
they went. So that gives us the reading where every one of Quentin’s friends went to some
fantasy land or another. It could be true if they all went to the same one, or it could
be true if they all went to different ones, or anywhere in between, doesn’t matter.
As long as they all went, it works, because what matters most is the “all” there.
Since this interpretation matches the ordering of the sentence when we say it, it’s known
as surface scope.
Now, you already know the sentence has another reading, one where all the kids went to
the exact same land. So you’ve probably guessed that “all” doesn’t always end
up winning. “a” could come out on top, and get scope over “all.” That’s how
you end up with the meaning where there is one single land where all of Quentin’s friends
went. Here the fact that “a” is the most important logical operator is the crucial
thing. It means there’s one single existing fantasy land that we’re talking about. So
there’s no more splitting up the group. All the kids still have to make a trip somewhere,
but now, the all have to go to the same place, or the sentence won’t be true.
Because this is the opposite ordering from what we have in the sentence itself, this
reading is known as inverse scope.
All right, so all these innocuous words, our alls and as and somes and thes, are fighting
it out all the time in an endless battle for logical dominance. But if that’s true,
then why aren’t we always adrift in a sea of ambiguity? Why don’t we feel confused
all the time?
It turns out that this comes back to the rules of conversation we talked about before.
Because in the end, we’re not LogicBots. We have this extra layer of stuff we can draw
from to make our interpretations, so we can avoid the confusion of our robot friends. We
take into account the context, what’s relevant, and what would make what the person is saying
true. This actually tends to follow a pattern, and it's really pretty neat. Let’s go through
it together.
So, for the sentence we’ve been looking at, here’s what you probably did: you thought
first that all of Quentin’s friends went to the exact same fantasy land, and then when I
said the sentence was ambiguous, you probably then worked out the other reading. Right? That’s because the
reading where they all went to the same place is actually true under both possible logical interpretations.
If all the kids went to the same fantasy land, then it doesn't
matter whether “all” or “a” wins, because the sentence will be true either way. It’s
only if some went to Fillory, some went to Narnia, etc. that we require one of the quantifiers
to dominate the other.
Without any context, we want the situation where it’ll be true for the most possible
scopes – and that’s when they all go to the same place. The interpretation of all
the kids going to the same fantasy land is the only one where both versions of the scope
relationship are true, and so that’s the reading our brain jumps to first. We
can usually only get to the second one if we think about it a bit, like an optical illusion.
So why is that? What’s making our brains decide pick the most versatile interpretation?
It all comes back to the Rules of Conversation we talked about in Topic 2. One of the maxims
that sit around inside our brains helping us interpret stuff says, “avoid ambiguity”. So without
even really thinking about it, we reject the interpretation that would be
true only in a smaller subset of logical cases. It goes like this: We perceive the sentence, map out
all the logical forms, and then we promote the one that makes the most readings true.
At the same time, we keep the other forms on the back burner, ready to be bumped up if we get new input that tells us
a given quantifier has to win. And all this, in the blink of an eye. Brains! Sweet, amazing
brains.
And on that note, we’ve reached the end of the Ling Space for this week. If you were
scoping out my meanings properly, you learned that we map out every sentence we hear onto a
logical forms to get the meaning; that the different logical pieces known as quantifiers
help us know what interpretations we can come up with; that the quantifiers battle it out
for which one gets scope over another; and that we prefer the interpretation that makes
the most scope readings true to avoid all that nasty ambiguity.
The Ling Space is written and produced by me, Moti Lieberman. It’s directed by Adèle-Élise
Prévost, our production assistant is Georges Coulombe, our music and sound design 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 have more material on this
topic. Check us out on Tumblr, Twitter, and Facebook, and if you want to keep expanding
your own personal Ling Space, please subscribe. And we’ll see you next Wednesday. Na shledanou!