So let’s talk about storytelling.
When we’re having a conversation, we usually want
whoever we’re talking to to believe the tales we tell.
We carefully craft our speech so that it jibes
with what’s come before.
And while sometimes this means choosing just
the right word, other times it can be more
about what we leave out.
So, what rules do speakers follow in managing
their shared knowledge and experience, and
how can we represent it?
I’m Moti Lieberman, and this is 
The Ling Space.
Meaning has two main parts: what our words
refer to, and the instructions telling us
how to put them together.
And this makes up the semantics of our language.
But there are lots of different ways to deliver the same
message, with rules constraining how we talk.
And these rules form the pragmatics of our
language — how our words actually get used.
Teasing these systems apart, though, is easier
said than done.
Like, take the sentence “Hunter knows that
Nina had a near-death experience.”
It says that Hunter knows something, whoever
he is.
But it also carries an assumption — specifically,
that Nina had a near-death experience.
It would be a strange thing to say if there
weren’t already agreement on whether that
was true; and it would be downright bizarre
if people were sure that it was false, and that
she’d never had a brush with mortality.
This sort of assumption that sentences can
come bundled up with is called a presupposition,
and it’s especially resilient.
Presuppositions are so strong, that even if
we pop a “not” in there, they stick around:
“Hunter doesn’t know that Nina had a near-death
experience” still suggests that she had one,
even if news of it hasn’t reached Hunter.
So where does this presupposition come from?
Is it part of the meanings of the words, or
is it more about the rules of conversation?
And how do we even figure that out?
A good way to get to the bottom of this is
to try to take what’s going on and formalize it.
That means making our description as exacting
as possible, using the tools of math and logic.
We’ve already used things like set theory
to talk about word meanings, and that’s
given us a lot of insight into how language
works.
So, let’s see if we can do the same thing here.
We said before that a sentence seems weird
when its assumptions come into conflict with
what the people in the conversation already
agree on.
So, we need a precise way to capture this.
One way we can do that is to think of shared
opinions as a collection of all the ways conversation
partners think the world might be.
Not necessarily the actual world, since we
can always be mistaken about what’s really
true, but all the possibilities that line
up with their shared experience.
So, if two people agree that Homer’s Iliad
is a great piece of writing, then all the
worlds in this set will be ones where it’s
great!
On the flip-side, if neither of them have
particularly strong opinions about classical
music, then there’ll be worlds where it's awesome, worlds where it isn't so awesome,
and everything in between - anything could
be possible there.
This collection of hypothetical worlds that
people agree are candidates for the real one
forms their common ground.
And as they talk to each other, every sentence
updates that picture a little bit more.
But while a sentence like “Hunter knows
that Nina had a near-death experience” makes
sense if everyone involved knows it, too,
it comes across as strange otherwise.
So, there’s a constraint on which sentences
are allowed to update the common ground: sentences
with assumptions that synch up with it get
in, but the ones that don’t get turned away.
It’s like a secret handshake, and only the
sentences that are in-the-know can make it
through to the other side.
With these ideas of the common ground, and
the rules that decide what gets in, we’ve
got nearly all the ingredients we need.
But, we still need a way of explaining why some
sentences come with presuppositions, and others don't.
To do this, we just need to remember what we've
said in the past about what sentences actually mean.
More than being just true or false, we’ve
argued that it’s better to think of sentences
like descriptions of worlds.
They’re functions — or connections — between different
possible worlds and the values “true” and "false."
We can symbolize how this works using the Greek letter
lambda, to represent the fact
that we’re dealing with a function.
So, if you take a sentence like “Homer played
football” and apply it to our own world,
where let’s say he actually did, then the sentence acts
like a function & you get “true."
But if not, then you get “false.”
To represent how a sentence can presuppose
something, we just have to limit the worlds
where it’s allowed to apply.
So, for our sentence from before, we take
the function and tack on a restriction about
the worlds that it covers.
That statement after the colon tells you what
the function can accept as input.
And it ends up making the function only apply to some
worlds — worlds where that statement holds true.
This actually lines up nicely with how we
tend to think of sentences that have presuppositions,
anyway: when the assumption’s true, the
sentence can either end up true or false;
but when it’s wrong, though, the sentence doesn't
obviously come out one way or the other, just
kind of undefined, like the linguistic equivalent
of dividing by zero.
As for how presuppositions find their way
into sentences in the first place, well, a
sensible guess is that it’s because of certain
words.
After all, if we switch out “know” for
another verb like “imagine,” so that Hunter
only imagined everything, we lose that assumption.
So, the meaning of a word like “know”
would look something like the meaning for
“believe,” combining sentences with the
people that believe them, while also mixing
in the requirement that those sentences actually
be true.
In this way, “know” basically means “believe,”
but with an added presupposition.
Other words like “the” and “both”
have meanings analogous to “a” and “all,”
while also imposing their own restrictions
on what they can and can’t combine with:
“the” only works when there’s one unique
thing being talked about, while “both”
only works when there’s two!
So our picture of how presuppositions work
has two parts to it: a rule on what gets into
the common ground, and certain words with
built-in limits on when and where we can use them.
But does this work for every sentence we see?
Well, a good way to test this is to try to
apply it to other kinds of assumptions.
And one variety that looks like it might fit
the bill is antipresuppositions.
Where presuppositions require that people
take something for granted as true, antipresuppositions
demand that they don’t.
So, just like it’s strange to say someone
knows something, when that something hasn’t
been established yet, it’d be weird to say something
like “Nancy thinks her daughter is missing”
when everyone knows for sure that she is.
Using the verb “thinks” antipresupposes
that the sentence that follows it is true,
so it’s only meant to be used when something
is unknown.
Now, at first glance, it looks like we could
just say that antipresuppositions are like
negative presuppositions.
In other words, just like how the sentence
“She gained her sight” presupposes that
she didn't have it at first, maybe the meaning
of “think” looks like this, with the function
assuming that the sentence it combines with
is false.
But this can’t quite be right.
While it sounds like a contradiction to say
“She gained her sight, and she always had
it,” it’s easy to imagine someone saying “She thinks her daughter’s missing, and she’s right.”
That’s because, unlike presuppositions,
antipresuppositions can turn out either true or false.
All that matters is that they aren’t taken
for granted when they’re used.
So what does that say about where they might come from?
Well, since antipresuppositions can go either
way, they aren’t really about functions
only applying in some worlds, while avoiding
others.
It’s more like they’re saying something
about the common ground, itself — that it’s
a bit of a mixed bag.
And while it is possible to build that into
the meanings of words like “think,” the
logic of it actually gets pretty convoluted,
opening up other problems.
Fortunately, a much simpler explanation is
available.
Like we’ve talked about before, speakers
tend to follow certain conversational maxims,
or rules, which govern what’s said and how
it gets interpreted.
One of these maxims says that we’re always
trying to be as informative as we can, meaning
that if we deliberately leave something out,
there must be a reason.
And when we consider the kinds of words we’ve
been talking about so far, it becomes clearer
what could be going on: for every word that
carries an antipresupposition, we find a corresponding
word carrying a presupposition.
That means that a speaker using one of these
words implies that they’re deliberately
choosing not to use the other, since they
would if they could.
Saying “think” in place of “know”
suggests that using “know” would be inappropriate,
and that the following sentence can’t actually
be taken for granted.
Antipresuppositions emerge out of a kind of
competition between separate but related words.
If we can safely assume, then, that conversational
maxims can be extended to include presuppositions,
we already have all the tools we need to explain
not only when things get taken for granted,
but when they don’t.
When it comes to sharing our stories, the
words we set aside can be just as important
as the ones we keep around.
So, we’ve reached the end of The Ling Space
for this week.
If our stories synched up, you learned that
certain sentences take some information for
granted, in the form of presuppositions; that
these kinds of assumptions come out of the
words we use, and how well they line up with
our shared knowledge; and that other kinds
of assumptions, like antipresuppositions, have more
to do with the words that we choose not to say.
The Ling Space is made by all these amazing
people over here.
If you want to learn more about just why presuppositions
are so darn resilient, check back on our website!
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See you next time! Mia dogo!
