So let's talk about other worlds.
There are lots of ways that things could be: mythical creatures lurking in the shadows;
hidden portals to other dimensions; maybe even a time traveller or two!
Of course, these ideas are pretty fringe.
But thankfully, language gives us ways to talk about all these possibilities, and just
how likely they really are.
So how do words like "must" and "maybe" work, and what can they tell us about how we think?
I'm Moti Lieberman, and this is The Ling Space.
One of the main goals of semantics is to get a better understanding of the meaning that
each word contributes to the sentence that it's in.
But figuring this out can be trickier for some words than others.
Take modal verbs: the word "need" in a sentence like "Peter needs to talk to his father."
It points out that something is necessary; while a word like "might" in "Peter
might talk to him" suggests that we're dealing with just one of many possibilities.
Taken together, these sorts of expressions convey modality.
That means they qualify the truth of a sentence, by saying something about its overall probability.
So, how do we capture all the different ways we communicate modality?
Where do we even start?
A good first step is to figure out exactly how these words combine with sentences in
the first place.
One thing to notice with modal verbs like "can" and "must" and "may" is
that even though they usually show up in the middles of sentences, sandwiched between the
subject and verb phrase, it probably makes more sense to think of them as combining with
the sentence in its entirety.
In "Walter must have forgotten some of his past", even though Walter is closer to "must"
than to "forget," he's really more of a forgetter than a 'muster' . . . whatever that is.
In other words, it's not the subject by itself that 'must' anything, it's really
the sentence as a whole.
This is easier to see with a bit of re-wording, as in "It must be that Walter's forgotten some of his past."
Now, if modals really do combine with fully-formed sentences, we might think that we can take
a cue from other sorts of words we've already seen do the same thing.
Logical words like "and" and "or" and "not" usually connect up to complete
thoughts, and affect their truth values, so maybe modals do too.
After all, a word like "not" can really just be seen as something that combines with
a sentence and flips over its truth-value, so that if "Nina has a cybernetic arm"
is true, "Nina doesn't have a cybernetic arm" ends up false.
Pretty straightforward.
But it turns out that modals don't easily fit into this kind of pattern.
Let's say that, right now, Olivia isn't doing anything; obviously, then, "Olivia's
starting a fire" would be false.
But "Olivia can start a fire" is certainly true.
So here the addition of "can" ends up making a false statement true.
But take "Olivia is flying around under her own power," which is also false.
Adding "can" here doesn't make a bit of difference: "Olivia can fly under
her own power" is just as wrong.
Because of this, we say that modal words like "can" are non-truth-functional, which
means they don't seem to have as predictable an effect on the truth of a sentence as other,
more logical kinds of words.
So, if the truth of a sentence doesn't have any influence on its modal-ized counterpart,
what does?
And are tools like logic even useful here?
As it turns out, thinking about modality goes back all the way to Aristotle.
But it wasn't until around the 1950s that logicians and linguists finally began to get
a firm grip on how these words work.
If you remember back to our episodes on logic, we explained how we can use symbols to represent
sentences and the relationships that hold between them, to more easily explore how and
why we can make certain inferences.
So, something like "Dr. Bishop doesn't know Astrid's name" could be written out like so.
In this case, "A" stands for "Dr. Bishop knows Astrid's name," while that
little squiggle at the front stands in for our truth-inverting "not."
Well, in the early twentieth century, ways of symbolizing modality finally made their
way into the language of logic.
And not long after after, philosophers like Saul Kripke came along and spelled out exactly what it meant.
So, to represent something like "It's possible that Dr. Bishop knows Astrid's
name," we use the diamond operator.
And if we want to make a stronger statement, like "It's necessarily true that
Dr. Bishop knows Astrid's name," we can tilt it 45 degrees and use the box operator instead.
As for how these symbols actually work, the basic idea is twofold.
First, we need to think of sentences not just as being true or false, but as being true
or false in a particular world.
In other words, whether a sentence is true or false really depends on the way the world
is — the circumstances in which the sentence is being evaluated.
So a sentence like "Broyles is angry" isn't just true, it's true under some
set of circumstances — in any possible world, really, where there's someone named Broyles
and he's angry!
The second ingredient, then, is to think of that diamond and that box as quantifiers,
which are expressions about amounts of things.
So, "It's necessarily true that Broyles is angry" is really saying something like
"in all the different ways the world could be, no matter which one we look at,
Broyles is angry."
Or put another way, in all the possible worlds w, Broyles is angry in w.
For something like "It's possible that Broyles is angry," what the symbols are
really saying is that in all the different ways the world could be, at least one of those
worlds has an angry Broyles in it.
So, there exists some possible world where he's angry.
Coming back around to natural language, we can see that these ideas actually get us pretty far.
For instance, most people have the intuition that a sentence like "You must report to
the Colonel", which spells out a requirement, also means that "You may report to the Colonel",
that you have permission.
If words like "must" and "may" are just like our boxes and diamonds from before,
this inference makes perfect sense: if in all possible circumstances you report to the
Colonel, then there's at least one where you do!
Otherwise, it's a contradiction!
So words like "can" and "might" work by first combining with some sentence p, which
is like a description of a world, and then acting just like that diamond that we saw in logic
and saying that there's at least one world that fits that description.
On the flip side, "must" and "need" do the same, but they act like that box operator
instead, and apply that description to all possible worlds.
So, is this all there is to these words?
Do they work just like "all" and "some," but with whole worlds in place of individual people and things?
Unfortunately, this can't quite be the full story.
Take the following two sentences.
"Dr. Bell must complete his experiments" seems to be saying something about his goals,
whereas "Dr. Bell must want to change the world" seems to be saying something about
our own state of knowledge.
In general, words like "must" and "might" can take on different flavours of modality.
For example, teleological modality has to do with people's plans and goals, while
epistemic modality has to do with knowledge, and deontic modality has to do with rules
and regulations.
In principle, there's an infinite variety of different flavours, and that actually poses
a pretty serious problem, since it would mean we have an infinite number of different musts
and mights stored inside our heads.
But this can't be true!
So how do we explain it?
Starting in the 1970s is when we really began to crack open this problem.
In particular, linguist Angelika Kratzer noticed that you could think of the sentences that
we just pointed out in more explicit terms.
That is, "Dr. Bell must complete his experiments" really means "Given his goals, Dr. Bell
must complete his experiments."
In a similar way, "Dr. Bell must want to change the world" is actually saying "Given
everything we know, Dr. Bell must want to change the world."
Phrases like "given his goals" or "given what we know," then, restrict the set of
worlds we should look at when trying to understand these sentences.
In both cases, "must" is still saying something about all the worlds under discussion;
but now, exactly which worlds those are gets defined by the context of the conversation.
So, a more complete meaning for a word like "must" would look like this two-place
function -- one that relates some collection of worlds to another.
When it's used in an actual sentence, like "Dr. Bell must complete his experiments,"
its job is to first combine with a set of worlds that have been defined by the context
of the conversation.
This set is often called the modal base, and it can be anything from the set of all the
worlds where certain rules are followed — like the rules of law — to the set of worlds
where all your dreams come true!
In this case, it combines with the set of all those worlds where Dr. Bell's goals are achieved.
Next, it combines with the the set of worlds described by the sentence -- where Dr. Bell
completes his experiments -- and says the whole thing's 'true' just as long as
in all those worlds where his goals are met, Dr. Bell completes his work.
That is, just as long as the first set fits inside the second.
In other cases, where the base is the set of worlds representing our own knowledge,
everything works the same — just with different sets.
And with a word like "may," as in "Dr. Bell may want to change the world," instead
of fitting one set inside another, we work out their intersection, meaning that there's
at least one world that fits in both.
What's really remarkable is that when we look at modal words in this way, their meanings
line up exactly with the meanings we've already given to words like "some" and "all".
This suggests that this kind of comparison between sets might be fundamental to how we
think -- something that runs deep throughout languages.
So what might've at first seemed to be square outside the limits of logic, actually fits
nicely into our theory of how language works, giving us a glimpse into how we think about
the world around us.
So, we've reached the end of The Ling Space for this week.
If you picked out your favourite modal flavour, you learned that at first glance, modal verbs
like "must" and "might" don't easily fit into our understanding of language; that
the idea of possible worlds helps to bring these kinds of words into the fold; and that
we find deep connections between different parts of language that otherwise seem totally
unrelated to each other.
The Ling Space is made by all these amazing people over here.
If you want to learn more about the syntax of modals, check back on our website!
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See you next time!
Dha weles skon!
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