So let’s talk about events. Everything that happens has its own time and place, along
with the potential to shape the path we take through life. Though most events pass right
by without us ever giving them a second thought, a single one might define our past, determine
our future, or even change the whole course of history. So how do we actually talk about
them, and how does the way our language is put together let us understand how we sense
and structure the world around us? I’m Moti Lieberman, and this is The Ling Space.
Since our earliest episodes on the study of meaning, we’ve argued for the idea that
the invented, symbolic languages of logic and math are good ways to think about the
natural languages that humans use every day. We’ve used symbols to represent the meanings of
connecting terms like “and” and “or,” to track the order that words combine in,
to separate the actual from the merely possible, and to visualize how meanings can narrow down
to nothing or expand without limit.
At the very foundation of it all, we made the basic assumption that verbs like “lie”
or “witness” act a lot like predicates, the terms that drive the sentence. In the
language of logic, predicates just show up as another kind of symbol — usually upper-case
letters like “L” or “W.” What makes them special is that they combine with other
letters — typically lower-case — to form complete logical statements.
So, a sentence like “Olivia lied” could be written out in logic as “Lo,” with
that “o” standing in for “Olivia”; meanwhile, “Jennifer witnessed her own demise”
would be “Wjd,” with that “j” and “d” pointing out Jennifer and her demise,
respectively. Logic is handy here, because verbs and predicates seem to have a lot in
common, at least on the surface. They’re both a bit fragmentary by themselves, but
lead to completed expressions when we pair them off with the right kinds of things. We
can even use logic to capture the fact that verbs need to combine with specific numbers
of words to feel whole, by tacking placeholder symbols onto our predicates like “x” and
“y”; “Lx” signals that the predicate is looking to combine with one item, like
how “lie” needs a subject, while “Wxy” needs to combine with two, just like how the
verb “witness” needs both a subject and an object.
It seems safe to suppose, then, that verbs and predicates are basically the same kind
of thing, just in two different languages — one natural, one artificial. And we can
safely use our understanding of one to help get a better grip on the other.
But semantics, which is the study of meaning, isn’t just about how individual words and
their definitions fit together; it’s about whole sentences, too, and how they relate
to each other. And when we take this into account, we start to see cracks forming in
our otherwise neat and tidy logical model.
Think of the sentence “Katarina grieved for many years.” In ordinary English, it’s
easy to see that there’s a relationship between this and the much shorter “Katarina grieved.”
It’s clear that both uses of “grieve” involve one and the same verb. But as simple
and intuitive as this seems, it’s an idea that isn’t so easy to render in the language
of logic.
In the first case, we’ve got the verb combining with a subject and a prepositional phrase;
in the second, we’ve just got a subject. We could symbolize all this using two different
predicate symbols, say “Gx” and “Gxy,” where one combines with only one element to
produce a full statement, while the other combines with two. So, “Katarina grieved
for many years" would be “Gkm,” while “Katarina grieved” would simply be “Gk.”
But biting this logical bullet and supposing there are actually two marginally different
kinds of “grieving” — one that works with a prepositional phrase and one that doesn’t —
seems to miss the point. And it blurs the line between what’s essential for a
complete sentence, like a subject, and what’s only optional.
A deeper problem is that we completely fail to capture that intuitive connection we talked
about. There’s no rule in logic that recognizes that similar predicates otherwise built to
combine in slightly different ways are essentially the same. There’s no notion of similarity
in logic; things are either exactly identical, or they aren’t, with no in-between.
In general, then, if we want to use logic as a tool to model and understand language,
we need a way of representing the meanings of things like prepositional phrases and adverbs
and other modifiers, which sometimes show up and sometimes don’t.
In trying to get a handle on the problem, back in the 1960s, philosopher Donald Davidson
proposed a fundamental change to the makeup of logic. Davidson suggested that, in order
to get a grip on how verbs really work, we need to add in an extra ingredient. Instead
of thinking of predicates as simply relating an individual to an action, he supposed that
predicates should really be thought of as describing whole events — which might include
actions, but could also offer up details about who participated, when it happened, where
it took place, and how it all went down.
In symbolic terms, this means that each of the predicates we’ve been working with up
to now don’t apply directly to individuals, but instead characterize events. A predicate
like Gx would instead be recast as “Ge,” with that “e” acting as a placeholder
for any event the predicate might describe.
Under this view, making a statement in logic amounts to saying there exists some event
which fits that description. So “Katarina grieved” would be written out like this,
with that backwards “E” saying that the predicate following it applies to at least
one event out there in the world, an event involving grief. And the job of describing
who did the grieving shifts over to another predicate whose focus is to introduce the agent.
By explicitly referencing events, we add a little complexity to our logical system, but
we also make important gains. Now, if we want to say that “Katarina grieved for many years,”
all we have to do is stick in an extra predicate — one that combines with the same act of
grieving from before and says it took place over many years.
This lets us preserve the connection between the logical representations of all these different
sentences, no matter how long or short, since each one of them involves the same core predicate
symbol “G.” Any other information, like about where or when the event took place,
can be tossed in as needed, without making any changes to the main predicate at the centre
of it all. The work of one predicate now gets spread out over many.
So talking directly about events in this way is convenient, because it lets us represent
in logic the same kinds of relationships we see in natural language. But does this mean
this is how language actually works? After all, logic is a tool, and it could turn out
that this fix of ours is nothing more than some handy redecorating that doesn’t really
say anything deep about our psychology. So while it makes a certain amount of sense that
meanings of verbs should reference events, is there any independent evidence to suppose
this gets us closer to understanding what we know when we know a language?
Well, consider the following sentence: “James is a scruffy, no-nonsense time-traveller.”
Notice that at least a couple of things follow from this. For one, it ends up being true
that “James is a scruffy time-traveller,” and that “James is a no-nonsense time-traveller!”
It also follows, of course, that “James is a time-traveller.”
For obvious reasons, these sentences form what’s called a diamond entailment pattern,
with every sentence entailing — that is, guaranteeing the truth of — the sentences
below it.
Filling in the rest of the diamond, when we consider the conjunction of the middle two
sentences, so “James is a scruffy time-traveller and James is a no-nonsense time-traveller,”
we see they also entail the sentence above. The reason this pattern is interesting is
because, somewhat mysteriously, it doesn’t always work. Consider the sentence “James
spoke to Ramse in the forest at night.” It’s again true that “James spoke to Ramse
in the forest” and that “James spoke to Ramse at night.” And of course it follows
that “James spoke to Ramse.” But what’s interesting is that when we join up the middle
sentences, so “James spoke to Ramse in the forest and James spoke to Ramse at night,”
they no longer guarantee the truth of the sentence at the top. In other words, they
could both be true on their own, without those conversations having happened in the same
place and at the same time.
In fact, it’s perfectly reasonable to guess that James has probably spoken to his good
friend Ramse more than once, and that one of those conversations might’ve been in
the forest, but during the day, with another happening somewhere else at night. We can’t
conclude that both sentences necessarily describe the very same event. And so our diamond can’t
be polished off. But why should this be?
To better understand what’s going on here, let’s go ahead and adjust our first example.
Instead, let’s say “Someone is a scruffy, no-nonsense time-traveller.” Now we get
the same effect as our second example; everything below still follows from the top, but the
compound sentence “Someone’s a scruffy time-traveller and someone’s a no-nonsense
time-traveller” doesn’t entail what’s above it, since each half could be talking
about someone different, meaning no one person fits both descriptions. “Someone” puts
a crack in our diamond. And this makes sense, since none of these sentences are talking
about anyone in particular, they’re just making the general claim that some person
or other fits the bill.
If our event-driven logic from before is the right way to think about how sentences with
verbs like “speak” or “grieve” work, we can easily account for this. If every sentence
is, at its base, a claim about the existence of some event, in the same way that any sentence
with “someone” in it is a claim about some unnamed person, the parallels between
them make sense, as do the differences with more particular statements that describe specific
individuals, like our first example, where the diamond pattern holds.
Taking this event logic to heart, it gets a lot easier to explain how the meanings of
expressions like “at the facility” or “in the past” come about, and how they
combine with verb phrases. Much like how adjectives restrict the individual or individuals described
by a noun phrase, prepositional phrases like these narrow down the events described by
the verb, in both time and space. And manner adverbs, like “quickly” or “quietly,”
end up working much the same way.
Finally, talking about events gives us inroads into understanding the class of verbs that
deal with direct perception, like “see” or “hear,” as in “Cassandra saw James
disappear.” In these sentences, it looks like the object of the verb is an entire other
event. But with our new semantic technology, explaining these kinds of sentences, along with the semantics
of adverbs and prepositional phrases and the like, is a cinch!
So, we’ve reached the end of The Ling Space for this week. If you made it to the event
on time, you learned that while traditional logic gets a lot right about how the meaning
of a verb fits into different sentences, it can miss how those sentences relate to each
other; that making direct reference to events gives us the fix we need, explaining how details
about time and place can put limits on the meaning of a verb phrase; and that diamond
entailment patterns provide evidence that the logic of events forms an important part
of our mental grammar.
The Ling Space is made by all these amazing people over here. If you want to learn more
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you next time! Ke tla go bona!