#predicates

Back in our episode about event semantics, we argued that we’ve actually been thinking about verbs all wrong in terms of how we treated them semantically. Up until now, we’ve treated verbs as though they were kind of like naturally occurring versions of the predicate symbols you find in the artificial language of logic. So we could model the meaning of a verb like “travel” by taking advantage of this correspondence.

    (1)    “travel”    ≈    Txy

Those variable symbols “x” and “y” following the predicate capture the fact that a verb like “travel” tends to combine with both travelers and destinations, in order to produce complete sentences. Borrowing letters nearer to the beginning of the alphabet to stand in for specific people and places, replicating those completed sentences in logic is fairly straightforward.

    (2)    “Athan traveled to London”        ≈    Tal

After giving it some thought, though, we decided that a better way to think of the meaning of a verb like “travel,” along with other verbs, is not to treat it as a description of an individual, or even a relation between individuals and locations, but a property of events. Using this new logic, the meaning of “travel” would look more like “Te,” signifying that the act of traveling really refers to a set of coordinates in space and time — that is, an event. The verb “travel,” then, picks out any and all instances of traveling, in a way similar to how the noun “scientist” picks out, well, anyone who’s a scientist!

    (3)    “travel”    ≈    Te

In our updated system, the meaning of “Athan traveled to London” now looks like a different kind of logical statement — one that’s existentially quantified. That means it’s a statement saying there’s at least one event out there in the world that fits the bracketed description following the backwards “E.”

    (4)    “Athan traveled to London”        ≈    ∃e(Te ∧ Aea ∧ Del)

In particular, it says there exists an instance of traveling, and that the person doing the traveling — the agent — is Athan, and that the destination is London. As you can see, the job of introducing other information, either about who did it, or how it happened, falls to other constituents. (We left it open exactly how the events described by verbs become existentially quantified, but a good first guess is that it’s tense that does the job, alongside locating the event in time.)

In making this move, we’ve ended up changing the typical verb’s argument structure, which is something we’ve touched on before. It means that we’ve fiddled with the number and kinds of things that any given verb is built to combine with. A verb like “hallucinate,” on a conceptual level, doesn’t combine directly with its subject anymore; instead, it’s meant to combine with an event, with the subject coming in obliquely. In the language of the lambda calculus, which is especially useful for keeping track of what combines with what, the meaning of “hallucinate” shifts over from (5a) to (5b) —  from a function that accepts individuals as its input, to one that accepts events.

    (5a)    λ x . x hallucinated

    (5b)    λ e . e is an event involving hallucination

But it seems fair to ask whether this applies across the board: are all verbs created equal? Well, consider the following two sentences.

    (6a)    There’s a man drinking whiskey

    (6b)    *There’s a man liking whiskey

While the first sounds perfectly natural, the second seems off. And intuitively, the most noticeable difference we might point to between these verbs is that the first describes something done over a shorter period, while the second applies to an individual over a longer stretch, maybe even a lifetime. A bit more technically, linguists have attributed the split behaviours of these words to the fact that “drink” is a stage-level predicate, while “like” is an individual-level predicate.

Digging even deeper, it’s been recognized that more punctuated events (e.g., arriving, noticing, exploding) form only a small part of a much larger category of eventualities, which isn’t just some undifferentiated mass, but also includes things like lengthier processes (e.g., speaking, walking, sleeping) and even longer-term states (e.g., knowing, owning, loving).

The underlying difference, then, between stage-level verbs like “drink” and individual-level verbs like “like” might simply be that they apply to different kinds of eventualities (i.e., processes vs. states). It’s even been suggested that individual-level words dispense with event-based logic entirely, and work more like the predicates found in classical logic. This would actually go a long way in explaining why expressions of time and space, which we supposed place restrictions on events, don’t go well with every verb.

    (7a)    Katarina often speaks German

    (7b)    *Katarina often knows German

    (8a)    Ted is being held captive in the facility

    (8b)    *Ted resembles his father in the facility

It could also explain why perception verbs like “see” and “hear” and “smell,” which seem to be looking to combine with something fairly ‘eventive’ in nature, get along with some verbs much better than others.

    (9a)    Cassandra saw James talk to himself

    (9b)    *Cassandra saw James love her