Quick summary:

Some sentences have multiple meanings, but how does that work? Where do those meanings come from? Sometimes, it's the interplay of the different logical bits in a sentence. These powerful little operators, known as quantifiers, are lurking in some of the smallest words in our sentences, like "all" and "a." Put two of these quantifiers in one sentence, and they'll fight it out to see which one is more powerful, and gets scope over the other one.

So if we look at a sentence like "All Quentin's friends went to a fantasy land," we can find two interpretations. The first is where all of Quentin's friends went to some fantasy land or another, but not necessarily the same one; this is where all gets scope over a, and since this matches the ordering in the sentence itself, it's known as surface scope. On the other hand, there's the other interpretation, where all of his friends had to go to the exact same fantasy land, say, Fillory, for it to be true. That meaning comes from a getting scope over all, and because that's the reverse of the sentence order, it's known as inverse scope.

What keeps us from getting confused here all the time? We follow the rules of conversation, and those tell us to pick the interpretation that's true the greatest amount of the time. Since the reading where all of the friends go to some fantasy place or another is true if they happen to go to the same one, we latch onto that interpretation, until something else about the situation forces us towards the other meaning.


Extra materials:

As you'd probably expect, there are more of these logical operators than just every and a to keep track of. Another important one is negation, like not. Let's take a look at an example:

  1. Every Brakebills student didn't turn into a goose.

So like the sentence we talked about in the video, this one also has two different interpretations, which we can paraphrase in (2).

     2. (a) No Brakebills student turned into a goose.

         (b) Not every Brakebills student turned into a goose.

If we compare these readings, (2a) requires that every single one of the students has to not transform into a bird for the sentence to be true. In this case, every has power over not, and so this is the surface scope interpretation. On the other hand, for the sentence in (2b), some of the students could have morphed into geese, and it would be true. As long as not all of them undergo the change, then it's okay. Here, not is on top of every, making this the inverse scope case.

How easy is it to get both of these interpretations? Are they always available? Generally, if someone says a sentence like (1), and some student to avian transformations have occurred, we'll go in for the inverse scope reading in (2b). That's because according to the rules of conversation, we'll want to be charitable to speakers, and assume that they're telling the truth when they talk. So if only one reading makes the sentence true, we'll take that reading - if surface scope, like (2a), is false, but the inverse scope reading is true, then we take the inverse.

But do we always have access to both readings, or is this something we have to grow into? Julien Musolino, with a number of different collaborators, argued in a series of papers from the late 1990s that children start off with only the surface scope reading available, acquiring the inverse scope reading only as they got older. Because the children were stuck with the sentence being interpreted with surface scope, this hypothesis was known as isomorphism, since it had to be the same shape. A paper by Musolino, Stephen Crain and Rosalind Thornton from 2000 summarized this early work on the topic.

In the part of the study concerning sentences like (1), they presented short stories to 20 English-speaking children, averaging just under 6 years old, as well as a group of English-speaking adults. Then the experimenters asked the participants to judge whether the sentence accurately described what happened. (For the kids, they'd have a puppet give the sentence, because puppets are more worth paying attention to than adults.)

Adapting the story into our example here, in one, three students (say, Quentin, Alice, and Penny) all could be turned into geese, but only Quentin and Alice are; Penny decides not to get changed into a bird at all. Then the puppet is asked to describe what happened. The puppet would say "Every student didn't turn into a goose," and the child would be asked to say whether that was the truth.

Adults accepted this description 100% of the time in the study, but the children only accepted this description 7.5% of the time. And then when they were asked about why the puppet was wrong, they would point to the two people who had turned into geese, and complain that they'd transformed, so it couldn't be right. They were stuck with the surface scope.

Musolino found similar results with sentences like (3).

     3. The children didn't find some rams.

Let's say there's a situation where the children are searching for two rams, but they find only find one of them, after looking for a long time. Then, the puppet would describe what happened, as in (3). Here, if isomorphism is correct, the surface scope reading would require no rams be found, so this wouldn't be acceptable to the kids. A younger group of children (average age 4 years and 7 months) accepted this only 35% of the time; an older group (average age 5 years and 7 months) accepted it 65% of the time, and adults were fine with it 100% of the time. So isomorphism looks pretty good!

But not everyone was sold on this idea. Andrea Gualmini argued that the problem here was that the requirements for using negation nicely weren't being met. When do you want to use negation? Usually, you don't just use it out of the blue. You want to use it when they the outcome and the listener's expectations are not the same thing. If you're not motivating that use of negation in the situation - if you're not making negation appropriate - then you're not going to get children to accept it. Maybe adults have the cognitive capacity to work through to a workable interpretation despite not having negation be appropriate, but children can't get that far.

Gualmini adapted the situations so that using negation made more sense. In his situation, a firefighter is supposed to find four dwarves, who he is playing hide and seek with. He has a hard time finding any of them! But when he looks more, he finds one dwarf. The firefighter tries to quit, but the dwarf tells him to keep looking. Then he finds a second dwarf! And though he tries to stop again, he gets pushed to look more again... only to finally give up.

Now, the children get presented with two descriptions of the situation by the puppet:

     4. The firefighter didn't find some dwarves.

     5. The firefighter didn't miss some dwarves.

These sentences are equally true, and they both require inverse scope readings. Since the firefighter both found two guys and missed two dwarves, the surface scope readings, which would require all the dwarves to be missed or found, aren't good fits.

But here's the difference: the expectation was that the firefighter should have found all the dwarves. That's the point of hide and seek! So having the negation works better in that case, where the firefighter failed at his job. That makes (4) a pretty easy sentence to take. On the other hand, (5) is weird, because he shouldn't have missed any of the dwarves. He should have found all of them, and missed none of them. So that's strange.

Under isomorphism, that shouldn't make a difference - both (4) and (5) require inverse scope to be accepted, and inverse scope is bad. But Gualmini found that kids accepted (4) 90% of the time, but (5) only 50% of the time. And the adult control group showed a similar pattern: the sentence in (4) was judged good 77% of the time, but (5) was thought to be an okay description only 48% of the time.

So Gualmini argued that isomorphism wasn't really what was going on underneath here. Instead, it was presenting the materials in a way that didn't come across cleanly to children, and so they acted according to what matched their knowledge of how interpretation should work, and rejected the sentences far more often.

While the debate continues about how best to capture child interpretation, one thing isn't ambiguous: when we deal with experiments about meaning, we need to be really careful about our design. Little changes go a long way!



So how about it? What do you all think? Let us know below, and we’ll be happy to talk with you about semantics, quantifiers, ambiguity, and how we get past it. There’s a lot of interesting stuff to say, and we want to hear what interests you!

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