Words that Ever Play Well

Here’s a wholly unremarkable English sentence:

A week ago, I would have had nothing to say about this sentence. It does have the idiom “to lift a finger”. Most English speakers would define that as “to take action”. If those have the same semantics, we should be able to swap them out:

Yup, seems to work! Now, we all know someone who’s just not going to sit around when there’s villain-stopping to be done!

That last sentence is objectively wrong (though subjectively entertaining). But what makes that sentence wrong? What was missing in our definition of the idiom that didn’t carry over? You might be hoping for a simple answer; you might be saying “ok Tyler, that expression only works in some fixed phrases”. Unfortunately, we just hit the tip of an iceberg — this is one of those cases where the more you look into something, the more complex and interesting it gets.

So, take my hand, and let’s jump down the rabbit hole that is Negative Polarity Items!

Strange Lexical Items

Let’s start by zooming out: “lift a finger” isn’t going to be the only lexical item¹ we’re worried about. In fact, let’s look at a set of way more common items:

Hopefully this convinces you that these words form a special class. First identified by Klima (1964), he noted they only seem to be licenced by some kind of negative context (go ahead and look — only the “negative” sentences seem to work!). This is where the name Negative Polarity Item comes from. And like many great names, NPI is completely misleading, and totally misses the mark.

How “Negative Context” Falls Short

Finding counter-examples in linguistics just happens to be a hobby of mine. Let’s break this “Negative Context” hypothesis:

Welp, there goes negativity! The last sentence seems pretty reasonable — and decidedly non-negative. The question, then, is still open: under what context would an NPI be accepted?

Dissecting those sentences might point us in a direction…

The only difference between these sentences are the quantifiers². The next step might be to test an NPI with a set of quantifiers.

“Ever” and Some Quantifiers

“Ever” could show up in both the Noun Phrase and the Verb Phrase of a sentence. We can test how both work with this example:

Now we just try out some quantifiers, and see which sentences work. The following table shows a few results.

Ok, great!… Now what? Is this getting us any closer to a unifying concept of when these words are licenced?

Downward Entailment

Ladusaw (1980) gave us a pretty reasonable answer, based on something called downward entailment. This is a concept which merits its own post, so I’ll try and be brief. Here are two simple entailments:

1. You are a father. \(\vDash\) You are a man.
   
2. No man can swim. \(\vDash\) No father can swim.

The set of fathers \(F\) is a subset of the set of men \(M\) (we typical write this as \(F \subseteq M\)). The thing to note here is the direction of entailment. In (1), we go from subset up to superset. In (2), we go from superset down to subset. This is the most basic example of upward and downward entailment.

Entailment and Quantifiers

The sentences we’ve been talking about have been of the form “[Quantifier] + NP + VP”, where NPs and VPs form sets.

“Every person I’ve ever met likes dogs”

NP: The set of people I’ve met.

VP: The set of things that like dogs.

Sentences gives us information about what entailments we can make from them. If I thought “All apples are red”, then anything I know about all red things would be true for apples too. I would also, likely, have a very emotional experience in the presence of a granny smith.

Every quantifier provides an entailing environment for NPs and VPs that could either be up or down (to a superset or subset)³. We can test these very simply with a NP and a VP.

Testing the quantifier “every”, we get

3. “Every fruit is red” \(\vDash\) “Every apple is red”
   
4. “Everyone sings well” \(\vDash\) “Everyone sings”

In (3), we go from superset to subset. That’s downward entailment! In (4), however, we go from subset to superset — upward entailment! Try going through our list of quantifiers, and seeing which entailment environments each has. Here’s a table of the results:

We’ve got a winner! … … … right?

Have We Found our Solution?

I was introduced to NPIs by Kate Kearns’s book “Semantics” -Kearns (2011) in a chapter on Generalized Quantifiers, so this was my first look at NPIs and downward entailment. But it turns out that

1. There are actually other contexts that licence NPIs
2. Downward entailment still catches those

Well that was an emotional roller coaster. I’m not sure I want to give you a list of these but… I’m going to go ahead and give you a list.

For more examples, see page 458 in Ladusaw (1980). In all of these cases, you can see a natural direction of entailment.

Try making tests for the other sentences in the table, and convince yourself that only those with downward entailment are acceptable.

Summary

The original question was when can words like ever, any, or yet be used? These words and others form a class known as Negative Polarity Items. In the end, the idea of downward entailment seemed to capture which contexts allow NPIs.

Why would we need words like this in communication? They don’t seem to add any information — just add emphasis. This is just my conjecture, but it could be related to the un-intuitive nature of downward entailment. The more “normal” direction is upward. The use of an NPI in a sentence may, in fact, signal that the entailment direction in the sentence was unusual.

Originally there was thinking that ever was bringing attention to the negative polarity of the sentence (possibly making up for English’s lack of negative concord). Now we might think it’s bringing attention to entailment directions.

Finished?

I’ve labeled this post as Part I, because, horror of horrors, we actually haven’t come up with an answer! Remember this sentence?

This sentence doesn’t exactly jive with our idea of downward entailment. Actually… it doesn’t jive with our idea of upward entailment either.

This is called a non-monoton quantifier. In Part II, we’ll expand our licencing context for NPIs even further, to include these (and some other situations as well). And (hopefully) we will have enough time to get into Positive Polarity Items and some cross-linguistic examples! No promises, though!

Read on to Part II once you’ve finished!

References