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In this episode, we looked at how some sentences carry presuppositions, and asked how these kinds of assumptions come about. We worked out that they grow out of an interaction between the meanings of certain words, and a rule on how new information impacts the relationship that exists between speakers in any given conversation.

We also mentioned that once a presupposition gets its claws into a sentence, it tends not to let go. If we try to shake it loose by flipping the sentence upside down — adding in a “not” — we find that it manages to hang on. Consider the following two sentences.

     (1a)    Nina regrets that she searched for her father

     (1b)    Nina doesn’t regret that she searched for her father

The word “regret” is a presupposition trigger; whenever it appears in a sentence, the clause that follows must be true — at least, if the sentence has any hope of making sense. So, (1a) presupposes that Nina searched for her father, since it would be a very strange thing to say if she hadn’t. Interestingly, even with that “not” in there, in (1b), the assumption sticks around.

So, how does this work? First, let’s take a look at how a presupposition makes its way into a sentence in the first place. If certain words, like “know” and “regret,” are responsible for introducing presuppositions into sentences, their meanings must somehow encode this. Setting aside the finer details, and focusing in on how it combines with other words, the semantic value of “regret” would look like this:

     (2)    “regret” = λp. λx. λw: p is true (in w). x regrets p (in w)

Left-to-right, “regret” is a word which first combines with some idea — say, that she (Nina) went looking for her father. Below, the sentence on the right plugs into the p-shaped parts of the meaning of the verb on the left, giving you the (abbreviated) result up top.

And then that result connects up to some person x — in this case, Nina — such that she holds the regret in question.

All the while presupposing that the original idea is actually true. We can see that, from the very start, the notion that Nina really did search for her father shapes the assumption that gets carried by the sentence as a whole. The words following the colon keep track of all this, by describing the function’s domain — those worlds where the function actually applies.

Once everything’s put together, then, we’ve got a sentence with a restriction tacked onto it. And that’s the presupposition, in its raw form. So, to explain how that restriction survives the sentence combining with a word like “not,” we’ve got to take a closer look at how exactly that little logical word makes its living, and how it typically interacts with the words around it.

In the simplest case, we might think of “not” as being designed to combine with a sentence and reverse its truth value. So, if we take a sentence like “Buck gets along with everyone” and assume it’s true, “not” turns it around 180° and makes in false (i.e., “Buck doesn’t get along with everyone”). It’s semantic value, then, would have to look something like this (ignoring, for the sake of simplicity, that “not” isn’t usually found at the beginnings of fully-formed sentences, but somewhere in the middle):

     (3)    “not” = λp. λw. p is false (in w)

So, the combination of “not” and “Buck gets along with everyone” would work like so; it takes a sentence as its input, and spits out the mirror image.

When we try to combine this same version of “not” with a sentence packing a presupposition, though, the issue we’re facing becomes clear; the presupposition that was part of the original sentence effectively disappears, forming no part of the new one. This can’t be right, because it’s no longer taken for granted that the regret is true.

Looking at the problem this way, the answer to how we should account for the fact that presuppositions hang around even after a sentence combines with a word like “not” seems more obvious: we need a way of passing the presupposition up the structure, by opening a kind of “hole” inside the meaning of “not” — one just big enough to let it through. So we tweak our definition from (3) a bit, giving “not” its own kind of restriction:

     (4)    “not” = λp. λw: w is in the domain of p. p is false (in w)

This added ‘loophole’ gives us the result we’ve been looking for. By specifying that the original sentence’s domain should become part of the domain of the newly negated sentence, we keep the presupposition intact.

So, it turns out, presuppositions are able to survive a word like “not” by way of its peculiar semantics. It lets this kind of assumption pass through unfiltered because of the way it’s built. And other words with similar logical jobs, so quantifying words like “somebody” and “everyone,” behave in a similar way, preserving the presuppositions of whatever they happen to combine with.

     (5a)    Somebody regrets that they searched for their father

     (5b)    Everyone regrets that they searched for their father

As is par for the course in semantics, by formalizing the question in a precise enough way, this presumptuous puzzle practically solves itself!




So how about it? What do you all think? Let us know below, and we’ll be happy to talk with you about presuppositions and the conversational worlds we build together. There’s a lot of interesting stuff to say, and we want to hear what interests you!

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