Disjunction and ignorance

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In the last two modules we developed the idea of the "Competence Assumption", i.e., the assumption that a speaker uttering some utterance has an opinion about whether or not its alternatives are true.

How often do we make this assumption? Some pragmaticists have argued that it applies "by default", i.e., we assume that a speaker is "competent" (has an opinion about whether or not a more informative alternative utterance is true) unless we have specific evidence otherwise. (See, e.g., Goodman & Stuhlmüller, 2013, for an experiment showing how this happens when a is shown to not be "competent".) There are several kinds of situations where the Competence Assumption does not seem to apply.

One such situation is disjunction, i.e., utterances with the word "or". Let's look at an example. Imagine you walk into the room and find me watching TV. I'm in the middle of watching a game show where a person is looking at three doors. You ask me what the show is about, and I say, "There's a prize behind Door #1 or Door #2" (If you haven't figured it out already, this is just the second half of the classic Monty Hall problem, just viewed by an outside observer.) This utterance with "or" raises several implicatures. (The analysis I describe here is directly from Geurts, chapter 2.)

First there is a typical weak implicature: I do not believe there are prizes behind both doors. This implicature is derived in the typical way that we saw in the module on "Weak and strong implicatures" before: I could have said "There are prizes behind Door #1 and Door #2", but I didn't say "and", so I implied that I don't believe it. (Keep in mind that this is a weak implicature: ¬BELS("there are prizes behind Door #1 and Door #2").)

What about a strong implicature? Recall that a strong implicature applies if we apply the Comptence Assumption to a weak implicature. But it's actually not clear that the Competence Implicature applies here. To see why, let's first look at some other implicatures that arise from this same utterance.

If I say "There's a prize behind Door #1 or Door #2", I am being somewhat vague; I could have said something more specific (i.e., I could have said a stronger alternative utterance). We just looked at one of those stronger alternatives above ("There are prizes behind Door #1 and Door #2"). Here are several other more specific things she could have said:

  1. There's a prize behind Door #1.
  2. There's a prize behind Door #2.

Once again, we can get weak implicatures for any of these. If I didn't just say "There's a prize behind Door #1", that means I don't believe there's a prize behind Door #1. (Keep in mind the difference between "I don't believe there's a prize behind Door #1" and "I believe there is not a prize behind Door #1"!!! If you don't see the difference, review the previous module.) Likewise for the others. So for alternatives (1-2), we get the following weak implicatures:

  1. 1'. ¬BELS("There's a prize behind Door #1")
  2. 2'. ¬BELS("There's a prize behind Door #2")

If we applied the Competence Assumption, we could turn these into strong implicatures:

  1. 1". BELS(¬"There's a prize behind Door #1")
  2. 2". BELS(¬"There's a prize behind Door #2")

But doing this will lead to a contradiction. To see how, let's walk through several steps of logic. (To keep things neat, I'm going to abbreviate "There's a prize behind Door #1" as "D1", and "There's a prize behind Door #2" as "D2".)

  1. BELS( D1 or D2 )
  2. ¬BELS( D1 )
  3. ¬BELS( D2 )

Everything's fine so far; the previous three steps are ones that we already justified above. The contradiction will arise after we adopt the Competence Assumption in the next step.

  1. BELS( D1 ) or BELS( ¬D1 )
  2. BELS( ¬D1 )
  3. BELS( D2 )
  4. contradiction

The important thing to notice here is that the problem arose when we adopted the Competence Assumption in step (iv); after that, the contradiction was inevitable.

For this reason, it seems like the Competence Assumption doesn't necessarily apply in utterances with disjunction. When I say "There's a prize behind Door #1 or Door #2", I imply that I don't know which door the prize is behind. This is often called an ignorance implicature (Geurts also refers to it as a "non-competence inference").

Video summary

In-class activities

Are there other situations where the Competence Assumption does not apply? (Either other general situations like disjunction, or more specific scenarios you can imagine?)

Does disjunction always lead to ignorance implicatures? Or can you find situations where it doesn't?

The way I described this door example was slightly different from the classic Monty Hall problem; recall that I described it from the point-of-view of an outsider (a person watching it on TV).

In the classic Monty Hall problem, the game show host knows which door has the prize, and the game show host tells the player "There's a prize behind Door #1 or Door #2". Clearly the Competence Assumption does apply here, because a person playing the game knows that the host knows where the prize is.

And yet, if the game show host says "There's a prize behind Door #1 or Door #2", the contradiction we saw in the module still does not arise, even though the Competence Assumption applies. Have students discuss and try to figure out why not.

(The answer is that the maxim of quality would never yield the weak implicatures (ii) and (iii) in this scenario. Remember that the maxim of quality means we expect speakers to be as informative as is appropriate for the scenario. In this scenario, it's a game show, so we know the host won't tell the answer; that would ruin the game. So we don't consider "There's a prize behind Door #1" or "There's a prize behind Door #2" to be possible alternatives; a game show host in this scenario would never say those things. Since they're not possible alternatives, those weak implicatures never arise, and therefore the later contradictions related to them also do not arise.)

Throughout this module we have been developing an argument that the competence assumption doesn't necessarily apply in "or" statements. It still can apply, though. Here we will see some examples where the competence assumption still works, by analyzing free choice implicatures, which also come from statements with "or" but which are very different than the sort of ignorance implicatures we saw above.

First, some background concepts. "Or" is often thought to trigger two kinds of implicatures: ignorance implicatures and exhaustivity implicatires. Ignorance implicatures are what we've seen in this module: "X or Y" is often interpreted as meaning that the speaker does not know X and the speaker does not know Y (i.e., at least one of them is true but the speaker doesn't know which one). This is the implicature that arises when the competence assumption doesn't hold.

The exhaustivity implicature, on the other hand, is when people interpret "X or Y" as meaning "X or Y but not both". (Logicians call this interpretation "exclusive or", or "XOR", in contrast with the logical definition of "or" which means "X and/or Y".) This implicature is a scalar implicature, just like the example we saw in previous modules with "Josh is smart" (implicating that the speaker doesn't think Josh is brilliant): it comes from thinking about a stronger term. Specifically, if someone says "X or Y", we might think "Why didn't he say 'X and Y'? He must not believe it!"

Now with those preliminaries out of the way, let's get to the issue at hand: free choice implicatures. To start, let's look at an example.

During the Russian invasion of Ukraine in 2022, people in many other countries debated whether or not their militaries should intervene. On the "pro" side, people argued that (1) it's a humanitarian crisis and the people of Ukraine need and deserve the world's help in defending their country; and (2) the world needs to send a message that wars of aggression are not tolerated, and standing aside now would constitute "appeasement" (see Geoffrey Nunberg's article on the origins and connotations of this term) that basically just rewards Vladimir Putin for imperialist behaviour and encourages him and others to keep doing it. On the "con" side, one argument (among others) was that starting a world war with Russia would lead to a much greater humanitarian disaster than the one that's already happening; and in the most extreme case it could even lead to nuclear war, i.e., the end of humanity.

Noam Chomsky lays out those options explicitly in an interview: "Like it or not, the choices are now reduced to an ugly outcome that rewards rather than punishes Putin for the act of aggression – or the strong possibility of terminal war."

The bit in italics is an utterance with "or", and it triggers a free choice implicature, which we'll see below.

Here, Chomsky is not expressing that he doesn't know which option is available. What he really means is that he knows (or at least believes) both options are available, but we can only choose one and not both. In other words, this utterance still has an exclusivity implicature (we can have appeasement or war, but not both), but it does not have an ignorance implicature (it doesn't mean he doesn't know which we can have).

This is a classic free choice implicature. When we combine disjunction (or) with a modal verb like "can", we often get this sort of interpretation. For example, "You can have cake or you can have ice cream" is often understood to mean that both are available, but once you choose one you can't get the other. To appreciate how this is different from the literal meaning of or, let's look at a truth table of what that utterance would literally (semantically) mean:

you can have cake you can have ice cream You can have cake or you can have ice cream

In other words, if it's true that you can have cake and it's also true that you can have ice cream, then the utterance "You can have cake or you can have ice cream" is true. But, semantically, this utterance is still true even if you can't have ice cream. For example, if there is no ice cream (maybe the ice cream is all gone) but there is cake and you can have the cake, then "You can have cake or you can have ice cream" is still literally true, because at least one of its parts (you can have cake) is true. This is not how we usually interpret it in reality; in reality we usually interpret it as meaning that (1) you can have cake, (2) you can have ice cream, but (3) you can't have both. Thus, the way we interpret these sentences is not the literal, semantic interpretation, but is instead based on a free choice implicature. (See Geurts, chapter 6, for a more detailed discussion of free choice implicatures and how they work.)

Remember that, as we discussed above, the competence assumption doesn't apply for ignorance implicatures related to "or". But it does apply for free-choice implicatures. If we think someone is making a free-choice implicature, we believe they have an opinion about each option. If someone tells me "You can have cake or you can have ice cream", and if I interpret that as meaning that both are available and I can choose either one of them (a free choice implicature), then I believe the speaker knows cake is available and knows ice cream is available; I don't think he would have said "You can have cake or you can have ice cream" if he actually isn't sure whether or not there is any cake. Likewise, if Chomsky says "we can have an ugly outcome that appeases Putin or we can have a civilization-ending war", we don't think that he means he doesn't know which of these is possible; we think he knows (or at least believes) that both are possible (he wouldn't have said that if he had no opinion about whether or not a world-ending nuclear war is possible).

Discuss and compare free choice implicatures, exhaustivity implicatures, and ignorance implicatures. Can students figure out an explanation for how and why free choice implicatures arise, based on the cooperative principle and/or the competence assumption? Can students think of examples where the same disjunctive sentence might get different interpretations (different implicatures) in different contexts?

⟵ Negative strengthening
Clausal implicatures ⟶

by Stephen Politzer-Ahles. Last modified on 2022-03-11. CC-BY-4.0.