Ramble, Part 55: Imply or Implicate?
Jul. 8th, 2008 04:15 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
stoutfellowIn the last Ramble, I discussed mathematical aspects of the inclusive/exclusive "or" question. Here, I'll turn to some linguistic aspects. Arnold Zwicky has done yeoman's work on this in a series of posts on LanguageLog, and much of what I'll be saying is adapted (in some cases, outright stolen) from there. If you'd rather go to the horse's mouth, this search picks up the whole series (plus one or two unrelated posts, but what can you do?)
Let me start with a stipulation. As I pointed out last time, logical operators in ordinary speech can join more than two components. Mathematicians have a penchant for reducing things to binary operations, but this doesn't work for exclusive "or"; the commonsense interpretation of (exclusive) "x or y or z" is that exactly one of the three is true, and this interpretation is not captured by the binary operator XOR. For the rest of this post, I will assume the commonsense interpretation of exclusive "or".
Now, first, there are situations in which ordinary-language "or" absolutely must be interpreted inclusively. For example, in the UK, the National Blood Service has a series of screening questions for blood donors, including:
Second, there are situations in which the inclusive/exclusive distinction makes no difference. If x and y are incompatible - logically, physically, or in any other manner - then the truth of "x or y" is the same whether "or" is inclusive or exclusive. (A linguist might say that the distinction is "neutralized" in those contexts.) To be clearer: to test whether "x or y" is inclusive or exclusive, you need to check whether it would be true in the situation where x and y are both true. If such a situation is inconceivable, then you can't make the test.
So what about other situations? That there is a tendency to interpret "or" as exclusive is made evident by the persistence of such formulations as "x or y, or both", or "x and/or y". (It's worth pointing out that the first, taken literally with an exclusive "or", is no improvement; the only way exactly one of x, y, and "both" can be true is if exactly one of x and y is true. Oddly, using the binary exclusive "or" actually does work, but that's an accident.) What's going on?
There are three principal ways in which, by stating x, I can give you information about y. One of them is ordinary implication (logical, scientific, or some less stringent version); I'm not going to discuss that. One is presupposition: it may be that x cannot be said to be either true or false unless y is true. ("Have you stopped beating your wife?" does not admit a "yes" or "no" answer unless you actually have a wife and that at some time in the past you beat her.) The third is a weaker one, known as "conversational implicature".
Implicature rests on the fact that ordinary conversation is a cooperative affair; there are certain unstated, even unconscious, rules that people are expected to follow. (Some of the peculiarities of conversation with children stem from the fact that they may not have internalized those rules. There is also non-cooperative conversation, such as interrogation or the questioning of witnesses, and these, again, have features that reflect this.) The details of those rules are much discussed among linguists of a certain stripe; here, I will only say that one rule (in overbroad terms) requires the speaker to make the strongest relevant statement that s/he knows to be true. The application is that if there is a stronger statement that the speaker could have made (but did not), it may be taken to be false.
For example: if I say that I have a sister, the fact that I do not make the stronger statement that I have more than one allows you to presume that this is false - that I have exactly one sister. If I say that I tried hard to pass a test, my failure to say that I passed it entitles you to conclude that I didn't. But this is a weak kind of conclusion; it is, among other things, immediately cancellable without contradiction.
How do "or" statements fit in here? Well, the statement "x and y" is stronger than the statement "x or y" (with the "or" taken inclusively); hence, saying the latter implicates that the former is false - i.e., that the "or" should be interpreted exclusively. But this implicature is cancellable; that's where "x or y, or both" comes in. This last doesn't have quite the same form as the cancellations above, but it seems to fill the same purpose. In other words, the behavior of "or" - the fact that it sometimes is clearly inclusive, and the fact that it is often interpreted as exclusive - can be explained if we assume that its core meaning is inclusive, but that conversational implicature makes it appear to be exclusive in many situations.
There are a number of points where mathematical logic behaves differently from ordinary speech. Quite a few of them can be explained by the fact that the rules of conversational implicature do not apply in mathematical argumentation; I'll point out one or two more of them as we go on. (At some point I may offer some ideas as to why this state of affairs holds; we shall see.)
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Let me start with a stipulation. As I pointed out last time, logical operators in ordinary speech can join more than two components. Mathematicians have a penchant for reducing things to binary operations, but this doesn't work for exclusive "or"; the commonsense interpretation of (exclusive) "x or y or z" is that exactly one of the three is true, and this interpretation is not captured by the binary operator XOR. For the rest of this post, I will assume the commonsense interpretation of exclusive "or".
Now, first, there are situations in which ordinary-language "or" absolutely must be interpreted inclusively. For example, in the UK, the National Blood Service has a series of screening questions for blood donors, including:
"Have you ever had jaundice or hepatitis?"Clearly, an exclusive interpretation could easily lead to, um, unsatisfactory results.
"Have you ever been given money or drugs for sex?"
Second, there are situations in which the inclusive/exclusive distinction makes no difference. If x and y are incompatible - logically, physically, or in any other manner - then the truth of "x or y" is the same whether "or" is inclusive or exclusive. (A linguist might say that the distinction is "neutralized" in those contexts.) To be clearer: to test whether "x or y" is inclusive or exclusive, you need to check whether it would be true in the situation where x and y are both true. If such a situation is inconceivable, then you can't make the test.
So what about other situations? That there is a tendency to interpret "or" as exclusive is made evident by the persistence of such formulations as "x or y, or both", or "x and/or y". (It's worth pointing out that the first, taken literally with an exclusive "or", is no improvement; the only way exactly one of x, y, and "both" can be true is if exactly one of x and y is true. Oddly, using the binary exclusive "or" actually does work, but that's an accident.) What's going on?
There are three principal ways in which, by stating x, I can give you information about y. One of them is ordinary implication (logical, scientific, or some less stringent version); I'm not going to discuss that. One is presupposition: it may be that x cannot be said to be either true or false unless y is true. ("Have you stopped beating your wife?" does not admit a "yes" or "no" answer unless you actually have a wife and that at some time in the past you beat her.) The third is a weaker one, known as "conversational implicature".
Implicature rests on the fact that ordinary conversation is a cooperative affair; there are certain unstated, even unconscious, rules that people are expected to follow. (Some of the peculiarities of conversation with children stem from the fact that they may not have internalized those rules. There is also non-cooperative conversation, such as interrogation or the questioning of witnesses, and these, again, have features that reflect this.) The details of those rules are much discussed among linguists of a certain stripe; here, I will only say that one rule (in overbroad terms) requires the speaker to make the strongest relevant statement that s/he knows to be true. The application is that if there is a stronger statement that the speaker could have made (but did not), it may be taken to be false.
For example: if I say that I have a sister, the fact that I do not make the stronger statement that I have more than one allows you to presume that this is false - that I have exactly one sister. If I say that I tried hard to pass a test, my failure to say that I passed it entitles you to conclude that I didn't. But this is a weak kind of conclusion; it is, among other things, immediately cancellable without contradiction.
- "Do you have a sister?" "Yes; in fact, I have three."
- "How did the test go?" "Well, I tried hard to pass it, and sure enough, I did!"
How do "or" statements fit in here? Well, the statement "x and y" is stronger than the statement "x or y" (with the "or" taken inclusively); hence, saying the latter implicates that the former is false - i.e., that the "or" should be interpreted exclusively. But this implicature is cancellable; that's where "x or y, or both" comes in. This last doesn't have quite the same form as the cancellations above, but it seems to fill the same purpose. In other words, the behavior of "or" - the fact that it sometimes is clearly inclusive, and the fact that it is often interpreted as exclusive - can be explained if we assume that its core meaning is inclusive, but that conversational implicature makes it appear to be exclusive in many situations.
There are a number of points where mathematical logic behaves differently from ordinary speech. Quite a few of them can be explained by the fact that the rules of conversational implicature do not apply in mathematical argumentation; I'll point out one or two more of them as we go on. (At some point I may offer some ideas as to why this state of affairs holds; we shall see.)
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