by Jon N. Hall 9/10/14
A logician once told me that “and” is the least ambiguous conjunction. I offered him this: A mother has to leave the house for a minute to post some mail and she tells her eldest child, her five-year-old son: Don’t tease your brother and sister while I’m outside. The mother posts her mail and when she returns from the mail box finds her youngest, the daughter, in tears. She says to her eldest: I thought I told you not to tease your brother and sister. The boy replies: I didn’t, I only teased my sister.
When carelessly used, conjunctions can cause confusion and lead to multiple interpretations, i.e. ambiguity. This is especially the case when negation is involved. A better route for the mother might have been to avoid negation: If you tease your brother or sister while I’m out, I’ll tell your father.
On April 29, NBA Commissioner Adam Silver imposed a sanction on the owner of the L.A. Clippers: “I am banning Mr. Sterling for life from any association with the Clippers organization or the NBA.”
I would bet that Mr. Silver intended to ban Mr. Sterling from both those outfits, but that’s not what he said. What he actually said is that he’s banning Sterling from one of the two outfits, and he’s not saying which one. That’s a rather wacky thing to say, however, so many Anglophones interpret Silver’s “or” as “and.” If clarity were one of Silver’s goals, he could have said: “I am banning Mr. Sterling for life from any association with [both] the Clippers organization [and] the NBA.”
For the purpose of illustration, let’s distill Silver’s statement thus: He may not associate with his team or the NBA. By using “or,” this is a disjunction of negations. But language experts think this can (and perhaps even should) be interpreted as a conjunction of negations; i.e. He may not associate with his team and the NBA. But why can’t “or” be interpreted as “or”?
The Cambridge Grammar of the English Language (2002) is a 1,842-page tome by Rodney Huddleston, Geoffrey K. Pullum, and thirteen other contributors. At the Cambridge University website, the CGEL is touted as the “definitive grammar for the new millennium.”
Well, a thousand years is mighty long, but maybe that claim will prove true for the beginning of the new millennium. In any event, let’s see whether this descriptivist grammar can shed some light on the issue of ambiguity from conjunctions. (You can pay $237.50 for the book at Amazon or you can download a free PDF of it; it’s your choice.)
Chapter 15, “Coordination and supplementation,” is by linguists Rodney Huddleston, John Payne, and Peter Peterson, (“coordination” is a term that linguists use for conjunction). In section “2.2.2 And and or in combination with negation” (page 1298, or 1312 of the PDF) we are assured that the following two statements are equivalent:
I didn’t like his mother or his father.
I didn’t like his mother and I didn’t like his father.
That suggests that the CGEL thinks the first statement cannot be interpreted as written, that is, as a disjunction of negations. Rather, the CGEL thinks its first statement should be interpreted as a conjunction of negations, whereby “or” is interpreted as “and.” How can the CGEL justify this?
If “or” must be transformed into “and,” one might assume that the CGEL is applying De Morgan’s laws, as found in formal logic. That might also be assumed because just to the right of the above two statements appears this “Morganian” equation: “[“not A-or-B” = “not-A and not-B”].” Which would lead one to conclude that the CGEL thinks the first statement is actually a “negation of a disjunction” rather than a disjunction of negations. However, at the bottom of the page we’re given this example:
I didn’t like his mother and father. [Emphasis added.]
In keeping with the above “Morganian” transformation, one might expect that the “and” in this last example would be transformed into “or.” But no, as we learn on the next page, it will most likely be interpreted as written, i.e. as “and.” Thus, according to the CGEL this last statement can be interpreted exactly like their first statement! But the two are structurally the same; there is no notation, such as the parentheses required by De Morgan, to signal that the CGEL’s first statement works differently than this last statement. Also, De Morgan’s laws apply to both disjunction and conjunction, but throughout section 2.2.2, the laws are applied inconsistently.
(NOTE: What may be the CGEL’s main problem in section 2.2.2 is their misunderstanding of “scope,” a concept that originated in formal logic and mathematics. The section begins with scope and returns to it several times. In the second example, the CGEL holds that “and” has “scope over the negative.” That’s not how scope works. Rather, “and” has scope over its conjuncts, just as “or” has scope over its disjuncts. And in their examples, the conjuncts and disjuncts are the same: his mother and father.)
What the CGEL is doing here is describing the way that Anglophones interpret “and” and “or” under negation. And in that, they are correct; folks do indeed interpret such statements in a non-literal way. But the CGEL doesn’t explain why Anglophones perform their mental transformations some of the time, but not all of the time. But I will.
And it has nothing to do with De Morgan, nor scope. The reason folks transform disjunctions of negations into conjunctions of negations is because the former are so indefinite. So folks transform “or” into “and” in order to create some definiteness.
It’s doubtful that De Morgan’s laws have anything to do with the way Anglophones interpret disjunction under negation. It’s doubly doubtful that the vast majority of Anglophones have even heard of De Morgan. Indeed, I’d wager that your average Anglophone isn’t even aware that he might be performing any kind of transformation when he takes in statements like the CGEL’s first example. And if that’s all so, the CGEL shouldn’t be dragging the logician’s equations into their explanations — unless, of course, the brain is “Morganian.” But, if the human brain is “Morganian,” then what about the last example, where transformation doesn’t happen?
Linguistics is supposed to be a science. But it shouldn’t take too much science to find out how the majority of Anglophones interpret the CGEL’s examples. What would require a bit of science is to demonstrate that the wiring of the brain accounts for these “Morganian” transformations.
In the less than two pages that section 2.2.2 takes up, “Morganian” equations are trotted out twice. If the CGEL does think that De Morgan’s laws do obtain, then it is bad form that they don’t cite the good logician; they drag out his equations and then don’t mention him.
What would a “Morganian” structure in English look like? Perhaps this is a “Morganian” construct: It is not true that: I liked his mother or his father. But the more elegant alternative is simply to use “and” in the first place, or better yet, “parents,” as in: I didn’t like his parents.
One little problem for the CGEL is that a disjunction of negations is perfectly grammatical and perfectly logical. So the first statement can be interpreted literally. Yes, it would be a strange kind of statement if it were interpreted as a disjunction of negations, leaving the receiver to wonder which of the two wasn’t liked. But it’s no stranger a statement than if negation had been left out: “I [liked] his mother or his father.”
Passing strange, no? In that disjunctive affirmation, the strangeness would be evident, and folks would ask: Don’t you know which of his parents you liked? But negation masks the oddness, the indefiniteness, and allows folks to supply the meaning that they think is intended. So, if a disjunction of negations is grammatical and logical, how does the CGEL propose that one express that in, you know, English?
Although there are numerous mentions of ambiguity in the CGEL, there are none in Chapter 15’s section 2.2.2. Yet, they do remark that their examples provide for “natural” interpretations as well as those which are “less salient.” But nowhere does the CGEL allow that their first example can be read literally, as a disjunction, where “or” is “or.” So consider this: It was baffling; I knew that I didn’t like his mother OR his father, but I couldn’t tell which one I disliked because they were always together. I sensed that if I could interact with each of them separately that I might well have liked one of them. But then, if I had gotten to know each separately, I might have discovered that I loathed both of them, and would have wanted to send both of them straight to Hell, (or maybe even Cambridge).
The authors of the CGEL cleave to descriptivism. What seems quite beyond the ability of descriptivists is the recognition that the examples provided in section 2.2.2 are often “bad English.” The idea that there is such a thing as “bad English” is not one that descriptivists seem to want to entertain. But constructions like the CGEL’s first example should be discouraged; only pros should attempt disjunctions of negations.
Imagine how Anglophones would receive the news that their grammarians had instituted a new rule stipulating that when negation is applied to lists, “or” will be interpreted as “and,” and “and” will be interpreted as “or.”
This business with “or” brings out the latent prescriptivist in me. However, prescriptivists are of little help here. Indeed, on this matter, prescriptivists may as well be descriptivists. On the issue of “or” under negation, the entire language industry is deficient: the prescriptivists tell us to avoid “nor” and instead use “or,” and then the descriptivists condone “or” being interpreted as “and.” C’mon, boys, let’s get some “coordination” going.
See “Language Experts and the History of an Error”; it’ll tell you how prescriptivists have handled this issue.
Jon N. Hall is a programmer/analyst from Kansas City. • (2648 views)