Linguistic commentary from a guy who takes things too literally

Talks at Appropriate Times

Posted by Neal on April 7, 2011

Doug’s report card came home last week, and on the list of nonacademic, behavioral characteristics, he had a minus for “Talks at appropriate time.” I knew from the conference with his teacher last month that Doug had no problem speaking up at appropriate times. What he does have a problem with is not talking at inappropriate times. I tweeted about the grade:

Glen tweeted in response:

Good point! In other words, take the conditional statement (1):

(1) If it’s an appropriate time, Doug talks.

Even if (1) is true, (2) doesn’t have to be true:

(2) If it’s not an appropriate time, Doug doesn’t talk.

Alternatively, Glen could have noted that a statement doesn’t imply its logical converse. That is, even if (1) is true, (3) doesn’t have to be true:

(3) If Doug talks, it’s an appropriate time.

In fact, (2) and (3) are logically equivalent. However, if you negate both clauses and reverse them — in other words, if you get the inverse of a statement and then get the converse of that — the resulting statement is still true. That’s known as the statement’s contrapositive:

(4) If Doug doesn’t talk, it’s not an appropriate time.

So a statement and its contrapositive are logically equivalent, and its inverse and converse are logically equivalent. This is easier to take in as a diagram (click to view full-size). Read p → q as “if p, then q,” and ¬ p as “not p” (or if you want “it is not the case that p“). The logically equivalent statements are in same-colored boxes; the statements in green are contrapositives of each other, as are the statements in blue. The arrows go two ways because the inverse of an inverse is the original statement, and likewise for the converse of a converse.

There’s one little problem in all this. The report card didn’t phrase the behavioral desideratum as a conditional. It didn’t say, “If it’s not an appropriate time, Doug will not talk.” It simply said (with an understood subject), “Talks at appropriate times.” Can that be accurately rephrased as a conditional in the first place? Take a sentence like:

Dagwood sings in the shower.

Does that mean that if Dagwood’s in the shower, he sings? Or does it mean that if Dagwood’s singing, he’s in the shower? Of course, generic sentences like this can have exceptions, but what is supposed to be more surprising: Dagwood taking a shower and not singing, or Dagwood singing in someplace other than the shower? Or is it supposed to be a biconditional: That Dagwood sings if and only if he’s in the shower? Any of those readings could be the intended one, based on context and intonation.

So in the same way, (Doug) talks at appropriate times could be interpreted either (1) or (2) (or to be complete, (3) or (4) as well). It’s only the context of that parent-teacher conference we had last month, and the general knowledge of how American kids are expected to behave in school, that tells me that (Doug) talks at appropriate times is to be interpreted as both (1) and (2), i.e. as the biconditional (5):

(5) Doug talks if and only if it’s an appropriate time.

Logicians have occasion to talk about biconditionals so much that they have abbreviated if and only if into iff. I don’t know exactly how that’s pronounced to distinguish it from if (probably just by saying “if and only if”), but in text it works, once you’ve realized it’s not a typo. But how can we get that biconditional reading unambiguously in the report card criterion, which isn’t phrased as a conditional? I tweeted back to Glen:

6 Responses to “Talks at Appropriate Times”

  1. Paul Clapham said

    “Iff” is pronounced “if and only if”. At least that was the case when I was a practicing mathematician… perhaps it’s changed since then.

  2. James said

    I noticed that on the Stockholm metro system, the ascending escalators are marked “Upp”. I guess this makes the point that you shouldn’t attempt to use them for going down (however strong the temptation…).

  3. Ran said

    So interesting!

    Oddly, the affirmative version — “He talks at appropriate times” (meaning, in part, “He doesn’t talk at inappropriate times”) — doesn’t seem so bad to me. There’s a logical gap there, but some sort of implicature fills it in. It’s only the negative version “He doesn’t talk at appropriate times” (meaning “He talks at inappropriate times”) that falls apart, and doesn’t work for me at all. I guess it’s because the former can be made explicit by adding “only” (“He talks only at appropriate times”), whereas the latter could only be corrected by reducing the scope of the negative.

    Another, maybe-similar case: “He gave the right answer” clearly implies that he gave only the right answer (as opposed to, say, circling both A and B, with B being correct); whereas “He didn’t give the right answer” easily covers the case that he gave no answer at all (especially if the full sentence is “He didn’t give the right answer to any of the questions”, which means that each question was either answered wrong or left blank).

    I think the key is in the adjectives “appropriate” and “right”, which aren’t generally used affirmatively unless the inverse/converse is also true.

  4. Tom said

    All of this, of course, comes from the general piece of teacher wisdom to use positive statements and not negatives. It’s good classroom management advice — “let’s listen to X” or “eyes on me” is almost always a better move than “be quiet” — but it has also created a kind of creepy teacher-speak that feels bureaucratic and at times downright inhuman. I’d content that the only context in which we understand a “-” next to “speaks at appropriate times” positively is one in which we assume the teacher is trying not to say “is quiet.”

    What’s a little disturbing is that the obvious meaning of a “+” in this column (that the student participates in class) should be something important to communicate… some might even think it’s more important to know if a student is actively participating where appropriate than to know whether they’re being quiet when the teacher wants them to.

    What I’d really like to see is a teacher put a “+/-” next to “speaks at appropriate times” — good luck figuring *that* one out!

    (Regarding the motive behind teacher-speak in the first place, I often wonder how much changing the *words* teachers use makes a difference anyway — I imagine that a good teacher can deliver the words “I need you to stop talking” in a way that feels thoroughly humane and positive whereas I imaging a struggling teacher can deliver the words “Let’s pay attention to Johnny now” in a way that feels anything but… of course, your example comes from written communication so it’s a moot point, but my gut is that these written forms have their basis in classroom management advice).

  5. Glen said

    “Dagwood sings in the shower.”

    This statement may have multiple readings — e.g., does he *always* or just *sometimes* sing in the shower? But under no circumstances would I take it to mean that Dagwood *only* sings in the shower. Indeed, I assume the correlation between shower-singers and car-singers is rather high.

    Given the statement “[Doug] talks at appropriate times,” I know what it means for the same reason you do (context), but it nevertheless feels like a mistake. I can’t get the “Doug talks *only* at appropriate times” reading for the same reason I can’t get the “Dagwood sings *only* in the shower” reading. However, I wonder about the ability of emphasis/italics to alter logical meanings. If the statement had italicized the word ‘appropriate’, I would have gotten the intended meaning without hiccup or complaint.

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