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Alicorn comments on How to Not Lose an Argument - Less Wrong
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Most of the comments in this discussion focused on topics that are emotionally significant for your "opponent." But here's something that happened to me twice.
I was trying to explain to two intelligent people (separately) that mathematical induction should start with the second step, not the first. In my particular case, a homework assignment had us do induction on the rows of a lower triangular matrix as it was being multiplied by various vectors; the first row only had multiplication, the second row both multiplication and addition. I figured it was safer to start with a more representative row.
When a classmate disagreed with me, I found this example on Wikipedia. His counter-arguement was that this wasn't the case of induction failing at n=2. He argued that the hypothesis was worded incorrectly, akin to the proof that a cat has nine tails. I voiced my agreement with him, that “one horse of one color” is only semantically similar to “two horses of one color,” but are in fact as different as “No cat (1)” and “no cat (2).” I tried to get him to come to this conclusion on his own. Midway through, he caught me and said that I was misinterpreting what he was saying.
The second person is not a mathematician, but he understands the principles of mathematical induction (as I'd made sure before telling him about horses). And this led to one of the most frustrating arguments I'd ever had in my life. Here's the our approximate abridged dialogue (sans the colorful language):
Me: One horse is of one color. Suppose every n horses are of one color. Add the n+1st horse, and take n out of those horses. They’re all of one color by assumption. Remove 1 horse and take the one that’s been left out. You again have n horses, so they must be of one color. Therefore, all horses are of one color.
Him: This proof can't be right because its result is wrong.
Me: But then, suppose we do the same proof, but starting with on n=2 horses. This proof would be correct.
Him: No, it won’t be, because the result is still wrong. Horses have different colors.
Me: Fine, then. Suppose this is happening in a different world. For all you know, all horses there can be of one color.
Him: There’re no horses in a different world. This is pointless. (by this time, he was starting to get angry).
Me: Okay! It’s on someone’s ranch! In this world! If you go look at this person’s horses, every two you can possibly pick are of the same color. Therefore, all of his horses are of the same color.
Him: I don’t know anyone whose horses are of the same color. So they’re not all of one color, and your proof is wrong.
Me: It’s a hypothetical person. Do you agree, for this hypothetical person—
Him: No, I don’t agree because this is a hypothetical person, etc, etc. What kind of stupid problems do you do in math, anyway?
Me: (having difficulties inserting words).
Him: Since the result is wrong, the proof is wrong. Period. Stop wasting my time with this pointless stuff. This is stupid and pointless, etc, etc. Whoever teaches you this stuff should be fired.
Me: (still having difficulties inserting words) … Wikipe—…
Him: And Wikipedia is wrong all the time, and it’s created by regular idiots who have too much time on their hands and don’t actually know jack, etc, etc. Besides, one horse can have more than one color. Therefore, all math is stupid. QED.
THE END.
To the best of my knowledge, neither of these two people were emotionally involved with mathematical induction. Both of them were positively disposed at the beginning of the argument. Both of them are intelligent and curious. What on Earth went wrong here?
^One of the reasons why I shouldn’t start arguments about theism, if I can’t even convince people of this mathematical technicality.
Why didn't you drop the "horses" example when it tripped him up and go with, I dunno, emeralds or ceramic pie weights or spruckels, stipulated to in fact have uniform color?
I suspect that I lost the second person way before horses even became an issue. When he started picking on my words, "horses" and "different world" and "hypothetical person" didn't really matter anymore. He was just angry. What he was saying didn't make sense from that point on. For whatever reason, he stopped responding to logic.
But I don't know what I said to make him this angry in the first place.
Leaving aside the actual argument, I can tell you that there exist people (my husband is one of them, and come to think of it so is my ex-girlfriend, which makes me suspect that I bear some responsibility here, but I digress) whose immediate emotional reaction to "here, let me walk you through this illustrative hypothetical case" is strongly negative.
The reasons given vary, and may well be confabulatory.
I've heard the position summarized as "I don't believe in hypothetical questions," which I mostly unpack to mean that they understand that hypothetical scenarios are often used to introduce assumptions which support conclusions that the speaker then tries to apply by analogy to the real world, and that a clever rhetoritician can use this technique to sneak illegitimate assumptions into real-world scenarios, and don't trust me not to sneak in assumptions that make them look stupid or manipulate them into acting against their own interests.
I don't know if that's a factor in your case or not, but I have found that once I trigger that reaction, there's not much more I can do... they are no longer cooperating in the communication, they are just looking for some way to get out. If I press the point, I merely elicit anger and defensiveness and a variety of distractors.
The best way around this I've found so far, and it's only hit-or-miss, is to avoid the stance of "here let me show you something" altogether.
I am a lot more successful if I adopt the stance of "I am thinking about a problem that interests me," and if they express interest, explaining the problem as something I am presenting to myself, rather than to them. Or, if they don't, talking about something else.
At the risk of sounding like Robin, the fact that this is successful leads me to believe that at least sometimes, what's really going on is that I've stepped on some status-signaling landmine, and the reaction I'm getting actually translates to "I refuse to cede you the role of instructor by letting you define the hypothetical."
And suggesting that this might be what's going on works about as poorly as you'd expect it to were it what's going on. Of course, that's precisely what makes status-signaling a fully generalizable counterargument, so I take it with a grain of salt.
You know, come think of it, that's actually a very good description of the second person... who is, by the way, my dad.
This hasn't ever occurred to me, but I'll try it the next time a similar situation arises.