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mszegedy comments on How to offend a rationalist (who hasn't thought about it yet): a life lesson - Less Wrong
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I suspect that what frustrated you is not noticing your own confusion. You clearly had a case of lost purposes: "applying a math thing to social justice" is instrumental, not terminal. You discovered a belief "applying math is always a good thing" which is not obviously connected to your terminal goal "social justice is a good thing".
You are rationalizing your belief about applying math in your point 2:
How do you know that? Seems like an argument you have invented on the spot to justify your entrenched position. Your point 3 confirms it:
In other words, you resolved your cognitive dissonance by believing the argument you invented, without any updating.
If you feel like thinking about the issue some more, consider connecting your floating belief "math is good" to something grounded, like The Useful Idea of Truth:
This is reasonably uncontroversial, so the next step would be to ponder whether in order to be better at this social justice thing one has to be better at modeling reality. If so, you can proceed to the argument that a consistent model is better than an inconsistent one at this task. This may appear self-evident to you, but not necessarily to your "socially progressive" friend. Can you make a convincing case for it? What if s/he comes up with examples where someone following an inconsistent model (like, say, Mother Teresa) contributes more to social justice than those who study the issue for a living? Would you accept their evidence as a falsification of your meta-model "logical consistency is essential"? If not, why not?
You're completely right. I tried, at first, to look for ways that it could be a true statement that "some areas shouldn't have consistent belief systems attached", but that made me upset or something (wtf, me?), so I abandoned that, and resolved to attack the argument, and accept it if I couldn't find a fault with it. And that's clearly bad practice for a self-proclaimed rarionalist! I'm ashamed. Well, I can sort of make the excuse of having experienced emotions, which made me forget my principles, but that's definitely not good enough.
I will be more careful next time.
EDIT: Actually, I'm not sure whether it's so cut-and-dry like that. I'll admit that I ended up rationalizing, but it's not as simple as "didn't notice confusion". I definitely did notice it. Just when I am presented with an opposing argument, what I'll do is that I'll try to figure out at what points it contradicts my own beliefs. Then I'll see whether those beliefs are well-founded. If they aren't, I'll throw them out and attempt to form new ones, adopting the foreign argument in the process. If I find that the beliefs it contradicts are well-founded, then I'll say that the argument is wrong because it contradicts these particular beliefs of mine. Then I'll go up to the other person and tell them where it contradicts my beliefs, and it will repeat until one of us can't justify our beliefs, or we find that we have contradictory basic assumptions. That is what I did here, too; I just failed to examine my beliefs closely enough, and ended up rationalizing as a result. Is this the wrong way to go about things? There's of course a lot to be said about actual beliefs about reality in terms of prior probability and such, so that can also be taken into account where it applies. But this was a mostly abstract argument, so that didn't apply, until I introduced an epistemological argument instead. But, so, is my whole process flawed? Or did I just misstep?
From your original story, it doesn't look like you have noticed that your cached belief was floating. Presumably it's a one-off event for you, and the next time you feel frustrated like that, you will know what to look for.
Now, I am not a rationalist (IANAR?), I just sort of hang out here for fun, so I am probably not the best person to ask about methodology. That said, one of the approaches I have seen here and liked is steelmanning the opposing argument to the point where you can state it better than the the person you are arguing with. Then you can examine it without the need to "win" (now it's your argument, not theirs) and separate the parts that work from those which don't. And, in my experience, there is a grain of truth in almost every argument, so it's rarely a wasted effort.
Very insightful, that.