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Alejandro1 comments on Rationality Quotes March 2013 - Less Wrong
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This is not a good way to argue about anything except mathematics. It takes the wrong attitude towards how words work and in practice doesn't even make arguments easier to debug because there are usually implicit premises that are not easy to tease out.
For example, suppose I say "A (a thing that affects X) hasn't changed. B (a thing that affects X) hasn't changed. C (a thing that affects X) hasn't changed. Therefore, X hasn't changed." There's an implicit premise here, namely "A, B, C are the only things that affect X," which is almost certainly false. It is annoyingly easy not to explicitly write down such implicit premises, and trying to argue in this pseudo-logical style encourages that mistake among others.
(In general, I think people who have not studied mathematical logic should stop using the word "logic" entirely, but I suppose that's a pipe dream.)
I agree that the formal "premiss + premiss + premiss = conclusion" style of arguing is not good outside formal contexts. But still, the appropriate response would be "Your argument is wrong because it doesn't take into account D", not "that's your opinion and I have mine".
Well, that depends on what the premises and conclusion were. "That's your opinion" can be used as a deflecting move if someone doesn't want to have a particular debate at that particular moment (e.g. if the premises and conclusions were about something highly charged and the woman was not interested in having a highly charged debate). Ignoring a deflecting move could be considered a social blunder, and maybe that's what the woman was responding to. There are a lot of ways to read this situation, and many of them are not "haha, look at how irrational this woman was."
Unfortunately, a lot of people have taken to using these kinds of deflective moves to protect their irrational beliefs.
To avoid this, try the more honest "You're dead wrong, possibly literally, but not important enough to be worth the time it'd take to save from your own stupidity by explaining why."?