In response to: Failure by Analogy, Surface Analogies and Deep Causes
Analogy gets a bad rap around here, and not without reason. The kinds of argument from analogy condemned in the above links fully deserve the condemnation they get. Still, I think it's too easy to read them and walk away thinking "Boo analogy!" when not all uses of analogy are bad. The human brain seems to have hardware support for thinking in analogies, and I don't think this capability is a waste of resources, even in our highly non-ancestral environment. So, assuming that the linked posts do a sufficient job detailing the abuse and misuse of analogy, I'm going to go over some legitimate uses.
The first thing analogy is really good for is description. Take the plum pudding atomic model. I still remember this falsified proposal of negative 'raisins' in positive 'dough' largely because of the analogy, and I don't think anyone ever attempted to use it to argue for the existence of tiny subnuclear particles corresponding to cinnamon.
But this is only a modest example of what analogy can do. The following is an example that I think starts to show the true power: my comment on Robin Hanson's 'Don't Be "Rationalist"'. To summarize, Robin argued that since you can't be rationalist about everything you should budget your rationality and only be rational about the most important things; I replied that maybe rationality is like weightlifting, where your strength is finite yet it increases with use. That comment is probably the most successful thing I've ever written on the rationalist internet in terms of the attention it received, including direct praise from Eliezer and a shoutout in a Scott Alexander (yvain) post, and it's pretty much just an analogy.
Here's another example, this time from Eliezer. As part of the AI-Foom debate, he tells the story of Fermi's nuclear experiments, and in particular his precise knowledge of when a pile would go supercritical.
What do the above analogies accomplish? They provide counterexamples to universal claims. In my case, Robin's inference that rationality should be spent sparingly proceeded from the stated premise that no one is perfectly rational about anything, and weightlifting was a counterexample to the implicit claim 'a finite capacity should always be directed solely towards important goals'. If you look above my comment, anon had already said that the conclusion hadn't been proven, but without the counterexample this claim had much less impact.
In Eliezer's case, "you can never predict an unprecedented unbounded growth" is the kind of claim that sounds really convincing. "You haven't actually proved that" is a weak-sounding retort; "Fermi did it" immediately wins the point.
The final thing analogies do really well is crystallize patterns. For an example of this, let's turn to... Failure by Analogy. Yep, the anti-analogy posts are themselves written almost entirely via analogy! Alchemists who glaze lead with lemons and would-be aviators who put beaks on their machines are invoked to crystallize the pattern of 'reasoning by similarity'. The post then makes the case that neural-net worshippers are reasoning by similarity in just the same way, making the same fundamental error.
It's this capacity that makes analogies so dangerous. Crystallizing a pattern can be so mentally satisfying that you don't stop to question whether the pattern applies. The antidote to this is the question, "Why do you believe X is like Y?" Assessing the answer and judging deep similarities from superficial ones may not always be easy, but just by asking you'll catch the cases where there is no justification at all.
It seems like there's a paradox about attacking analogies: if you say "Here are examples of Argument by Analogy not being valid, so your Argument by Analogy is not valid", you're engaging in Argument by Analogy yourself. It's also not clear what the point of mentioning the airplanes with beaks is. If people were saying "Birds have beaks, therefore planes must need beaks", that would be poor logic, but if people were saying "Birds have beaks, so we should try beaks", that's quite reasonable. It's all well and good to look with hindsight at people trying something that turned out to not be right and laugh at how silly they are, but being willing to try out different hypotheses even if people are going to think you look silly if the hypotheses are wrong is an important skill.
EY keeps adding the qualifier "surface" to the term "similarities", but that's largely begging the question. "Analogies based on invalid bases are invalid" is a bit of a tautology.
It's also frustrating how people insist on pretending that analogies are comparing the elements of the analogy, rather the relationship between the elements. For instance, SSM advocates argued that the Full Faith and Credit clause compelled states to recognize SSMs from other states. Obama pointed out that there was case law saying that states don't have to recognize marriages that violate their age of consent or consanguinity laws. Dan Savage then proceeded to accuse Obama of comparing homosexuality to pedophilia and incest. Make comparisons between robbery and rape, and feminists will accuse you of comparing women's bodies to personal property.