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.
I'm also reading this book, and I'm actually finding it profoundly unimpressive. Basically it's a 500-page collection of examples, with very little theoretical content. The worst thing, though, is that its hypothesis seems to fundamentally undermine itself. Hofstadter and Sander claim that concepts and analogy are the same phenomenon. But they also say that concepts are very flexible, non-rigid things, and that we expand and contract their boundaries whenever it's convenient for reasoning, and that we do this by making analogies between the original concept (or its instances) and some new concept (or its instances). And I agree with that. But that means that it's essentially meaningless to claim that "concepts and analogy are the same thing". We can draw an analogy between the phenomenon we typically call "categorization" and the phenomenon we typically call "analogy", and I think it's very useful to do so. But deciding whether they're the same phenomenon is just a question of how fine-grained you want your categories to be, and that will depend on the specific reasoning task you're engaged in. So I'm just massively frustrated with the authors for not acknowledging the meaninglessness of their thesis. If they just said "it's useful to think of analogy and categorization as instances of a single phenomenon" then I'd totally agree. But they don't. They say that analogy and categorization are literally the same thing. Arggggghhhh.
(Metaphors We Live By, on the other hand, is one of my favorite books in the universe. It changed my life and I highly recommend it. (Edit: ok that sounds kind of exaggeraty. It changed my life because I study language and it gave me a totally different way of thinking about language.))