The Correct Use of Analogy

For those interested, Douglas Hofstadter (of the famous Gödel, Escher, Bach) wrote recently a book called Surfaces and Essences: Analogy as the Fuel and Fire of Thinking which develops the thesis that analogy is the core and fuel of thinking, and does it quite brilliantly.

I'm only half-way through the book yet, but so far I liked it very much, the first part on language for example develops somewhat similar ideas, but with a quite different viewpoint, than the "Humans Guide to Words" Sequence on Less Wrong, and both complement each other well.

Perhaps you could see trying to think of analogies as sampling randomly in conceptspace from a reference class that the concept you are interested in belongs to.

Imagine a big book of short computer programs that simulate real-life phenomena. I'm working on a new program for a particular phenomenon I'm trying to model. I don't have much data about my phenomenon, and I'm trying to figure out if a recursive function (say) would accurately model the phenomenon. By looking through my book of programs, I can look at the frequency with which recursive functions seem to pop up when modeling reality and adjust my credence that the phenomenon can be modeled with a recursive function accordingly.

Choosing only to look at pages for phenomena that have some kind of isomorphism with the one I'm trying to model amounts to sampling from a smaller set of data points from a tighter reference class.

This suggests an obvious way to improve on reasoning by analogy: try to come up with a bunch of analogies, in a way that involves minimal motivated cognition (to ensure a representative sample), and then look at the fraction of the analogies for which a particular proposition holds (perhaps weighting more isomorphic analogies more heavily).

Analogies are pervasive in thought. I was under the impression that cognitive scientists basically agree that a large portion of our thought is analogical, and that we would be completely lost without our capacity for analogy? But perhaps I've only been exposed to a narrow subsection of cognitive science, and there are many other cognitive scientists who disagree? Dunno.

But anyway I find it useful to think of analogy in terms of hierarchical modeling. Suppose you have a bunch of categories, but you don't see any relation between them. So maybe you know the categories "dog" and "sheep" and so on, and you understand both what typical dogs and sheep look like, and how a random dog or sheep is likely to vary from its category's prototype. But then suppose you learn a new category, such as "goat". If you keep categories totally separate in your mind, then when you first see a goat, you won't relate it to anything you already know. And so you'll have to see a whole bunch of goats before you get the idea of what goats are like in general. But if you have some notion of categories being similar to one another, then when you see your first goat, you can think to yourself "oh, this looks kind of like a sheep, so I expect the category of goats to look kind of like the category of sheep". That is, after seeing one goat and observing that it has four legs, you can predict that pretty much all goats also have four legs. That's because you know that number-of-legs is a property that doesn't vary much in the category "sheep", and you expect the category "goat" to be similar to the category "sheep". (Source: go read this paper, it is glorious.)

Anyway I basically think of analogy as a way of doing hierarchical modeling. You're trying to understand some situation X, and you identify some other situation Y, and then you can draw conclusions about X based on your knowledge of Y and on the similarities between the two situations. So yes, analogy is an imprecise reasoning mechanism that occasionally makes errors. But that's because analogy is part of the general class of inductive reasoning techniques.

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.

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 [...] Take the plum pudding atomic model. I still remember this falsified proposal of negative 'raisins' in positive 'dough' largely because of the analogy...

I think this part is really important. It seems like humans really do have hardware for analogies and that leads to better retention of information that you analogize. Of course using analogies to try do derive new information about the original subject is a fallacy (and I think that's where most of the animosity toward analogies on LW stems from), but drawing an analogy is an invaluable tool for understanding and remembering things. It forces you to think things through on a mechanistic level and gives an easy path to retrieval.

What do the above analogies accomplish? They provide counterexamples to universal claims.

Excellent point.

Related -- here are some attempts to formalize and understand analogy from a category theoretic perspective:

http://link.springer.com/article/10.1023/A:1018963029743 http://pages.bangor.ac.uk/~mas010/pdffiles/Analogy-and-Comparison.pdf