Children go through three stages in learning the past tense of English irregular verbs. First, they learn the irregular forms. Then they apply the general rule, as in drawed, goed, eated. Then they go back to the irregular forms.

I'm not sure if I would call a general rule a principle, and I certainly would not call generalization the application of principles. For principles I would like abstraction, which most kids do not develop before age 8 or so.

A possibly embarrassing example of generalization is calling every man with glasses and a beard Daddy. Don't laugh. I've had two children that I just met call me daddy. One of the mothers told me, "She calls every man with glasses and a beard Daddy."

In bilingual kids it can be amusing. There's a verb in Irish déan, its meaning includes make and do but also encompasses some senses of perform, execute, manufacture, commit (in the sense of a crime) and so on. So it's a verb you use a lot, it gets even worse when combined into phrases e.g. ag déanamh uisce (doing water or making water literally) which means bilging. So translating it straight across to do/make/commit/whatever in English is risky.

So my three year old at the moment: "Will I do that for you Siún?" "Yeah you can make it Dada." "There you go, I did it for you." "Yeah you made it for me Dada."

She's not gotten old enough yet to not make this error. She hears do, translates it in her head as déan, and answers back with the most common English word she associates with déan which is make. My six year old son on the other hand never makes mistakes of this kind, the kind of thing he does is if he doesn't know a word in one language but he does in the other language he'll take the word from language B treat it as a word from language A and apply the associated grammatical rules to it and put it in a sentence in language A. So he could take an Irish word like marú (to kill), put it in the English past tense by forming marúed and put it in a sentence like "He was marúed." They don't tend to confuse the grammatical rules of the language, I've never seen him speaking in English and using Irish grammar, it's only with borrowed words that it gets a bit confused.

hyperpape, my ability to learn from principles was about as great as a 4 years old child as it was later and is today. (I do not recall well the degree of my ability to learn from examples at the age of 4.)

This learning process seems quite applicable to learning go as well. I think that adult learners are much more likely to jump in at step 2 (apply a proverb everywhere) and stick there without looking at other options as much, because they were pointed to these principles too early, as opposed to developing them through repetition. This can bootstrap you into some semblance of decency more quickly, but perhaps makes it harder to step beyond the interface of proverbs to see the game as it is.

Herman, that article refers to "normal" men. It is right that memory about childhood can be difficult; therefore, I refer only to things I can remember.

A very few prodigies are reported to speak a few foreign languages fluently at the age of 2... I wonder how, because my self-reflecting consciousness (and basic arithmetics with natural numbers to 100) started at 4. I can still recall the age and exact place, because the first moment of self-reflecting consciousness was associated with great astonishment. Other achievements of understanding long time ago I can recall well because of related great importance or joy.

Does the article take into account such factors?

Indeed, language learning is precisely not a case of learning by general principles. The child sees examples and distills principles, some of which are correct, and some of which are incorrect. And it is virtually impossible to correct children's linguistic behavior via language.

As for set theory, I'll get back to it later.

Herman, empirical scientific articles are good for making statements about averages or distributions. Personal anecdotes (those that are reliable because and if the person's memory about a particular anecdote is very clear) are good as counter-examples for too general statements of the kind "all children...".

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A possibly embarrassing example of generalization is calling every man with glasses and a beard Daddy. Don't laugh. I've had two children that I just met call me daddy. One of the mothers told me, "She calls every man with glasses and a beard Daddy."