Okay, I think I should take a minute to clarify where exactly we disagree. Starting from your conclusion: [...] This by itself isn't objectionable: of course you can move your probability distribution on your future observations closer to reality's true probability distribution without controlled experiments. And Bayesian inference is how you do it. But you also say: [...] I agree that children learn how to solve AI-complete problems, including reliable prediction in this environment (and also face-recognition, character-recognition, bipedal traversal of a path barring obstacles, etc.). But you seem to have already concluded (too hastily, in my opinion) that the answer lies in a really good epistemology that children have that allows them to extract near-maximal knowledge from the data in their experiences. I claim that this ignores other significant sources of the knowledge children have, which can explain how they gain (accurate) knowledge even when it's not entailed by their sense data. For example, if some other process feeds them knowledge -- itself gained through a reliable epistemology -- then they can have beliefs that reflect reality, even though they didn't personally perform the (Bayes-approximating) inference on the original data. So that answers the question of how the person got the accurate belief without performing lots of controlled experiments, and the problem regresses to that of how the other process gained that knowledge and transmitted it to the person. And I say (based on my reading of Pinker's How the Mind Works) that the most likely possibility for the "other process" is that of evolution. As for the transmission mechanism, it's most likely the interplay between the genes, the womb, and reliably present features of the environment. All of these can be exploited by evolution, in very roundabout ways, to increase fitness. For example, the DNA/womb system can interact in just the right way to give the brain a certain structure, favorabl

Danger! You're not looking at the whole system. Children's knowledge doesn't just come from their experience after birth (or even conception), but is implicitly encoded by the interplay between their DNA, the womb, and certain environmental invariants. That knowledge was accumulated through evolution. So children are not, in their early development, using some really awesome learning algorithm (and certainly not a universally applicable one); rather, they are born with a huge "boost", and their post-natal experiences need to fill in relatively little information, as that initial, implicit knowledge heavily constrains how sensory data should be interpreted and gives useful assumptions that help in modeling the world. If you were to look only at what sensory data children get, you would find that it is woefully insufficient to "train" them to the level they eventually reach, no matter what epistemology they're using. It's not that there's a problem with the scientific method (though there is), or that we have some powerful Bayesian algorithm to learn from childhood development, but rather, children are springboarding off of a larger body of knowledge. You seem to be endorsing the discredited "blank slate" paradigm. A better strategy would be to look at how evolution "learned" and "encoded" that data, and how to represent such assumptions about this environment, which is what I'm attempting to do with a model I'm working on: it will incorporate the constraints imposed by thermodynamics, life, and information theory, and see what "intelligence" means in such a model, and how to get it. (By the way, I made essentially this same point way back when. I think the same point holds here.)