In a past post, I made the claim that Induction was subsumed by Critical Rationalism and that all cases of induction ‘working’ are really cases of Critical Rationalism working. However, I’m now going to do my best to challenge that idea using the hardest cases I can think of. This post is my first attempt at such self-criticism.
My daughter was in class and they were asked on an assignment what might be used to keep a Soda drink cold. One of the options was a wool sock. My daughter soon found herself arguing with everyone else in her group because the rest of the group thought that wool kept things warm, so it wouldn’t keep a Soda cold. She tried to explain to them that it actually just keeps things insulated, so it keeps warm things warm and cold things cold. They weren’t buying it. 
This little episode demonstrates something kind of interesting. The rest of the class had an explanation that looked something like this:
Theory 1: Wool warms things up.
My daughter had an explanation that was something like this:
Theory 2: Wool insulates things.
It’s not too hard to see how the rest of the class came up with their theory. They have lots of experience with using wool to keep things warm, like say their feet. Therefore they developed a theory that wool keeps things warm.
So here are my questions for Critical Rationalists (especially those interested in modeling how humans think, i.e. AGI):
Question 1: You may have missed it, but I just made the claim that the rest of the class came up with a theory through experience. Or did I? Does that mean the rest of the class was using empiricism? If not, how did they actually derive their theory?
Question 2: You may have missed it, but I just made the claim that the rest of the class came up with a theory via repeated observations. Or did I? Does that mean the rest of the class was using induction? If not, why not? And how did they actually derive their theory?
Now you already know my opinion that Induction is really just a subsumed theory and that Critical Rationalism can always explain examples of Induction. But is that the case here? It’s less obvious, isn’t it? It seems doubtful that anyone explained to these children that wool warms things. Yet a large group of children all seem to have consistently come up with something like an explanation that wool is used for warming things. How did they all so consistently come up with the very same incorrect explanation when no one ever explained it to them? What are they basing their theory on? How are they coming up with it?
See if you can do what I did back on my Trump and Truth post and come up with a Critical Rationalist account of this to explain how this Inductive event is really Critical Rationalism instead. I find this example to be harder than the Trump and Truth example. (Though if I’m right that Induction was subsumed by Critical Rationalism, then this should be possible.)
Also, consider this questions:
Question 3: Is Theory 1 an (false) explanation or a (good/useful) heuristic? What’s the difference between an explanation and a heuristic?
I’ve been calling Theory 1 an explanation, but is it? Or is it a heuristic? And if it is a heuristic and not an explanation, what’s the difference between these two?
Induction, Machine Learning, and AGI
Now here is the next question for you to consider. I’ve had various people in the 4S group argue to me that Induction is real. Ella has argued in favor of something like ‘weak induction’ in the case of machine learning and animal learning (though she sees it as non-knowledge creating) and Dan Elton has made a similar argument but with the added idea that Induction exists as a parallel knowledge-creation process. Dennis’ view is a bit harder to pin down, so I’ll not try to explain it here. But his stance involves a complete denial of any sort of induction. I’d love to see all three of these views pose their own accounts of what is going on here.
This brings me to my question on AGI:
Question 4: Are these questions directly relevant to the study of AGI? If so, why? If not, why? If you argue that humans do use induction, will AGI have to use induction too? If you argue that induction is impossible, then what is the non-inductive explanation for why most of the kids are holding theory 1 instead of the correct theory 2?
Disclaimer: After the reaction to my last post, I want to clarify again that I’m not advocating that induction is not refuted. If that is your position, that is fine. Just explain yourself. But please don’t tell me induction is refuted. That’s my whole point. Now that we agree, what does that mean and how — given that view — do you perceive this scenario? And why is there a clear bias towards a wrong answer here?
 When my daughter confronted them over the fact that wool has nothing in it that creates heat and suggested instead that the human body creates heat it’s interesting how these children then defended themselves. They pointed out that if your foot is cold then according to my daughter’s theory the foot would stay cold when there was wool on it. She did try to suggest to them that perhaps a human foot, even when cold, still has some heat. They felt this couldn’t be correct.
This is a golden example of how humans are not necessarily inductive at all. These arguments take real creativity and take the form of explanations. But there is still the question of why there was the initial consistency around a single (incorrect) explanation in the first place. An inductivist would simply argue that they inductively generalized from many different experiences. What is the critical rationalist view of what seems to be a clear bias? That is what I am asking.