Do you disagree with the general principle that new knowledge doesn't overthrow old knowledge when the context of the old knowledge is included? Or do you see the situation with first-level generalizations as not being an example of this principle?
I'm not sure that I actually agree with it, at least not how it's being used. I do believe there is some validity to it, in that there are cases where new knowledge is not really overthrowing old knowledge. So I don't reject it. But I also don't think it applies to all cases. If it did, errors would be technically impossible.
It seems to me that the general principle must have bounds. I believe there is the possibility of error. And yet, this loose use of the principle seems to try to convert every case of error to be "true within a context". I know Objectivists hate to be wrong, but I never thought it was a basic premise of the philosophy!
Perhaps, as you mention, this is simply a lack of integration with the contextual theory and the correspondence theory.
Take the example of the child who rolls the ball. In many ways, that example is so obvious to us that we assume the child could not possibly mis-integrate the information. We see it rolling, and we assume that it is the shape of the object that matters. But what if we saw a child roll a ball, and then say "when I push on toys, they roll". The child then goes and takes a cube and tries to do the same thing, and it doesn't work. He would probably realize he had made an error. Now maybe some Objectivists would hear the child say that toys roll, and think "That's contextually true!". But I would hear it and say, the poor kid has incorrectly generalized. It isn't the fact that the ball is a toy that makes it roll. It is the shape of the object. And if I wanted, I could provide several other examples to the child to show him that it is indeed the shape. But the point was that the original generalization wasn't true in some contexts. It was false. All toys roll or all tables burn are clearly errors, and new knowledge does in fact invalidate them.
If we simply say that something is "true within the context of our knowledge", then error is impossible. We've just defined it away, and abandoned correspondence with reality. But is that what the contextual theory is all about? Isn't it about how each of our ideas is interconnected with the rest of our knowledge. That a statement is made within a context, and you need to be aware of that context. And that you can't rip the statement out of the appropriate context and still expect it to be true?
How about the idea that new knowledge does not necessarily invalidate previous knowledge. Is Newtonian physics wrong because of relativity, or correct within a context? I think it is correct within the context. But I see that as complete different from a statement that all tables burn when only some do. The Newtonian physics was correct in the recognition of certain relationships and factors. But saying that all tables burn has misidentified the source of the causal condition. It was not the table qua shape that mattered. It was the table qua material that mattered. The generalization is not just words thrown together. It is a statement about the causal connection. It is drawing a connection between tables and fire. And "tables" is a concept, which is a kind of mental categorization. The categorization is based on the shape or function of the referents. Connecting that concept to that causal interaction is a misunderstanding.
So I think there is a big difference between saying that all wood burns and all tables burn. All wood burns may have contexts in which it isn't true, such as when there is no oxygen or when the wood is soaked in water. But within the proper/normal context, the wood will burn. It applies to all wood, unless some outside factor changes. But the table example is just false. It just doesn't apply to some tables, no matter what context. It seems that you could still say that some knowledge is not invalidated by new facts, or radically different contexts. Within the appropriate context of reality, the statement is true. Within normal context, all wood does burn. But not all tables!
One interesting aside is that if the contextual theory can really excuse any false statement, then there would be absolutely nothing wrong with saying that all swans are white. If you ever found a black one, you could say that you weren't wrong but instead were just contextually right. And with that approach, it seems the whole need to justify a generalization through causal means would be unnecessary. Enumeration would be find. You could say that all swans are white because you've only seen white ones.
Presumably the point of trying to link generalization to causality is because the generalization must be justified in some way. To say that all A is P should be based on some underlying justification that supports the wide generalization. Without that justification, you are generalizing without reason. You'd be committing an error of reasoning. But look what happens when you treat the context theory as meaning that anything is true, if it is true within the context of your knowledge. Suddenly all swans are white, all tables do burn, and there is no such thing as a faulty generalization. I think these two ideas, that contextual knowledge omits error, and that generalizations must be justified, are incompatible. The former makes the latter unnecessary.
Going back to first level generalizations, you asked whether new knowledge can invalidate old knowledge there. I think in the case of error, it can. In the case you correctly generalized, new knowledge doesn't overthrow the previous knowledge but adds to it.
But now, I don't accept the validity of first-level generalizations. I could probably accept the idea that certain causal events are directly perceivable, and would therefore would act as a foundation of knowledge. But when the generalization happens, I don't see "first-level" generalizations as any different from any other. It seems both unnecessary, and incorrect.
If the reason causality is viewed as central to the process of generalization is because it provides the justification for it, then we can't just automatically generalize by naming what we see. The table burns does not automatically and correctly become all tables burn. The justification does not exist. Harriman tries to argue that somehow putting it into words does not need justification, because it automatically arrives at the truth. But only a perversion of contextual theory that dismisses any possibility of error could justify this, and that same theory would justify any approach! They are trying to make an exception for "first-level" generalizations so it doesn't need to be justified, and can therefore act as an equivalent to perception as an automatic and flawless process that become the foundation for further knowledge. I think that even these "first-level" generalizations need to be justified, and I think the attempt to treat them as automatic and flawless is wrong. I think they don't really justify that approach, and I think there are counterexamples.