How can understanding of issues be advanced even when definitive knowledge can’t be had?

I'm not entirely sure what you have in mind by 'definitive knowledge'. I suspect you mean a sort of certainty, so that we have definitive knowledge that p when (and only when) we know for certain that p is true. If I understand your question this way, it boils down to how we can understanding something if we don't know it for certain. Philosophers have differing views about what understanding is, and specifically in relation to knowledge. But, setting those aside, I might be able to help you with your question by noting a connection between understanding and explanation. Suppose you want to understand you caught the flu. That is, you seek to explain why you got the flu. You do some research, ask a doctor, etc., and learn that the flu is caused by the influenza virus that is spread by, let us say for the sake of the example, exposure to the bodily fluids of an infected person. You may not be CERTAIN that the research you did is correct, but you could be reasonably confident that it is correct. Furthermore, you note that exposure to an infected person's bodily fluids does not guarantee, 100%, that one will get the flu. And you cannot be certain that the *only* way to get the flu is by exposure to a sick person. Still, it seems, you do possess an explanation for how you got the flu, if, for example, you recently kissed your flu infected significant other. I think we'd want to say, in this case, that although you don't possess "definitive knowledge" about why you got the flu or your case of the flu, you do understand why you got the flu. This may not be exactly what you had in mind when you asked your question, but perhaps it helps you to start on an answer. My example raises the question: what is the relation between knowledge and certainty, and explanation and knowledge, that you are assuming when you ask this question? This may be a case in which getting clear on the question and its assumption will settle the question.

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