Your example of Norman the clairvoyant provides an interesting insight into the relationship between evidence, belief, and truth. While I agree that the "fact of the matter" holds importance in having knowledge, it is also essential to consider the epistemic responsibilities of individuals when forming beliefs. In the case of Norman, even though the clairvoyant feeling turned out to be true, it would be epistemically irresponsible for him to base his beliefs solely on that feeling, given the more robust evidence pointing to the president being in Florida.

Our epistemic responsibility lies in cultivating beliefs based on the most reliable and available evidence. If we anchor ourselves with the principle that evidence should be taken as reasonable in the absence of counter-evidence, then we strive to form beliefs that are more likely to be true, even though we can't guarantee their truth.

In the context of education, the "fact of the matter" still holds value, but the process of refining our beliefs and knowledge should be emphasized. We should teach students to evaluate evidence critically and engage in open-minded inquiry, which can lead them to a better understanding of the world.

While the "fact of the matter" is important for knowledge, focusing on the epistemic responsibility of individuals and the refinement of our belief-forming processes can help address the challenges posed by coherentism and other epistemological theories. This focus on evidence and critical thinking also provides a practical framework for addressing issues in education and countering conspiracy theories.

The question I would ask is: "Can Norman describe his belief as knowledge?" We can do so in this scenario, but only because of our position as an omniscient outsider. Norman does not have that sort of privileged information.

The relevant question for Norman is what he ought to believe on the basis of the evidence he has. He's got his clairvoyant feelings and some other conflicting external evidence. He can give credence to one or both of those and construct a belief appropriately, which he'll likely do on the basis of other beliefs. In this case, the most reasonable belief in absence of other supporting beliefs (supposing Norman values his clairvoyance) is perhaps a middle position: the President is either in New York or the president is in Florida.

On the other hand, if Norman possesses an evidence-based belief that clairvoyance is impossible, he might dismiss his clairvoyant feelings and conclude that the president is in Florida. Norman would possess a reasonable belief in this case, even if his manifest clairvoyance was in fact accurate. If Norman were to gain additional evidence that the president was in fact in New York (such as a first-hand sighting), he'd be reasonable in revising that belief and in giving more credence to further clairvoyant experiences.

We can categorize Norman's belief as knowledge or non-knowledge in all of these scenarios based on privileged information, but Norman cannot, and Norman's case represents the baseline we should consider when assessing our own beliefs. We can't say if our beliefs amount to knowledge since we aren't omniscient, but we can say if they're reasonable.