Things can be facts or deductions of facts (or both). If I ask an LLM the date of birth of Napoleon and it doesn't have it in its dataset there are only 2 options: either it has other facts from which Napoleon's birthday can be deduced or it doesn't. If it does then by improving the LLM we will be able to make more and more deductions, it if doesn't then it can only hallucinate. Since there will always be a set of facts that the LLM is not aware of and which cannot be deduced we will always have hallucinations