I subscribe to the same definition as you. I've actually never heard someone referring to the mistakes as hallucinating until now, but I can see how it's a bit of a grey area.
I'm actually curious about how you both come to those definitions of hallucinations. It gets very difficult to distinguish these things when you dig into them. Simon dropped this paper[0] in another thread[1] and while they provide a formal mathematical definition I don't think this makes it clear (I mean it is one person (who doesn't have a long publication record, PhD, or work at a university), but following their definition is still a bit muddy. They say the truth has to be in the training but don't clarify if they mean in training distribution or literal training example.
To make a clear example, is the fact that when prompting GPT-5 with "Solve 5.x = x + 5.11" it answers "-0.21" (making the same mistake as when it GPT-4 says 5.11 > 5.9). Is that example specifically in the training data? Who knows! But are those types of problems in the training data? Absolutely! So is this a mistake or a hallucination? Should we really be using an answer that requires knowing the exact details of the training data? That would be fruitless and allow any hallucination to be claimed as a mistake. But in distribution? Well that works because we can know the types of problems trained on. It is also much more useful given that the reason we build these machines is for generalization.
But even without that ambiguity I think it still gets difficult to differentiate a mistake from a hallucination. So it is unclear to me (and presumably others) what the precise distinction is to you and Simon.
But I tend to instinctually (as a mere human) think of a "hallucination" as something more akin to a statement that feels like it could be true, and can't be verified by using only the surrounding context -- like when a human mis-remembers a fact on something they recently read, or extrapolates reasonably, but incorrectly. Example: GPT-5 just told me a few moments ago that webpack's "enhanced-resolve has an internal helper called getPackage.json". Webpack likely does contain logic that finds the package root, but it does not contain a file with this name, and never has. A reasonable person couldn't say with absolutely certainty that enhanced-resolve doesn't contain a file with that name.
I think a "mistake" is classified as more of an error in computation, where all of the facts required to come up with a solution are present in the context of the conversation (simple arithmetic problems, "how many 'r's in strawberry", etc.), but it just does it wrong. I think of mistakes as something with one and only one valid answer. A person with the ability to make the computation themselves can recognize the mistake without further research.
So hallucinations are more about conversational errors, and mistakes are more about computational errors, I guess?
But again, I agree, it gets very difficult to distinguish these things when you dig into them.
The reason it gets very difficult to distinguish between the two is that there is nothing to distinguish between the two other than subjective human judgement.
When you try to be objective about it, it's some input, going through the same model, producing an invalid statement. They are not different in no way, shape or form, from a technical level. They can't be tackled separately because they are the same thing.
So the problem of distinguishing between these two "classes of errors" reduces to the problem of "convincing everyone else to agree with me". Which, as we all know, is next to impossible.
I can't pinpoint exactly where I learned my definition of hallucination - it's been a couple of years I think - but it's been constantly reinforced by conversations I've had since then, to the point that I was genuinely surprise in the past 24 hours to learn that a sizable number of people categorize any mistake by a model as a hallucination.
