He suffers a first-order false belief: the belief that there was once a thing called a moon, which disappeared and sucked the evidence that it had ever existed into the black hole of its absence.
This plays out logically: first Daniel, and later his doctor (Marvin Pallister), examine all the inconsistencies, possibilities, misapprehensions et cetera that follow from such a premise. Hale, desperate to prove himself sane, looks in poetry books; notes that the other planets now have satellites, rather than moons; rants at the local newspaper for leaving moon phases out of the astronomy column. Pallister takes a certain relish in the more nonsensical of his patient's pronouncements: "Let me get this straight. Everyone knew about it. It was huge. And nobody noticed if it was there or not." [loc. 46]
Then, one afternoon, Daniel sits down with the book that Pallister has written about his case.
I had to reread the last few pages several times to appreciate their full weight. (My first thought was that they made a nonsense of the rest of the story: later, I understood it better.) The last page, in particular, is carefully crafted: punctuation, paragraph breaks, repetition all precise.
Brief, thought-provoking and oddly humorous. It's a story, I suppose, about mental illness, about whether a problem is internal or external, about fighting to hold onto a belief: but one would not wish for Marvin Pallister as a therapist.
I'll look out for more of Hull's fiction.