Quote 61
I did not believe in ghosts. Or rather, until this day, I had not done so, and whatever stories I had heard of them I had, like most rational, sensible young men, dismissed as nothing more than stories indeed. (5.30)
Even though the facts are staring him in the face, Arthur refuses to believe that the woman is a ghost. But if your conclusion (ghosts) is rationally impossible, then maybe your facts are wrong?
Quote 62
"It seems to me, Mr. Daily," I said, "that I have seen whatever ghost haunts Eel Marsh and that burial ground." (8.29)
The first step to progress is acceptance. Now that Arthur is no longer in denial about the existence of ghosts he can speak to Mr. Daily openly about the whole crazy affair. But notice how he's still using very rational, measured language to talk about it: "it seems to me."
Quote 63
And then, from somewhere within the depths of the house—but somewhere not very far from the room in which I was—I heard a noise. (9.20)
There's nothing worse than things that go bump in the night when you're trapped on an island in a potentially haunted house. Seriously. Nothing worse. We get chills just thinking about it.