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The following dialogue is part of episode 4 of Cosmos: A Spacetime Odyssey

John Herschel: Father, do you believe in ghosts?

William Herschel: Why, yes, my son!

John Herschel: You, you do? I would not have thought so

William Herschel: Oh, no, not in the human kind of ghost. No not at all. But look up, my boy, and see a sky full of them.

John Herschel: The stars, father? I do not follow.

William Herschel: Every star is a sun as big, as bright as our own. Just imagine how far away from us you'd have to move the Sun to make it appear as small and faint as a star. The light from the stars travels very fast, faster than anything but not infinitely fast. It takes time for their light to reach us. For the nearest ones, it takes years. For others, centuries. Some stars are so far away, it takes eons for their light to get to Earth. By the time the light from some stars gets here, they are already dead. For those stars, we see only their ghosts. We see their light, but their bodies perished long, long ago.John, I have seen further back in time than any man before me-- millions of years into the past.

My suspicion is that it's a short version of "without you saying this, I would not have thought so". That is, if you didn't tell me this, this idea would have never crossed my mind. Is that correct?

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This is one of the several variations on the family of "who would have guessed" expressions among which are never would have guessed and who would have thought. And they all mean pretty much the same thing. But the basic idea is that you say who would have thought when you are surprised or even slightly shocked by what you're hearing.

Example:

— Did you know that Adolph Hitler was actually a very good painter?
— Wow. Who would've thought! I didn't know that. That's quite surprising.

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I would say it's more like, "I am quite surprised! I didn't think you would believe in ghosts." In other words, it's not a "never would have crossed my mind" kind of an idea, but a "you just completely contradicted my assumptions" kind of idea.

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I believe it relates more to John, the son, not expecting his father to believe in "ghosts".

You, you do? I would not have thought so

This indicates that John is surprised, saying to the effect, "Wow Dad, I never thought you would be the kind of person that believes in ghosts".

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