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"It's a real story, and the reason I say that is... well, there's a couple of reasons really.
One is that Jesus refers to it as if it happened, so He makes a parallel between Jonah spending three days in the fish and Jesus spending three days in the grave. The way He speaks of it is just as that happened to Jonah, this will happen to Him, and so I've got to take Jesus at his word and the historicity of Jonah is important for understanding Jesus' own death and resurrection.
The other reason is that the narrative of Jonah itself is not mythical, it is rooted in history and time and space. Jonah is introduced as being a particular person, at a particular time, with a particular father, with a particular mission. It is not written as myth, it's written as historical.
I gather that there'd be one or two instances in history of people being swallowed by whales and that kind of thing and being alive at the end of it. I'm sure it doesn't happen very often, but it would seem to be possible. But the most important reason is that Jesus says that he treats it as historical fact."
38Then some of the Pharisees and teachers of the law said to him, “Teacher, we want to see a sign from you.”
39He answered, “A wicked and adulterous generation asks for a sign! But none will be given it except the sign of the prophet Jonah.
40For as Jonah was three days and three nights in the belly of a huge fish, so the Son of Man will be three days and three nights in the heart of the earth.
41The men of Nineveh will stand up at the judgment with this generation and condemn it; for they repented at the preaching of Jonah, and now something greater than Jonah is here.
42The Queen of the South will rise at the judgment with this generation and condemn it; for she came from the ends of the earth to listen to Solomon’s wisdom, and now something greater than Solomon is here.
43“When an impure spirit comes out of a person, it goes through arid places seeking rest and does not find it.
44Then it says, ‘I will return to the house I left.’ When it arrives, it finds the house unoccupied, swept clean and put in order.
45Then it goes and takes with it seven other spirits more wicked than itself, and they go in and live there. And the final condition of that person is worse than the first. That is how it will be with this wicked generation.”