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Yes, a lot of people still believe in superstitions, despite clear and contradictory evidence (or rational explanations for the origin of a superstition).
"Despite the evidence presented, the facts are irrelevant in this case!"
No, the government is not the Illuminati, though there are those who believe the Illuminati has an effect on the government. But, there are those who believe JFK, Elvis, Tupac, and Michael Jackson are all alive, living in the basement under the White House, despite evidence to the contrary.
Delusion
They are not mutually exclusive. A lot of religious people believe in evolution, and a lot don't, despite the evidence (fossil records etc) It's a personal choice whether to be religious, and whether to believe in evolution or not. If you aren't really bothered about either, you can just not think about it.
It isn't. At least not by Earth scientists! There is no reason based on the evidence to believe that there are significant void spaces (i.e. caverns) within the mantle (despite what you might see in films such as "The Core").
The police arrested suspects, but they did not have any hard evidence.
delusion
There is no evidence that Tim Burton is a Satanist, despite many rumors to the contrary.
A theory can be disproved, but despite the weight of evidence in its favour, it can never be proved.
David bundled the cat outside despite its protests.She got the job despite her bad behavior during the interview.Despite making every possible effort by producing new evidence, they could not reduce the sentence of the prisoner.I'll answer this question despite my inclination to let people do their own homework.
Puppets are not alive, despite what the ventriloquist/puppeteer might lead you to believe.