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Is there a word for telling a person is rigid in what he believes, and cannot be swayed into changing his beliefs? Someone who cannot be convinced by reason or facts? A religious person may fall into that category, but I want a generic term that doesn't only consider religious beliefs, but also scientific among others.

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A few words that come to mind to describe someone rigid in their beliefs include being dogged, stubborn, uncompromising, dogmatic, hardheaded, obstinate, adamant, adamantine, or narrow-minded. If they are wrong, wrong-headed.

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Dogmatic or prejudiced would fit.

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Pig-headed may also fit

(adj) (derogatory) Obstinate and stubborn to the point of stupidity.

https://en.wiktionary.org/w/index.php?title=pigheaded&oldid=51989227

Or obstinate

(adj) Stubbornly adhering to an opinion, purpose, or course, usually with implied unreasonableness; persistent. 

https://en.wiktionary.org/w/index.php?title=obstinate&oldid=52355849

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