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1. One who stubbornly believes or adheres to outdated, outmoded, and/or debunked theories, ideologies, ideas, or beliefs, despite overwhelming evidence against them. Taken from the now disproven belief that the Earth is flat, rather than spherical. There are too many flat-earthers in these parts, holding on to things their ancestors believed.
2. One who literally believes the Earth is flat. Flat-earthers have invented all kinds of ways to defend their conspiracy theory.