In a way that is contrary to established religious doctrine; in a manner characterized by heresy.
From heretical (adjective form of heretic) + -ly (adverb suffix). The adverb form emerged naturally from the adjective heretical, allowing description of heretical actions or beliefs in adverbial contexts.
When historians describe someone acting 'heretically,' they're usually describing someone thinking independently about religion in a society where the church demanded conformity—making heretical thought another word for free thinking.
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