In a manner related to or characterized by confession, confessionalism, or formal religious confessions; from the perspective of confessional theology.
From confessional + -ly (adverbial suffix). The adverb form allows the adjective to modify verbs and other adverbs, as in 'confessionally speaking' or 'confessionally committed.'
When historians write 'confessionally speaking' about a religious text, they're signaling that they're interpreting it through the lens of formal theological confessions rather than as historical documents, which is a technical move scholars use to frame their analysis.
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