In a manner involving logical refutation or proving contradictions; in the style of Socratic questioning and debate.
From 'elenchical' plus the adverbial suffix '-ly,' creating an adverb that describes how something is done in the elenchic method.
This adverb lets you describe someone's debating style perfectly—when someone 'speaks elenchically,' they're systematically showing you the holes in your logic rather than just telling you you're wrong!
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