In a way that uses opposite or ironic meaning; by saying the opposite of what you mean.
From antiphrastical + -ly (adverbial suffix). Traces back through Greek anti- (against) and phrasis (speech) with the productive English adverbial ending.
When you add '-ly' to an adjective, you create an adverb that describes how something is done. So 'antiphrastically' describes the manner of speaking ironically—it's the adverb version of the irony itself.
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