In a manner relating to or supposedly characterized by clairvoyance; as if through supernatural clear-sight ability.
From clairvoyant + -ly adverbial suffix. Builds naturally on the adjectival form to create an adverb describing how something is done or perceived.
The fact that we can add '-ly' to almost any adjective means English constantly generates new adverbs for rare or specialized situations—'clairvoyantly' is grammatically perfect even if nobody uses it much, showing the generative power of English morphology.
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