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inconceivable (adj.)1630s, from in- (1) "not, opposite of" + conceivable. Related: Inconceivably; inconceivability. An Old English word for this was unasmeagendlic.
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incogitable (adj.)"unthinkable, inconceivable," 1520s, from Late Latin incogitabilis "unthinking; unthinkable," from in- "not" (see in- (1)) + cogitabilis "thinkable, conceivable," from stem of cogitare "to think" (see cogitation).
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