'apodictic' (base of 'apodictically') originates from Greek, specifically the word 'apodeiktikos', from 'apodeiknumi' meaning 'to demonstrate', where the parts 'apo-' meant 'away, from' and 'deiknynai/deik-' meant 'to show'.

'apodictic' passed into Late Latin as 'apodicticus' and then into English (via scholarly/technical use) as 'apodictic'; the adverb 'apodictically' was formed in English by adding the adverbial suffix '-ally' to the adjective.

Initially it meant 'capable of being demonstrated' or 'that which can be shown', and it evolved into the current sense of 'logically certain; demonstrably true' used in careful or formal contexts.