'antidogmatically' originates from English, formed from the prefix 'anti-' (against) + 'dogmatic' (from Greek 'dogma'), where 'anti-' meant 'against' and 'dogma' meant 'opinion' or 'that which is thought'.

'dogma' comes from Greek 'dógma' via Late Latin 'dogma' and Medieval Latin/Old French into Middle English as 'dogma' and 'dogmatic'; the combining of English 'anti-' with 'dogmatic' produced 'antidogmatic', later extended with '-ally'/'-ally' to form 'antidogmatically'.

Initially it meant 'against doctrine or asserted opinion' (i.e., opposing set doctrines); over time it has been used specifically to mean 'in a manner rejecting dogmatism' without asserting fixed principles.