Antonyms of adj dogmatical

1 sense of dogmatical

Sense 1
dogmatic, dogmatical -- (characterized by assertion of unproved or unprovable principles)

INDIRECT (VIA narrow-minded) -> broad-minded -- (inclined to respect views and beliefs that differ from your own; "a judge who is broad-minded but even-handed")

Similarity of adj dogmatical

1 sense of dogmatical

Sense 1
dogmatic, dogmatical -- (characterized by assertion of unproved or unprovable principles)
       => narrow-minded (vs. broad-minded), narrow -- (lacking tolerance or flexibility or breadth of view; "a brilliant but narrow-minded judge"; "narrow opinions")