Antonyms for the phrase "by way of explanation" could include words such as "without clarification," "without elaboration," "unexplained," or "undisclosed." These antonyms would indicate a lack of detail or explanation, instead leaving the listener or reader to draw their own conclusions. Additionally, antonyms could include phrasing such as "without context," "with no background given," or "incomplete," further indicating the absence of necessary information. When writing or speaking, it is important to consider antonyms and their opposing meanings, in order to convey the intended message clearly and accurately.