Where might is master, justice is servant.
So… I don’t think the translation is relevant.
Trying a straightforward translation I get:
When you go beyond the irrational, it becomes right.
Unless in this case 通る means go along, in which case, maybe it makes more sense:
When you go along the irrational, it becomes reason.
That is, if you are constantly exposed to irrational behavior, it becomes the norm.
I have actually found an explanation (in Japanese) here:
@mike-lima
The English sentence is a proverb. If you are not comfortable with the English-Japanese pair, you need to change the Japanese translation, not the English proverb. But the Japanese sentence is one of the major translations, and I think it sounds natural and makes sense.
Let me give you all a follow-up explanation of the Japanese sentence structure.
通る (とおる; intransitive verb) and 通す (とおす; transitive verb) are common collocations for 無理, 我 (が; selfishness) or 要求 (ようきゅう; demands). 通る/通す means “to pass through” or “to penetrate”. So the connotation of 通る/通す is “there are obstacles to BREAK through to make it happen.” It’s not “to go ALONG”.
車がその道を通る (くるまがそのみちをとおる) means “a car takes the route” but the etymological origin is “the car occupies the pathway and other people and vehicles (obstacles) are forced to move away in order to clear it off.” — of course, we in the modern civilized society don’t have to clear it off. But I hope you get the image of 通る/通す.
無理 means “impossibility” or “irrationality”. When 無理が通る or someone does 無理を通す, there are obstacles to break through (e.g. other people are against the irrational idea and you need to kill the objection.)
“Might” in English means “a power of a supreme kind”. Someone with might can kill the objection.
If you prefer a more word-for-word translation in Japanese, an alternative would be 無理が通れば道理引っ込む (むりがとおればどうりひっこむ). 引っ込む = 引く (to pull) + 込む (to enter) = to retract, recede, or back off. Particle が is intentionally dropped from the second phrase 道理が引っ込む because it’s a standard technique in proverbs and poems.