Proof by Contradiction and Reductio ad Absurdum

These are just some random thoughts. This time, it is only about the nuance of the words.

The logical method of assuming the negation of $${P}$$, deriving a contradiction, and concluding $${P}$$ is called proof by contradiction (hairi-ho). In the past, it was also called reductio ad absurdum (kibyu-ho). When comparing which term more directly describes this logical method, "kibyu-ho" is overwhelmingly superior to "hairi-ho".

Kibyu-ho: A logical method that leads to a fallacy (reductio ad absurdum). It is truly easy to understand.

Hairi-ho: A logical method that goes against reason. I have no idea what that is supposed to mean.

The reason "kibyu-ho" fell out of use is likely due to the Toyo Kanji list. Since the Toyo Kanji list also covered technical terms, many mathematical terms were affected and changed when it was enacted.

However, the situation has changed now. The Toyo Kanji list has already been abolished. The Joyo Kanji list, which was established in its place, explicitly states that technical terms are excluded. There is nothing left to prevent the revival of "kibyu-ho." Let us use "kibyu-ho" with pride.

With that said, I tried to write "kibyu-ho" on the blackboard in class, but I was discouraged by the number of strokes in the character "謬" (byu). I am sorry, I am still writing "hairi-ho" on the blackboard.