This non-classical logic statement can be applied across many different domains (Language definitions). Apart from its application in logic, it is also a part of Buddhism. I find it to be of great value in philosophy and psychology as well. Especially when we hit antinomies of any kind (On the root of existence).
It still doesn’t give you a definitive answer, it might feel like a dirty or cheap trick, it might feel like it could be applied anywhere and solve everything. This is similar to what logicians call the principle of explosion.
But the key is to meditate on the paradoxical answers it does produce, and to understand that, epistemologically, you can never get an answer to the particular paradox/antinomy, or even if you could, after endless analytical calculations, the non-dual answer would still make more sense.
Take psychological issues as an example: when you try to assess if something is worth it or not. Analyzing such situations more and more leads to bigger problems most of the time. Such inquiries cannot be solved by over-analyzing. The key is to understand that using your current mental tools, context, and situation, you won’t be able to give a definitive answer. So it might be better for the issue/riddle/antinomy to resolve here and now, unfinished, as it is. And for the dilemma to be left as a nice shining gem of discovery, instead of fighting against the current. Maybe some of the answers that we are seeking lie in these boundaries.
However, we must keep in mind that in many cases we might just need to sharpen our tools of logic and scientific understanding to go beyond some of the antinomies, instead of relying on the paradoxes. The paradoxes that are important are of a different nature, orthogonal to logic and science. They have to do more with experiential qualities (The Light and the Logos).