Quote: On profound truths

"The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth."
- Niels Bohr

I do not find this quote self-explanatory. What did he mean by that? And nowhere on the internet does there seem to be any information on the context of the quote. All I know is that the quote is unsourced, but a variant appeared in a book by Niels Bohr's son. Internet, you have failed me!

At first, I thought the quote was criticizing "profound" truths. How true can it be, if its opposite is equally true? Perhaps we've been tricked by the profundity or cleverness in how it was stated. I find it is useful, whenever I come across an obvious truism, to consider the truism's opposite. If you find two truisms that are nearly opposite of each other, that's an indication that neither of the truths give the complete picture.

Examples? It's hard to think up examples on the spot, but take a look at a few posters from Despair.com. It just goes to show that even cynical ideas can be made to sound profound. Of course, the opposite of a profound idealistic truth is not always a profound cynical truth, sometimes it's another profound idealistic truth. Like mercy and justice or something.

But anyways, the evidence is not backing me up on my interpretation here. I suspect that Niels Bohr was actually thinking of wave-particle duality or "complementarity", whatever that means. That is just too bad because I don't think wave-particle duality is nearly as profound as popular science makes it out to be. So... light sometimes acts like a particle and sometimes acts like a wave. Pretty cool, yes, but did you know that the earth sometimes looks flat, and sometimes looks like a pale blue dot? Neither particle nor wave, neither flat-earth nor blue dot gives you the complete picture, and that's that.