I would have to say truth, is subject to individual interpretation.
Meaning what one perceives to be true, may actually be false, in another's eye.So the exact opposite of what is true to one person...may be a falsehood in another's perspective, thereby creating another "great" truth.
Something you may find interesting, is this article on the theories of TRUTH, as related to cognitive science...Click this link:
maybe if the first great truth is a lie, then the other great truth is that the first one is a great lie.
The complete quote seems to be one of these:
There are trivial truths and the great truths. The opposite of a trivial truth is plainly false. The opposite of a great truth is also true.
The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth.
Clearly, Bohr is distinguishing here between things we can understand with our ordinary mind, and truths which are so profound they go beyond that ordinary understanding. Beyond that, his exact meaning is far less clear, and that may be the point of the quote.
I have seen his meaning explained in terms of quantum physics, where things can be correctly described in two seemingly contradictory ways, and both are true. I'm not good enough at Quantum physics to be able to expound on that.
Another way to try to approach his meaning is by comparing the great religions and trying to understand how they really say the same thing when they appear to be saying the opposite. For example, we can say Buddhists don't believe in God, but if you get far enough into Buddhism, you realize that what Buddhists believe in is some very "great or profound truths" that are not in their most profound sense different from the Christian idea of God.
Of course, trying to talk about that fundamental a level of truth is almost impossible, especially if one is not as much of a genius as Bohr. So I'll stop.
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