Bohr was referring to the underlying principles of a truth
that are mutually exclusive. Mutually exclusive principles are
incompatible with one another – they cannot be reconciled.
These principles are unable to both be true at the same time – if
one is right, the other must be wrong. Yet Bohr says that the
opposite of a profound truth is often another profound truth.
Can the opposite of something that is right still be right? That
depends on which side of your brain you ask.