There is tremendous power in being able to simultaneously hold two ideas in one’s head that appear to be in opposition. Contradictions can create boundaries on thoughts—it’s usually unpleasant to have cognitive dissonance—and can lead to dogma. I’ve found that being able to stick with it, despite the discomfort, can be very powerful.
Here are a few examples:
Controlled self-deception where it’s optimal to be overconfident while fully aware of the role of luck plays in being successful.
A strange loop gives rise to human selfhood which is so powerful it is the thing we find to be the most real. Mindfulness shows us that the self is an illusion. Holding both ideas gives a much greater understanding of human nature.
Optimism that there is something new to find while also knowing there is pre-existing effort you will duplicate and trying to know the unknowable will lead to pessimism.