¿Qué significa Those who prefer their principles over their happiness, they refuse to be happy outside of the conditions they seem to have attached to their happiness. ?

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This is very deep. It's basically talking about people who want happiness, but must have it in a certain way only. Otherwise it won't make them happy. So that means they don't place happiness at the top of their priorities, they place their principles. When their principles are met, or the "happiness" is not against them, or in the way of their principles, then and only then will they be happy, if that makes sense.

They have conditions in place, and, if they have with a chance at happiness, but these conditions aren't met or fulfilled, these people won't be happy.