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First-principles thinking consists of deriving things to their fundamental proven axioms in the given arena, before reasoning up by asking which ones are relevant to the question at hand, then cross-referencing conclusions based on chosen axioms and making sure conclusions don’t violate any fundamental laws.
In physics and other sciences, theoretical work is said to be from first principles, or ab initio, if it starts directly at the level of established science and does not make assumptions such as empirical model and parameter fitting.