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Positivism is the name for (at least) two philosophical directions. They have in common the idea of a science without theology or metaphysics, based only on facts about the physical / material world.

Structural anthropologist Edmund Leach described positivism during the 1966 Henry Myers Lecture:
Positivism is the view that serious scientific inquiry should not search for ultimate causes deriving from some outside source but must confine itself to the study of relations existing between facts which are directly accessible to observation.

Positivism is also the name of a legal view, usually called legal positivism. Against natural law, it claims that a legal system can be defined independently of evaluative terms or propositions. Sometimes legal positivism is also understood as the view that the law must be obeyed, whatever its content. The late Carlos Nino used to distinguish between these two varieties by calling the former 'methodological' and the latter 'ideological', claiming that only the first was philosophically defensible.