A beneficent spirit, guardian angel, or supernatural being in Greek philosophy and theology that guides and protects a person throughout their life.
From Greek eu- (well) + daimon (spirit), literally 'good spirit.' The concept developed in Greek philosophy where each person was believed to have a personal daimon assigned to help guide them toward virtue and happiness.
Your eudaemon is basically what modern people might call your 'conscience' or 'better nature'—Socrates believed he had an inner voice from his daimon that warned him against bad decisions, and the idea influenced later concepts of guardian angels in Christianity.
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