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Sure good can exist without evil. Consider the nature of the two -- evil is parasitic on good. No person ever commits an evil act for the sake of evil, but for the sake of some good. For example, someone might do something evil for the sake of money, or for the pleasure. But people do perform good deeds merely for the sake of good -- not because it gives them pleasure or otherwise benefits them. Or, looking at it another way, good is a prerequisite for evil. You can't commit an evil action without having some good thing. Power is the easiest example here. You have to have some power to do something evil, but power is itself a good. So we can see that evil cannot exist without good, but the relationship is asymmetrical. So good can exist without evil.
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"Die Deutschen meinen, daß die Kraft sich in Härte und Grausamkeit offenbaren müsse, sie unterwerfen sich dann gerne und mit Bewunderung:[...]. Daß es Kraft giebt in der Milde und Stille, das glauben sie nicht leicht."
"The Germans believe that power must reveal itself in hardness and cruelty and then submit themselves gladly and with admiration[...]. They do not believe readily that there is power in meekness and calm."
-- Friedrich Nietzsche
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