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Lady Justice is widely depicted as carrying a scales. A scales has the property that whatever pulls one side down, pushes the other side up. This makes things very convenient and easy to track. It's also usually a gross distortion.

In human discourse there is a natural tendency to treat discussion as a form of combat, an extension of war, a sport; and in sports you only need to keep track of how many points have been scored by each team. There are only two sides, and every point scored against one side, is a point in favor of the other. Everyone in the audience keeps a mental running count of how many points each speaker scores against the other. At the end of the debate, the speaker who has scored more points is, obviously, the winner; so everything he says must be true, and everything the loser says must be wrong.

--EY

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References

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