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It is not the case that It is possible to prove that something of a certain sort does not exist.
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1.
If the description of a kind of object is self-contradictory, then no such object can exist.
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2.
A circular square is a self-contradictory object because it would have to be both circular and non-circular simultaneously.
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3.
We can prove that no circular square exists on the basis of this self-contradiction.
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