A lot of people claim that it is impossible to prove a universal negative. For example, while we may not have evidence that unicorns or dragons exist, we cannot prove that they do not exist. Unless we have a complete knowledge of the universe, we must admit the possibility that somewhere in the universe, there might be such creatures.
But the claim that omniscience is needed to prove a universal negative presumes that the concept which we are discussing is logically coherent. If the attributes which we assign to a hypothetical object or being are self-contradictory, then we can conclude that it /cannot exist/, and therefore /does not exist/. I do not need a complete knowledge of the universe to prove that cubic spheres do not exist. Such objects have mutually-exclusive attributes which make their existence impossible. A cube, by definition, has 8 corners, while a sphere has none. These properties are completely incompatible -- they cannot be held simultaneously by the same object.
Source: http://www.update.uu.se/~fbendz/library/cd_impossible.html
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