The greater mind is one that can articulate a conclusion of principle using logic. The smaller mind is one that focuses on matter irrelevant to whether a conclusion follows valid premises, such as the implementation of a principle, in an attempt to argue the merits of a conclusion.
A greater mind possessing legitimate objection to a conclusion could assert a conclusion does not follow because of X, where X is a logical fallacy fatal to the conclusion, and explain why if necessary.
A greater mind does not assert gibberish, gibberish, gibberish when presented a conclusion deriving from certain premises. Smaller minds do that sort of thing.
When presented with a conclusion the world is round deriving from certain premises the greater mind would not argue:
"The problem with absolutes is that they usually fall apart."
In the same way a greater mind would not respond the world can not be round because absolutely round worlds usually fall apart.
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