Mountaineer 1: "The highest mountain is K2."
Mountaineer 2: "But there is a higher mountain: Mt Everest."
Mountaineer 1: "Yes, but there is no mountain higher than K2."
Mountaineer 2: "That is an illogical statement. If there is a mountain higher than K2, then K2 is not the highest mountain. K2 can't simultaneously be the highest mountain, and yet not the highest mountain. Since your statement is logically incoherent, it is false that 'the highest mountain is K2.'"
II. Atheism vs Theism
Atheist: "The greatest conceivable being exists only as a concept, but not in reality."
Theist: "But there is a conceivably greater being: the one that exists both as a concept and in reality."
Atheist: "Yes, but the greatest conceivable being exists only as a concept."
Theist: "That is an illogical statement. If there is a conceivable being greater than the one that exists only as a concept, then the being that exists only as a concept is not the greatest. The greatest conceivable being cannot simultaneously be the greatest, and also not the greatest. Since your statement is logically incoherent, it is false that 'the greatest conceivable being exists only as a concept but not in reality.'"
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