数学是逻辑的延伸，而且数学的概念和边界非常明确，一个集合中的元素可以是完备的，“不存在”本身当然是可以被证明的。
I am not exactly clear what he implies. However, majority of the "exist or not," or to be more mathematical, set membership problem, is undecidable. That means in general, “不存在”本身是不可以被证明的。As a matter of fact, there are more undecidable problems in mathematics than decidable.