The challenge, he admits, is to explain why it is that mathematicalstatements can be definitively true or false, not subject to taste or whim.
他承认，挑战在于如何解释数学陈述的真假与口味或者一时兴起无关。
2
In the syntactic stage, his whole work can be described as attempts to build criteria of validity-analytic definitions - for logic-mathematicalstatements.
在句法阶段，他的整个工作可以描述为寻找一个逻辑—数学陈述的有效性标准(分析性的定义)的努力。
3
Those who espouse discovery note that mathematicalstatements are true or false regardless of personal beliefs, suggesting that they have some external reality.