The challenge, he admits, is to explain why it is that mathematical statements 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。

youdao

In the syntactic stage, his whole work can be described as attempts to build criteria of validity-analytic definitions - for logic-mathematical statements.

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。

youdao

Those who espouse discovery note that mathematical statements are true or false regardless of personal beliefs, suggesting that they have some external reality.

那些“发现说”的支持者们指出，数学陈述的对和错与个人的信仰无关，从而表现出某种客观现实性。

youdao

I'll show those again, but what I want to do mostly today is try to put a mathematical statement of the second law in place that corresponds to the verbal statements that we saw last time.

今天我还将跟你们讲这些，但今天的重点是,对上次口头表述内容中的热力学,第二定律,的数学推导,我们上次看到的。

麻省理工公开课 - 热力学与动力学课程节选