换句话说，这些命题——就好像宗教信仰里面认为上帝创造了世界一样——必须有事实证据做为支撑，并且可以通过讨论和在现实世界中做实验的方式来加以证明。

In other words, they are claims - like the claim that God created the world - that are supported by evidence, that are proved by arguments and tested against our experience of the world.

youdao

高德的不完备定理的主要结论是，所有的逻辑体系都会存在无法证明或证伪的命题。 因此，所有的逻辑体系都不“完备”。

The main conclusion of Gödel’s incompleteness theorems is that all logical systems will have statements that cannot be proven or disproven; therefore, all logical systems must be “incomplete.”

youdao

作为课后作业，我们需要证明以下命题：如果灯过去是关着的，并且现在它是开着的，请证明有人按了开关我真的试着证明它了。我花了许多小时，试图证明这个命题。

For our homework, we had to prove the converse: if the light was off, and it's on now, prove that you flipped it.

youdao