English 中文(简体)
为什么能证明这一合乎逻辑的说法?
原标题:Why can t this logical statement be proved?

下面,我看不出第二次发言与第四次发言有何不同。

我认为,我们可以证明,21个是自然的,我们可以证明是2个。

您是否解释了为什么可以证明第二份声明,而第四份声明不能或它们如何不同? 谢谢。


The following English statements are logical statements:

  • 0 is a natural number
  • 2 is a natural number
  • For all x, if x is a natural number, then so is the successor of x.
  • 21 is a natural number

<>序言:

 natural(0).
 natural(2).
 For all x, natural(x) → natural(successor(x))
 natural(21).

Among these logical statements, the first and third can be viewed as axioms for the natural numbers: statements that are assumed to be true and from which all true statements about natural numbers can be proved. The second statement can be proved:

2 = 继承(successor(0)和自然(0)-自然(sucessor(0))-自然(successor(0))>。

另一方面,第四篇声明不能从轴心中证明,因此可以假定是假的。

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