g****y
发帖数: 323 | 1 Suppose we have finite number of symbols.
Words are made of these symbols.
Sound means that only true statements can be proved.
complete means all true statements can be proved.
Godel proved that
in any logical system there exist TRUE theorems which CANNOT BE PROVEN
on the basis of the axioms and operations of that system.
Which means
There are TRUTHS that are not scientifically verifiable.
or you can say:
There are TRUTHS that are in the realm of the subjective. They can never
be proven true.
G | q*****g
发帖数: 1568 | 2
只要承认现在的逻辑和算术, 一切包括它们的体系就不可能是完备的.
换句话说, "现实世界要比形式逻辑世界复杂得多" 只是加强了这一结论
而已. 其实这个结论一点都不希奇, 我们的确不能够从逻辑推出绝对真理,
因为逻辑推理是纯粹的演绎过程, 而从现在的逻辑体系来看, 这需要一个
不言而喻的起点----公理. 公理为什么是对的是不可证的.
另外一点就是, 哥德尔不完全定理是基于现在的逻辑和算术体系的.
对于非策莫罗公理体系, 他并没有给出结论. 也许以后的人们可以解决
这一问题也未可知. |
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