This following is a reproduction of an attempt by Godel to prove the existence of God, a proof that emerged around 1970. The proof is courtesy of Clifford Pickover (2001) in his fantastic book, “Wonders of Numbers.”
拿来瞻仰一下,高者参透了点什么的都出来分享。
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Proof
Axiom 1. (Dichotomy) A property is positive if and only if its negation is negative.
Axiom 2. (Closure) A property is positive if it necessarily contains a positive property.
Theorem 1. A positive property is logically consistent (i.e., possibly it has some instance.)
Definition. Something is God-like if and only if it possesses all positive properties.
Axiom 3. Being God-like is a positive property.
Axiom 4. Being a positive property is (logical, hence) necessary.
Definition. A property P is the essence of x if and only if x has P and P is necessarily minimal.
Theorem 2. If x is God-like, then being God-like is the essence of x.
Definition. NE(x) means x necessarily exists if it has an essential property.
Axiom 5. Being NE is God-like.
Theorem 3. Necessarily there is some x such that x is God-like.
查到蹩脚的翻译仅供参考:
公理1:当且仅当一事物的否定为阴性的,该事物就是阳性的。
公理2:当一事物必然包括阳性的性质时,该事物的性质即为阳性的。
理论1:一个阳性的性质必然具有逻辑的一致性。
定义:当且当一事物所有的性质均为阳性时,它便拥有上帝的特征。
公理3:一事物具有上帝的特征,他便具有阳性的性质。
公理4:具有阳性的性质是合乎逻辑的,因而也是必然的。
定义:当且当X拥有特征P并且P必然是最基本的性质时,那么特征P即为X的本质。
理论2:如果X具有上帝的特征,那么具有上帝特征的存在便是X的本质。
定义:当X具有一种基本的性质,X便必然存在。
公理性:一种必然的存在便是上帝的特征。
理论3:肯定存在某些X,这些X具有上帝的特征。