## 关于哥德尔“上帝必然存在”的本体论证明。

http://tieba.baidu.com/f?kz=758125585
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□ ↔ ¬◇¬ （必然↔不可能不）
◇ ↔ ¬□¬ （可能↔不必然不）
□¬ ↔ ¬◇ （必然不↔不可能）
◇¬ ↔ ¬□ （可能不↔不必然）

Axiom 1: Any property entailed by — i.e., strictly implied by — a positive property is positive.
{Pos(φ) ∧ □ ∀x [φ(x) → ψ(x)]} → Pos(ψ)

Axiom 2: A property is positive iff its negation is not positive.
Pos(ψ) ↔ ¬Pos(¬ψ)

Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.
Pos(φ) → ◇ ∃x [φ(x)]

Definition 1: x is God-like iff x has as essential properties those and only those properties which are positive.
G(x) ⟺ ∀φ [Pos(φ) → φ(x)]

Axiom 3: The property of being God-like is positive.
Pos(G)

Theorem 2: The property of being God-like is consistent.
◇ ∃x [G(x)]

Axiom 4: If a property is positive, then it is necessarily positive.
Pos(φ) → □ Pos(φ)

Definition 2: φ is an essence of x iff for every property ψ, x has ψ necessarily iff φ entails ψ.
φ ess x ⟺ φ(x) ∧ ∀ψ {ψ(x) → □ ∀y [φ(y) → ψ(y)]}

Theorem 3: If something is God-like, then the property of being God-like is an essence of that thing.
G(x) → G ess x

Definition 3: x necessarily exists iff every essence of x is necessarily exemplified.
exemplified.
NE(x) ⟺ ∀φ [φ ess x → □ ∃y φ(y)]

Axiom 5: Necessary existence is a positive property.
Pos(NE)

Theorem 4: Necessarily, the property of being God-like is exemplified.
□ ∃x G(x)

## 对一道关于三扇门赌局的概率问题的解答

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1.无论你是否选中车，他都会打开另一扇没车的门。（此时换选就是2/3得车）
2.只要你没选中车，他就会打开另一扇没车的门。（此时换选就是100%得车）
3.只要你选中了车，他就会打开另一扇门。（此时换选就必然没车）
4.以上策略的概率混合策略……（根据不同的混合，换选会有不同的概率得车）