기적의 논리
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R(x) : exists in reality
E(x) : exists
1. ∀x (¬R(x) → E(x))
The negation of 1 is
2. ∃x (¬R(x) ∧ ¬E(x))
2 is a contradiction ("∃x" vs "¬E(x)")
Therefore, 1 is true
Conclusion
∀x (¬R(x) → E(x))
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M(x) : exists in the mind
1. ∀x (¬R(x) → M(x))
The contrapositive of 1 is
2. ∀x (¬M(x) → R(x))
2 is false, therefore 1 is false
The negation of 1 is true
The negation of 1 is
3. ∃x (¬R(x) ∧ ¬M(x))
Conclusion
∃x (¬R(x) ∧ ¬M(x))
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1. ∀x (E(x))
The negation of 1 is
2. ∃x (¬E(x))
2 is a contradiction ("∃x" vs "¬E(x)")
Therefore, 1 is true
Conclusion
∀x (E(x))
∀x (E(x)) and ¬∃x (¬E(x)) are equivalent.
The meaning of ¬∃x (¬E(x)) is "Something that does not exist does not exist".
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