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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".
Since the negation of ∀x (E(x)) is a contradiction,
then ∀x (E(x)) is a tautology,
and therefore ∀x (E(x)) is true regardless of the domain of x.
Absolutely anything exists
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화면 에러뜨노
무슨 언어인가요 이건?
∃x (¬E(x)) 존재하지 않는 것이 존재한다는 건가요?
네
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