Difference between Constructive proof and Existential Generalization?

  • #1
What is the difference between Constructive Proof of existence and Existential generalization?

Logically they seem to be the same because, for a given predicate and specific member of the predicate's domain, you are concluding the general statement about the predicate.
 

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  • #2
stevendaryl
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There are many varieties of constructive logic, but most of them can be thought of as placing additional restrictions on classical logic. So every rule of constructive logic is also a rule of classical logic, but not vice-versa. Both constructive logic and classical logic consider existential generalization valid.In contrast, constructive logic does not consider ##\exists x F(x)## equivalent to ##\neg \forall x \neg F(x)##, while classically, they are equivalent. So it's not that constructive logic has a special way to prove existential statements, it's that classical logic has additional (nonconstructive) ways to prove them.
 

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