Undergrad Difference between Constructive proof and Existential Generalization?

[StevenJacobs990]

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.

 

[stevendaryl]

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.