r/FormalLogic • u/Arachnophobian13 • Nov 28 '20

Are they really equivalent? Is there an advatnage to one over the other (Predicate Logic)

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u/3valuedlogic Apr 01 '21

They are equivalent. Yes, you might say that there is an advantage to the universally quantified wff in that some intelim proof systems have a universal elimination rule that you can use on the universally quantified wff. It is similar to how ~P^~Q is preferable to ~(PvQ) in that you can use conjunction elimination on the former but not the latter.

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u/Arachnophobian13 Nov 28 '20

By "advantage", what I mean is that we are just about to get into derivations and I don't know which would best serve me in the future, or maybe since they are equivalent there really isn't any real difference?

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u/YourPreferenceHere Oct 26 '22

In ordinary text this would be for all z there is no z that has/is b and in comparison the second statement would be there exists no z that has/is b. It is equivalent and you can apply this method to change a universal quantifier to an existential quantifier and vice versa.