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Is the rule of universal introduction necessary to predicate logic derivations?
Wiki User
∙ 15y ago
It depends what you mean by "necessary". There is a choice of different systems for (classical) predicate logic, but they all give the same results.
Universal introduction is certainly a valid principle in predicate logic, so the question is: Does universal introduction have to be one of the basic rules of the system?
The answer is no. It can be a derived principle. It is even possible to introduce "for all" as a derived symbol, and only have "there exists" in the basic system. The basic system would have a couple of rules controlling "there exists", and from these rules universal introduction would be a derived principle.
Wiki User
∙ 15y ago
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