Proof: Existential Generalization

The rule of existential generalization (EG) allows us to move from a singular to a quantified statement. Such an inference has the following form:

(x) (...x...)


If we know that object a has property P, we can certainly infer that something has this property. If we know that Tom is both an actor and a waiter, we can infer that some actors are waiters.

In existential generalization, then, we replace a name with a variable and add an existential quantifier. When we do so, we must be sure to place the quantifier at the beginning of the statement, so that the entire statement falls within its scope.

Equivalence rule |
Universal instantiation | Existential generalization |
Existential instantiation | Universal generalization


© Copyright 1998, W.W. Norton & Co.