Blackwell Reference Online

Extract

L ogic A rule of inference in predicate calculus that introduces existential quantifiers . If a statement fa contains a free variable a , it can be generalized into (∃ x ) fx . Using an example in ordinary language, we can generalize from “Socrates is mortal” to “Someone is mortal.” Existential generalization is a process that generates an existentially quantified statement from one instance of it. This is valid on the assumption of predicate logic that at least one thing exists in the universe. Existential generalization contrasts with existential instantiation , which generates one instance, say fa , from an existentially quantified statement like (∃ x ) fx . “Existential generalization … carries us from a theorem f to a theorem (∃x)Ψ where φ is like Ψ except for containing free occurrences of ‘y’ in all the positions in which Ψ contains free occurrences of ‘x’.” Quine, From a Logical Point of View ... log in or subscribe to read full text