| Existential generalization | |
| Type: | Rule of inference |
| Field: | Predicate logic |
| Statement: | There exists a member x Q |
| Symbolic Statement: | Q(a)\to \exists{x}Q(x), |
In predicate logic, existential generalization[1] [2] (also known as existential introduction, ∃I) is a valid rule of inference that allows one to move from a specific statement, or one instance, to a quantified generalized statement, or existential proposition. In first-order logic, it is often used as a rule for the existential quantifier (
\exists
Example: "Rover loves to wag his tail. Therefore, something loves to wag its tail."
Example: "Alice made herself a cup of tea. Therefore, Alice made someone a cup of tea."
Example: "Alice made herself a cup of tea. Therefore, someone made someone a cup of tea."
In the Fitch-style calculus:
Q(a)\to \exists{x}Q(x),
where
Q(a)
Q(x)
x
a
According to Willard Van Orman Quine, universal instantiation and existential generalization are two aspects of a single principle, for instead of saying that
\forallxx=x
Socrates=Socrates
Socrates\neSocrates
\existsxx\nex