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In
predicate logic First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables ove ...
, existential generalization (also known as existential introduction, ∃I) is a valid
rule of inference Rules of inference are ways of deriving conclusions from premises. They are integral parts of formal logic, serving as norms of the Logical form, logical structure of Validity (logic), valid arguments. If an argument with true premises follows a ...
that allows one to move from a specific statement, or one instance, to a quantified generalized statement, or existential proposition. In
first-order logic First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over ...
, it is often used as a rule for the
existential quantifier Existentialism is a family of philosophy, philosophical views and inquiry that explore the human individual's struggle to lead an Authenticity (philosophy), authentic life despite the apparent Absurdity#The Absurd, absurdity or incomprehensibili ...
(\exists) in formal proofs. 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\, Q(x) , where Q(a) is obtained from Q(x) by replacing all its free occurrences of x (or some of them) by a.


Quine

According to
Willard Van Orman Quine Willard Van Orman Quine ( ; known to his friends as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century" ...
,
universal instantiation In predicate logic, universal instantiation (UI; also called universal specification or universal elimination, and sometimes confused with '' dictum de omni'') is a valid rule of inference from a truth about each member of a class of individual ...
and existential generalization are two aspects of a single principle, for instead of saying that \forall x \, x=x implies \text=\text, we could as well say that the denial \text \ne \text implies \exists x \, x \ne x. The principle embodied in these two operations is the link between quantifications and the singular statements that are related to them as instances. Yet it is a principle only by courtesy. It holds only in the case where a term names and, furthermore, occurs referentially. Here: p.366.


See also

* List of rules of inference * Universal generalization


References

Rules of inference Predicate logic {{Logic-stub