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In
predicate logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...
, existential generalization (also known as existential introduction, ∃I) is a valid
rule of inference In the philosophy of logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions). For example, the rule of in ...
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 known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...
, it is often used as a rule for the
existential quantifier In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, w ...
(\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 Fitch notation, also known as Fitch diagrams (named after Frederic Fitch), is a notational system for constructing formal proofs used in sentential logics and predicate logics. Fitch-style proofs arrange the sequence of sentences that make up the ...
: : 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 individuals ...
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

*
Inference rules In the philosophy of logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions). For example, the rule of i ...


References

Rules of inference Predicate logic {{Logic-stub