Existential quantification
An existential statement is a statement or assertion to the effect that at least one object (element, individual, event) of a certain object domain has a certain property, i.e. that the property in question applies to at least one object.
An example of an existential statement is the sentence "There is at least one tuberculosis patient in Berlin."
Modernly, existential statements are also called existential propositions, existential statements or existential/existentially quantified propositions. In traditional logic, existential statements are called particular judgements - for this, see Categorical Judgement.
The logical properties of existential statements are treated modernly in predicate logic and have traditionally been treated as particular affirmative and negative judgments in syllogistics.
In the formal language of predicate logic, existential statements are formed by quantifying over predicates or statement forms with the help of the existential quantifier. The existential quantifier is usually symbolized by one of the characters 
or 
.
Example of quantification:
- x is a Berliner [and] x is sick with tuberculosis
- (
) (x is a Berliner [and] x is sick with tuberculosis) (= "existence quantification" of Theorem 1). - There's something about a Berliner that's tuberculosis.
- Something is a Berliner and tuberculosis sick.
- Some Berliners have tuberculosis.
- Someone in/from Berlin has tuberculosis.
- A Berliner has tuberculosis.
The verification of an existential statement is done by proving that there is indeed an object with the claimed property in the object domain. The falsification of an existential statement requires that all objects of the reference area can be assessed. If this is not possible, an existence statement can only be disproved to a greater or lesser extent. In the empirical sciences, this sometimes leads to the assumption that existence statements are statements "that can be empirically verified but not empirically falsified".
See also
- All statement
- Logic
