An existential statement is one which expresses the existence of at least one object (in a particular universe of discourse) which has a particular property.
That is, a statement of the form:
- $\exists x: P \paren x$
- $\exists$ is the existential quantifier
- $P$ is a predicate symbol.
- There exists at least one $x$ (in some given universe of discourse) which has the property $P$.
In the existential statement:
- $\exists x: \map P x$
the symbol $x$ is a bound variable.
Thus, the meaning of $\exists x: \map P x$ does not change if $x$ is replaced by another symbol.
That is, $\exists x: \map P x$ means the same thing as $\exists y: \map P y$ or $\exists \alpha: \map P \alpha$. And so on.
Conditionally Existential Statement
A conditionally existential statement is an existential statement which states the existence of an object fulfilling a certain propositional function dependent upon the existence of certain other objects.
Absolutely Existential Statement
An absolutely existential statement is an existential statement which states the existence of an object without that existence being dependent upon other conditions.
Also known as
An existential statement can also be referred to as a existential sentence, or more wordily, a sentence of an existential character.
- 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) ... (previous) ... (next): $\S 1.3$: Universal and Existential Sentences
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 3$: Statements and conditions; quantifiers