1.NounA singular statement that states the existence of its subject.
"The statement Jesus exists is a singular existential statement, because it is a singular statement and it states the existence of its subject."
2.NounIn Popperian epistemology, a statement that contains the equivalent of an existential quantifier and one or more proper names.
"The statement In 1697, during the expedition of Dutch explorer Willem de Vlamingh, there were black swans on the Swan River in Australia is a singular existential statement, while There are black swans is not."