What is "there exist"

Usage examples of "there exist".

Can you think that something sublime, like the Earthly Paradise, could exist in so many copies, as there exist so many cities with a river and a hill like that of Saint Genevi&egrave.

They do not know what Emperor is reigning, and there exist doubts regarding even the name of the dynasty.

He knew well that there exist on the Asian continent many things which defy analysis.

Holtzinan did there exist a mind capable of the insights of a genius, the data recall | of a major corap, and the daring of a 'thoptcr racer.

Does there exist, I wonder, some method of formulation whereby these astounding truths might be reduced to some lawful mathematick?