Complex sentence: Classical mathematics permits (and requires) the existence of undefinable objects, but many people find this philosophically disquietening, questioning how an object can be said to exist if no mathematical statement can be used to uniquely identify it.
Split into simpler sentences: Classical mathematics permits (and requires) the existence of undefinable objects. Some people find this philosophically disquietening, questioning how an object can be said to "exist" if no mathematical statement can be used to uniquely identify it.