Russell defined acquaintance as a direct, unmediated awareness of an object, a fundamental relation where one is directly aware of something without inference. For Russell, acquaintance is a fundamental and more primitive form of knowledge giving us direct access to Knowledge-of-universals.
As he writes,
“Our immediate knowledge of things, which we called acquaintance, consists of two sorts, according as the things known are particulars or universals. Among particulars, we have acquaintance with sense-data and (probably) with ourselves. Among universals, there seem to be no principle by which we can decide which can be known by acquaintance, but it is clear that among those that can be so known are sensible qualities, relations of space and time, similarity, and certain abstract logical universals.” (p.64)
He concedes that there is no principle to decide which universals are known by acquaintance, which shows the vagueness of this position. Why accept some universals are known directly, but not others?