My understanding (drawn also in part from Tara Smith’s series of lectures, “Rationality and Objectivity”) is that objectivity, in the epistemological meaning, is a relationship between an idea in one’s mind and the facts of reality. The nature of the relationship is a logical one. In others, an idea (concept, principle, theory, or whole philosophy) is objective if it is drawn logically from facts of reality. It is not objective if the idea is arbitrary or is drawn from wishes, emotions, or imagined “messages” from God or other alleged sources.

While objectivity is a relationship, rationality is the process used to establish objectivity.