Going back to the OP - Inter-subjective is a concept I employ a great deal myself. To put it simply,
Objective = true in all possible worlds
Subjective = true for me
Inter-subjective = true for us
Objectivity arises from the existence of a thing or the validity of a value whether or not there is a perceiver to perceive it. Subjectivity arises from what I know to perceive, and inter-subjectivity is what I perceive that, by the operation of my mind/brain/society/humanity I and others like me know or realize that it is something with truth in the context perceived.
I use it particularly in discussions of ethics. Can moral values be said to be objective, i.e. true in all possible worlds? I don't think so. A world in which intelligent life doesn't exist, or a God, would have no extra-mentally existing morality in the same way that a rock exists apart from our perceiving it. Can moral values be said to be subjective? Yes, but it seems clear there is something about at least some moral values that require a nearly universal application in a social context. To say that I believe murder to be wrong but someone else has the right to commit it is almost a moral equivalent of a fallacy, because I can't believe it is wrong to kill me yet at the same time allow someone to kill me without reproach, not to mention my own self-preservation instinct in the equation.
But what you can say is this - in a social context the collection of human beings working toward common survival creates certain emergent phenomena that requires the members to participate in a way that promotes societies goals of protection. Then you start to get toward an intersubjectivity. Humans qua humans will work in a social context in a certain way and thus a "truth" emerges that applies equally to all members of that society.
Dread is a sympathetic antipathy and an antipathetic sympathy.
-- Soren Kirkegaard
In the geometric proof of life you don't always get the Given.
-- Some kid from my high school days