Many of the forumlations belong to another age in the church, resulting from someone elses battles. They use the language of the time period and often bear little or no relation to the active faith of Christians, conservative, liberal, protestant or catholic today.
But if we are talking about the central doctrines of the Christian tradition that do hold sway, do command some level of alliegance, are meaningful for a broad cross section of the Christian church over time, I think we have some obligation to make sense of them.
Make sense of them in their historic formulation? Sure. But more important make sense of them in how they are understood, lived out today. That's a much wider category and will include all sorts of notions that I'm sure some church council condemned.
It's the way that these ideas get carried into the life of current and past communities, not just church councils, that determine the meaning and value of those ideas. If they have power, it's because those ideas make sense of one's life and experience.
We're not so much dealing with the unprovable as much as what refers back to experience. For instance, ancestor worship can make sense, if we think of our dependence on what our ancestors created for us. Atonement can make sense out of particular kinds of wrongs.
If it's possible to see what these ideas do for communities, what feature of experience they highlight it may be possible to reconstruct the symbol.Such a reconstruction would try to go for the same value that the idea has had, even if it's formulation is updated.
After all, the idea of earth is quite different from the 1500s or the 500s but it's still meaningful to talk about the idea, there is some continuity. And yet a difference. I'd suggest doctrines are much the same. They needn't rest on the unprovable but on experience and reformulated for present needs.