One undercurrent beneath the Federal Vision business is a hidden difference in epistemological assumptions. The Hellenistic method strips accidents away from the thing, looking for essences. The Hebraic way of definition adds layer upon layer, looking at the thing from as many different angles as possible, and in as many situations as possible. Peter Leithart talks about this latter way of knowing in his book The Kingdom and the Power, and there is also a section on it in Angels in the Architecture.
This leads to an assumption on the part of the former that once you have a “definition,” it is time to stop, and defend that orthodox definition against all comers. We can see this tendency in the definitions of the visible/invisible Church, or with statements about “outward” Christians and Christians “inwardly.” But I have no trouble with these distinctions, as far as they go. Yes, there are Christians outwardly and Christian inwardly. But I then want to take this matter under discussion and look at it from numerous other directions, trying grasp the whole by means of addition. In contrast, the Hellenistic approach to definition (and I am not using this pejoratively; there is an important place for this kind of definition) seeks to understand by means of subtraction. How much can we take away and still have the thing we are talking about? But the temptation is then to disallow other approaches, approaches that may operate with a different set of descriptive rules. The Hebraic way gives us man worshipping, man playing, man eating, man making love, man working, man sleeping, and man writing poems. The Hellenistic way gives us a featherless, bipedal carbon unit.
For the Hellenistic approach, a true Christian is one who is one inwardly, period, stop. And this is true. But I also want to say that we have inward Christians and outward Christians, faithful Christians and adulterous Christians, temporary Christians and Christians forever, slaves and sons, wheat and tares, sons of Hagar and sons of Sarah, washed pigs and washed lambs, fruitless branches and fruitful branches, Christians who die in the wilderness and Christians who die in Canaan, and so on.
Now if someone of the other party thinks that I am essentially doing the same thing he is doing (that is, picking one and one only out of this list in order to make it the “true” definition), he has every right to be concerned. For example, if we are limited to one, then inward/outward is one of the best metaphors. But it is a metaphor, and needs other metaphors. If I were to isolate “fruitless branches and fruitful branches” to the exclusion of all others, and make it “the definition,” then I have become an Arminian. I think that this is what our critics are worried about. But we are not seeking to substitute; we are seeking to layer.