I have argued in many posts, such as here and here, that when denominations are separate from each other they are necessarily (assuming a presbyterian system of church government) exercising discipline against each other, charging each other with schism, and rejecting each others' de jure legitimacy and authority.
A person might accept this basic line of reasoning but partially object to the conclusion, perhaps, in this way:
"OK, I accept that churches are exercising ecclesiastical discipline against each other when they refuse to be united to each other denominationally. I accept that they are not accepting each other as sister churches in good standing. But perhaps they are not entirely, but only partially, rejecting each others' de jure legitimacy and authority. To make a comparison, a presbytery might suspend a pastor from certain rights and duties ordinarily associated with his office without entirely revoking his pastoral role or authority. For example, they might suspend his right to vote in presbytery meetings while refraining from suspending his right to function as a teacher in his congregation. Likewise, perhaps two denominations might put each other partially under discipline and revoke some of each others' rights, such as the right to vote in a common general assembly, while still assigning some rights to each other, such as the right to rule over congregations, etc."
This is my response to this line of argumentation:
1. First of all, I acknowledge that the argument is correct in pointing out that what it describes could, theoretically (with some qualifications, as noted below), be a state of affairs between two churches. In this case, the denominations would not be entirely separate from each other but only partially separate.
But there are problems with this argument as well, both theoretical and actual:
2. As a matter of fact, no denomination actually understands its relationship to another denomination in this way. The OPC and the FPCS, for example, do not have any formal relationship with each other whatsoever. There is no formal granting of any rights, responsibilities, or duties, from one denomination to the other. There is nothing in the minutes of any OPC court which acknowledges FPCS pastors or elders to be on the roll of the church as pastors and elders, but under some specific disciplinary action. Nor is there anything like this in the records of the FPCS. But this is the sort of thing we would have to see in order to acknowledge that the situation suggested by the above argument actually describes any currently existing state of affairs.
3. There are also serious theoretical impediments to such a scenario. If the OPC, for example, were to formally recognize FPCS officer and church courts as being formally recognized but under partial discipline, it is still the case that the FPCS would not agree to this characterization of itself. FPCS courts and officers would not acknowledge themselves as being under discipline and as having any rights or duties revoked, and so they would continue to function as if they are not under such discipline. It would be absurd for such a situation to carry on indefinitely. If a presbytery brings discipline against an individual session, it expects that session to acknowledge that it is under discipline. If the session refuses to acknowledge or submit to the judgment of the presbytery, the session will end up sinking deeper and deeper into stronger discipline until its authority is finally entirely revoked. Thus, such a situation will be naturally unstable and tend to dissolve into complete separation before too long.
4. Another theoretical impediment is that it is difficult to imagine a sensible state of discipline in which voting rights in a higher church court are denied while full rights to rule over and teach in a congregation are maintained. If a church court is not deemed competent because of sin or error to have a role in voting in a higher church court, why would they be deemed competent to rule or teach in a congregation? Are the latter functions less important than the former? If anything, I would think it would be the opposite, though I would say they are of equal importance. Again, therefore, I would think that such a situation would be naturally unstable and, if anything, would simply be a very temporary stepping stone to either reconciliation or complete separation. Such a situation would surely not constitute a long-lasting (even centuries-long!) permanent relationship.
For these reasons, therefore, I do not believe we can see the relationship between existing denominations in the way the argument envisions. Rather, the kind of denominational division that actually exists between the various denominations today involves a refusal to grant any formal recognition to the de jure legitimacy and authority of other denominational church courts (though it does not necessarily involve rejection of the de facto being of the visible church in the various denominations).
(Someone might argue that fraternal relations between denominations constitute a form of partial de jure communion, but I would say that they do not. Fraternal relations do not involve the formal granting of any rights or responsibilities to officers and church courts as such beyond denominational lines, or any acknowledgement that one denomination considers the other denomination to be under partial discipline. I think that fraternal relations--assuming they have any coherent meaning at all in a presbyterian context--are best understood as an institutional recognition by one denomination that another denomination is a de facto part of the visible church of Christ along with a commitment to take certain steps of dialogue and action intended to work towards eventual de jure communion. I discuss these ideas a bit more here and here.)
UPDATE 4/8/13: Just briefly, I might add that I question whether a situation such as described by the argument dealt with above could even accurately be described as a situation involving separated denominations. When a session is under discipline by a presbytery, we don't say they have become (even partly) two separate denominations. We don't say they are now in "partial communion." Rather, we look at the situation as two bodies that are in the same denomination, in full communion, but with one body under the discipline of the other. So if was the case that the OPC looks at the FPCS as another branch of the formally recognized church, subject to mutually-binding councils but under discipline, I don't think we would describe this situation as one in which we have two distinct denominations interacting with each other. Rather, we would say there is one denomination in which one body is under discipline from another body.
But this is not the situation between the OPC and the FPCS (or between any other divided denominations). The fact is that the OPC and the FPCS are indeed separate denominations because they simply have no formal recognition of the de jure existence, legitimacy, or authority of each others' courts and officers.