Just a brief response to Doug’s thoughtful post here.
Doug says that my citizenship analogy (that just because an infant does not partake of communion does not mean that his membership in the visible church is questioned; and that this is analogous to citizenship in the US, where infants are not allowed to drive even though they are full US citizens) is faulty because communion is not primarily a matter of physical ability. I would say that indeed communion is not just a matter of physical ability. It takes spiritual discernment as well. All the more reason why infants should not partake! I would use his argument the other way. If it were merely a physical thing to do, then any infant that can eat solid food should participate. As we know, communion is not just a physical thing. For the paedo-communion argument to work, communion must become passive other than the bare eating.
But what is the mark of belonging to the visible church? Is it baptism, communion, or both? We have to be careful here. I affirm that the only necessary sign for belonging to the visible church is baptism. But what then of the visible/invisible church distinction? Obviously, not everyone who partakes of communion is regenerate. However, it is the duty of the church elders to fence the table as best they can. This involves judging fruit. If by their fruit you will know them, then elders need to judge by fruit (to the best of their ability: no one can know the heart of another person perfectly) whether a person should be admitted to the table or not. The question then becomes this: is the Table the sign of the visible church or the invisible church? Which unity does it signify? No doubt PC advocates will accuse me here of bifurcating the church into two churches simply by asking the question. But if that is the case, then the entire distinction between visible and invisible is moot. I would argue that it is the sign of the invisible church, even if some partake who do not belong to that invisible church.
This claim involves understanding the nature of covenant theology. If the covenant of grace is properly made with Christ and the elect seed in Him, then when Christ said that this was the sign of the new covenant in His blood, then the body and the blood signified by bread and wine are signifiers of the essence of the covenant of grace. Baptism is the sign of the administration of the covenant of grace (since it is given regardless of a profession of faith), not the essence of the covenant of grace. This argument could be fleshed out a great deal more, but here it is in bare outline.