Scott Clark is in the URC. In that tradition, when do children who were baptized in infancy generally come to the Table? They generally come when they have been catechized, which is when they are done or mostly done with high school. Then, when they are on the threshold of going away from home, they are fully brought into their home church. But this means that if we understand covenant community as being a full participation in koinonia, this is a tradition that does not really have any experience with covenant children. They are technically on the roster (having been baptized), but they have no experience of body life while they are children at all.
This comment highlights several defects in Wilson's thinking:
1) In the Reformed Churches, participation at the table is for those who can "discern the Lord's body." This was taught both by those who drafted the London Baptist Confession of Faith of 1689:
8. All ignorant and ungodly persons, as they are unfit to enjoy communion (m) with Christ; so are they unworthy of the Lords Table; and cannot without great sin against him, while they remain such, partake of these holy mysteries, (n) or be admitted thereunto: yea whosoever shall receive unworthily are guilty of the Body and Blood of the Lord, eating and drinking judgement to themselves.
m 2 Cor: 6,14,15.
n 1 Cor. 11.29. Mat. 7.6.
And also by those who drafted the Westminster Confession of Faith:
VIII. Although ignorant and wicked men receive the outward elements in this sacrament, yet they receive not the thing signified thereby; but by their unworthy coming thereunto are guilty of the body and blood of the Lord, to their own damnation. Wherefore all ignorant and ungodly persons, as they are unfit to enjoy communion with him, so are they unworthy of the Lord's table, and can not, without great sin against Christ, while they remain such, partake of these holy mysteries, or be admitted thereunto.
Thus, it can be seen that (on the topic of the sacraments) Doug Wilson does not have an historical connection to the Reformed churches, and to the extent that his comments reflect the general sentiments of the Federal Vision / Auburn Avenue Theology community, neither do they.
Now, of course, there are some who permit uncatechized (or only partially catechized) children to partake in the Lord's Supper. This would not automatically place a person outside of confessional subscription. Nevertheless, to have a policy of permitting all baptized members of the church to commune would be outside the bounds of Scripture and the historic Reformed doctrine.
Any pastor who does not fence the table to exclude ignorant adults and children is a bad shepherd, and his presbytery (or consistory) should consider whether such a man is fit to be a minister of the gospel. This is a matter sufficiently clear from Scripture that it has been adopted by both the Reformed Baptists and the Reformed Presbyterians.
To the extent that DW is advocating the idea that all baptized children and adults should participate in the Lord's Supper, his position is both clearly contrary to Scripture and (much less importantly) outside the Reformed community.
In other words, just so Frank Turk knows, (and, as best understood) DW does not represent us (Presbyterians, Reformed, and/or paedobaptists) - at least on the issue of the sacraments, and if DW has been understood correctly his fellow elders should take appropriate action to correct his doctrine.