(a) Dr John Kennedy - a Victorian Free Church man - says that the standard for someone wanting their child to be baptised is a "credible profession" i.e. they themselves have been baptised as children and their life and conduct is in keeping with the Christian faith.
(b) Whereas if someone is asking to take the Lord's Supper for the first time they should have an "accredited profession" i.e. they should speak to the Kirk Session about their faith, experience and knowledge.
It probably worked better as Kennedy said in the Highlands where at one time there were many true Christian people who didn't come to the table because of lack of assurance of faith. The system in the Lowlands where people coming for baptism for their children were asked to become communicant members in order to get baptism, was less productive of, protective of, and nurturing of, spirituality and established Covenant lines of descent, according to the good Doctor. I can certainly see that it's unwise to insist that everyone who gets baptism for their child must be a communicant member. What if you believe that one or both parents are believers and they are living in accordance with God's Word?
Those in category (a), i.e. people who have been baptised and don't take communion and want baptism for their child and have a credible profession of faith, have become fewer and fewer even in the Highlands, so fewer of those who aren't communicant members will get baptism. People who don't become communicant members are less and less likely to have a credible profession of Christian faith.
Kennedy looks upon baptism as the "outer door" of the visible Kingdom of God, whereas the Lord's Supper is the "inner door" of the visible Kingdom of God.
Here's the book online:-
http://www.archive.org/details/thedaysofthefath00kennuoft
See chapter four for how things were ordered in the Highlands and still will be in many congregations, Although there will be many fewer in category (a).
Some ministers abused it by not seeking a credible profession of faith on the part of those seeking baptism for their children. It also partly depends on how baptismal vows are couched.
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The Wiki article is simplistic. How many had been saved in a covenantal way as children, maybe before they could remember, and maybe lacked assurance and therefore didn't come to the Lord's Supper ?
The KJV translation of I Corinthians 11:29 is :-
For he that eateth and drinketh unworthily, eateth and drinketh
damnation to himself, not discerning the Lord's body.
I don't know what it was in the Geneva and other translations.
How many weak and gentle minds were intimidated by the word "damnation", if this was in many of the Bibles of the time, even with the explanation and reassurance of their pastors?
I believe that Rutherford and other Lowland ministers of the seventeenth century followed the policy outlined by Kennedy, although things had changed by the nineteenth century at least in the southern part of Scotland.
We know of whole families being circumcised in the Old Covenant before anyone partook of the Passover. And possibly whole families in the NT being baptised before anyone tasted the Supper.