The subject of this thread is taken from Dr. Lee's quotation of Calvin from his book,Baby Belief before Baptism, page 355. Calvin is critical of the practice of allowing unordainable women baptize dying infants (I'm assuming no ordained or ordainable man is present), "Joachim [Westphal] holds the necessity for baptism to be so absolute -- that he would sooner have it profaned by illicit usurpation,than omitted when the lawful use is denied."

My question is: Under what circumstances should a Reformed parent allow his or her child to die unbaptized? And, how would the answer vary for confessors of the 39 Articles, Westminster, the Second Helvetic, and the London Baptist confessions?