Mormons often argue that when Jesus appointed twelve Apostles to lead his Church he intended that the Church would continue to be led at all times by twelve such apostolic leaders. Catholics, instead, believe that the Apostles were the original twelve, but that they were to appoint leaders who, by the laying on of hands (i.e., the sacrament of ordination) would share in the vocation of leading the Church with all that that entailed. Thus, Catholics often refer to the whole priesthood as the “college of the twelve” (CCC 1577). For Catholics, the term ‘the twelve’ can be considered a sort of short-hand, in some contexts, for the original apostles and/or for the priesthood. Mormons take issue with such a claim.
Here’s an interesting connection I’ve never made before though; when Jesus rose again he is said in scripture to have appeared to the twelve (1 Corinthians 15:5). In fact, most scholars are in agreement that the creedal statement repeated in 1 Corinthians 15:3-5 is of extremely early origin (within 3-5 years of the crucifixion), and so consequently one cannot argue convincingly that the term ‘the twelve’ was anachronistic – as though it were developed in accordance with a later Church’s imagination. So, the early Church professed her faith very early on in these words; that Jesus appeared to the twelve. Obviously, however, Judas had already hung himself, and his replacement, Matthias, hadn’t taken his place until well after Jesus’ ascension (Acts 1:9, Acts 1:26). Therefore, Jesus had not appeared to all twelve at once. So, the early Church obviously thought that the group of Apostles could be referred to collectively as ‘the twelve’ even when there weren’t actually twelve of them. It seemed significant that Jesus chose twelve apostles in order to indicate that he was founding the true ‘Israel’ (Matthew 19:28), but beyond that it doesn’t seem to have made much of a difference to the early Church whether at any time there were in fact twelve such persons – they had developed the habit very early of referring to the group of Apostles as the twelve. So, when Paul recounts the creedal statement which says that Jesus appeared to the twelve, even though it was actually to ten or eleven (see John 20:19-24 and Luke 24:33, Mark 16:14, Matthew 28:16), we are to take that to indicate that Jesus appeared to the ‘Apostles’. Since the term ‘the twelve’ was already in the earliest Church being applied to the Apostolic leaders of the Church regardless of how many of them there were, perhaps this provides an argument of a kind for the Catholic perspective, according to which the fact of there being twelve was only important insofar as it indicated a purpose already fulfilled by there being twelve original apostles. Perhaps the reason Matthias was chosen to replace Judas was, apart from the prophetic, pragmatic or kerygmatic motivations, in order to insure the Church against the charge of being founded upon twelve pillars one of whom had defected. It was thus, more than anything, a symbolic act – one in which Peter meant to safeguard the dignity of Christ and the Church by providing the Church with twelve firm pillars. The foundations of the Church were solid, and to exemplify this a replacement for Judas was needed. However, there’s obviously no indication in either the New Testament or Christian history that there was ever any concern to do this again or to replace one apostle with one and only one successor.