Apostolic Succession. When the qualifications of an apostle are considered, it is readily apparent that the idea of "apostolic succession" is a contradiction in terms. According to Acts 1:21, an apostle must have been in the company of Christ and the disciples during the years of his ministry on earth (Paul being an exception to this), an eye-witness to the resurrection, and a receive a specific, public calling to the office in the Church. it is impossible for anyone to meet these qualifications today. Moreover, when we consider that the redemptive-historic function of the apostles was to lay the foundation for the building of the church (see #3 below and Eph. 2:20), we also see the uniqueness of the office. I claim no expertise in building construction, but friends of mine who do assure me that only one foundation is laid. Afterwards one builds on the foundation already laid, which removes the function of the apostolate after the foundation-laying age.
What is striking to me here is the very first line. Rick seemingly attempts to refute the doctrine of apostolic succession by claiming that it is self-contradictory, since Apostles had to be witnesses of Christ's life and ministry. But the Catholic doctrine concerning apostolic succession does not mean that the episcopal successors of the Apostles are themselves Apostles. The Catholic doctrine concerning apostolic succession is that the Apostles handed on their authority and the stewardship of their teaching to their successors (i.e. the bishops) through the laying on of their hands, and that this handing on of the Apostles' authority and teaching stewardship was commanded by the Apostles to be a permanent practice in the Church, from each generation of bishops to the next. It is these bishops who have the authority to tell us what apostolic succession is, and how the Apostles passed on their teaching and authority. We do not have to choose between the following two options: either the Apostles ordained Apostles as successors, or the Apostles did not pass on their ecclesial authority to the bishops whom they ordained. That's a false dilemma. Of course it is true, as Rick notes, that the office of Apostle was unique, in just the way he says. But that doesn't entail that the bishops whom the Apostles ordained did not receive the ecclesial authority of the Apostles, or that there is no apostolic succession in that sense. The Church has always believed in apostolic succession, from the first century. That is what is meant by the term 'apostolic' in the line of the Creed: "I believe in one, holy, catholic and apostolic Church". I have discussed apostolic succession in more detail here, here, and here.