Supreme episcopal jurisdiction of the pope, enunciated as follows by the Vatican Council: "We teach and declare.that the Primacy of jurisdiction in the entire Church of God was immediately and directly promised and conferred upon the Blessed Apostle Peter by Christ the Lord".
The Scriptural proofs for the Primacy of Peter and for the Divine origin of the papacy are the same, viz., the Petrine texts: "thou art Peter; and upon this rock I will build my church," etc. (Matthew 16); "But I have prayed for thee, that thy faith fail not," etc. (Luke 22); "Feed my lambs. ..Feed my sheep" (John 21).
By these words Christ endowed the papacy with" all powers necessary to promote the unity of the Church.
The incumbent of the office was designated supreme legislator, judge, ruler, and teacher.
Primacy of jurisdiction implies that all legislative and coercive governing power is vested, in its plenitude, in one person.
It is more than primacy of honor (first among equals), or primacy of order (right to preside over and direct an as- sembly, e.g., as Speaker of the House), or primacy of responsibility (duty of inspection, as in the opinion of Anglicans in the Conversations of Malines).
By Divine institution the Primacy is perpetual; i.e., by the will of God, Saint Peter will always have a successor, in such a manner that he can be recognized as such.
Temporary vacancy, or obscurity regarding the person, does not destroy continuity of succession.
The Roman Pontiff is the recognized legitimate successor of Saint Peter.
New Catholic Dictionary