Do you mean that he is the mouthpiece of a General Council, or that he is infallible independently?

The Pope is not merely the mouthpiece of a Council. He may, and usually does, consult other Bishops before giving an infallible decision. But he need not do so, and in the ultimate analysis the infallibility of a definition is due to his own personal authority. The infallibility of the Pope simply means that in his official teachings or definitions, provided he speaks as supreme head of the Church in questions of faith or morals and with the intention of binding all the faithful, God would not allow him to define erroneous doctrine. The Pope, as successor of St Peter, is Vicar of Christ, and the final court of appeal in the Church. But all the conditions I have enumerated must be present. The Pope’s word is not infallible whenever he speaks, though his decisions are always to be received with respect. But if he speaks merely as a private theologian, expressing his own views his opinions could be mistaken. Infallibility attaches to his decisions only when he speaks in his supreme and official capacity as supreme teacher of all the faithful.

Radio Replies Volume 1 by Rev. Dr. Leslie Rumble MSC and Rev. Charles Mortimer Carty