But Catholics have grown more concerned about the Pope's age and health and his future role in the Church.
On The CBS News Early Show Thursday, Father Richard McBrien, who is a theology professor at the University Of Notre Dame and author of Lives Of The Popes, said although John Paul is getting older, the significance is that he's the seventh longest-reigning pope in history. People are concerned about the Pope's overall health, but McBrien says they shouldn't worry about his mental capacity.
"However, the concern that people like me have is not whether he'll resign but whether he'll do something in the meantime to set up a system, legal system in the Catholic Church, to provide for a circumstance where he might lapse into a situation" of diminished mental capacity, said McBrien.
Father McBrien added that looking for the next pope "will be a safe choice:" Someone similar to Pope John Paul II.
The Pope's 80th birthday coincides with a jubilee of priests. CBS News Correspondent Allen Pizzey reports that more than 7,000 priests joined Pope John in celebrating Mass at the square. Special birthday masses were planned for churches throughout Poland.
At the start of the mass, the Pope's left hand trembled as he gripped his pastoral, which was preceded by words of affection pronounced by Cardinal Dario Castrillon Hoyos, the Colombian prelate who leads the Vatican's congregation for clergy.
"We feel guided by a man of God who has won love and respect beyond any human barrier. Truly the Lord prepared an athlete to tirelessly walk the paths of the world," said the cardinal, referring to a younger image of Karol Wojtyla, the robust Polish bishop who became pontiff in 1978.
The Cardinal then mentioned how the pope has been weighed down by ailments including tremors associated with Parkinson's disease. He offered thanks "for those white hairs, for the suffering that has made you even dearer in our eyes, for your physically tired steps so spiritually intrepid."
John Paul began the Mass by saying: "This is my confession of faith and my hymn of gratitude to the Father of life, who allows me today to celebrate the Eucharist with you with the exultance of the perennial youth of the Spirit on the occasion of my 80th birthday."
Later, in his homily, he said his birthday was "very significant for me" and while a chorus sang "alleluia" after the distribution of communion hosts, John Paul bowed his head, at times raising his clasped hands to his face, in apparent prayer or meditation.
Red roses decorated the altar area where the pope gave communion to some of the faithful chosen from the crowd.
At times his voice sounded tired. But he tells those closest to him that he still has goals.
"After more than 50 years of priestl life, I feel strongly within me the need to praise and thank God for his immense generosity," the pope said.
The pontiff whose staunch support of Poland's solidarity labor movement is credited for helping bring about the demise of Soviet bloc communism, seemed to be acknowledging his role in history.
God, he said, wanted to tie his existence as priest, bishop and pope to being a "witness to the love of God for all humanity in these times of ours, so fascinating."
But just last week, John Paul visited the shrine of the Madonna of Fatima, whose intervention he credits with sparing his life in a 1981 assassination attempt in St. Peter's Square.
After the pontiff placed before the Fatima statue a gold ring given him by his mentor, the late Polish Cardinal Stefan Wyszynski, newspapers speculated the gift meant John Paul is about to relinquish the papacy. The Vatican immediately branded the speculation as "150 percent wrong."
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