the doctrine of papal infallibility became standard Catholic teaching only at the time of the first Vatican Council in 1870, by which time Galileo had been dead for several hundred years. Nor is the doctrine of papal infallibility that Pope is never wrong, nor that the Pope never makes mistakes; whether one accepts it or not, it is a much more circumscribed teaching than that. Finally -- and this is an important point -- Galileo was ultimately tried under a Pope who had often had friendly meetings with him about scientific matters and who gave him political advice on how to avoid a conviction: the advice was essentially that Galileo should simply describe the Copernican system as a convenient device for accurate calculation, rather than insisting that the Copernican system was absolutely true, but Galileo did not follow this advice; Galileo instead persisted in regarding his mathematical models as
absolutely true until he had alienated enough conservative clergy to guarantee a conviction; the irony, of course, is that the Church, motivated by a desire to preserve its traditional authority against contemporary challenges (such as the Reformation) took what we today would regard as a more sophisticated and more modern philosophical view of scientific model building than the really great scientist Galileo did, though Galileo's practical scientific work was far better than any of his inquisitors could understand
THE CHURCH IN CRISIS: A History of the General Councils: 325-1870
CHAPTER 20. The First General Council of the Vatican, 1869-70
http://www.christusrex.org/www1/CDHN/coun21.html... The following four criteria must be present in order for a papal teaching to be considered
ex cathedra, that is, infallible. The Pope must teach as supreme doctor (teacher) of the whole world ... The Pope must be defining a doctrine of faith or morals. No other subject matter pertains to our salvation ... The Pope must make his intention known by clear words that he is defining a doctrine contained in the deposit of faith, and binding upon the consciences of men ... The Pope must attach the sanction of anathema to the decree, either explicitly or implicitly ...
The Infallibility of the Pope — Basic Facts About an Essential Dogma
http://catholicism.org/apologetics-infallibility.htmlThe Trial of Galileo
by Doug Linder (2002)
http://www.law.umkc.edu/faculty/projects/ftrials/galileo/galileoaccount.html