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The difference is that the non-Catholics in this case do not reflect truth. The atheist was reflecting false objections in the field of theodicy (the part of philosophy dealing with the existence of God), yet that's the specific point you endorsed. The heretic was denying an unambiguously defined doctrine of the Church (after it was defined), yet you brought him in as if he was an authority on that very doctrine.

Just so others will see what you are talking about I shall put my quote in context:



48. On the other hand, how different and much more faithful a reflection of limitless visions is the language of an outstanding modern scientist, Sir Edmund Whittaker, member of the Pontifical Academy of Science, when he speaks of the above-mentioned inquiries into the age of the world: “These different calculations point to the conclusion that there was a time, some nine or ten billion years ago, prior to which the cosmos, if it existed, existed in a form totally different from anything we know, and this form constitutes the very last limit of science. We refer to it perhaps not improperly as creation. It provides a unifying background, suggested by geological evidence, for that explanation of the world according to which every organism existing on the Earth had a beginning in time. Were this conclusion to be confirmed by future research, it might well be considered as the most outstanding discovery of our times, since it represents a fundamental change in the scientific conception of the universe, similar to the one brought about four centuries ago by Copernicus.”

 

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'The heretic was denying an unambiguously defined doctrine of the Church (after it was defined), yet you brought him in as if he was an authority on that very doctrine' you said.

 Now Stanley, will you show us all the defined doctrine you are referring to?

I think the framework of your view makes way more infallible (or "irreformable") statements than even conservative theologians writing after 1870 think. I happened to check the Galileo affair in the old Catholic Encyclopedia, and it says the Index can not define doctrine. (This is much more fundamental than your arguments about who signed what.)

Catholic Encyclopedias are written by men but you would like us to think they were written by the Apostles.

Again, when churchmen believed the geocentrism of the 1616 decree was proven wrong by science, they conjured up a story of the Galileo case to 'get the Church off the hook.' Now the Catholic Church does not need anyone to get it 'off the hook' as God protects its decrees on matters of faith and morals. As it turned out it was found that the geocentrism of the Bible has never been proven false.

To demonstrate the credibility of Stanley'sd preferred version, all I need do is show how the deception was carried out. One never absent from the Apologists version is the use of Bellarmine's 1615 Letter to Foscarini, put in a context that could fool the Catholic world.

Bellarmine was addressing the illusion that Galileo had found proof for heliocentrism. Here is what he actually said:

‘Third. I say that if there were a true demonstration that the sun was in the centre of the universe and the Earth in the third sphere, and that the sun did not travel around the Earth but the Earth circled the sun, then it would be necessary to proceed with great caution in explaining the passages of Scripture which seemed contrary, and we would rather have to say that we did not understand them than to say that something was false which has been demonstrated. But as for myself, I do not believe that there is any such demonstration; none has been shown to me. It is not the same thing to show that the appearances are saved by assuming that the sun is at the centre and the Earth is in the heavens, as it is to demonstrate that the sun really is in the centre and the Earth in the heavens. I believe that the first demonstration might exist, but I have grave doubts about the second, and in a case of doubt, one may not depart from the Scriptures as explained by the holy Fathers.

So what does Stanley's version say:

It is clear, moreover, that the authors of the judgment themselves did not consider it to be absolutely final and irreversible, for Cardinal Bellarmine, the most influential member of the Sacred College, writing to Foscarini, after urging that he and Galileo should be content to show that their system explains all celestial phenomena — an unexceptional proposition, and one sufficient for all practical purposes — but should not categorically assert what seemed to contradict the Bible, thus continued:

I say that if a real proof be found that the sun is fixed and does not revolve round the earth, but the earth round the sun, then it will be necessary, very carefully, to proceed to the explanation of the passages of Scripture which appear to be contrary, and we should rather say that we have misunderstood these than pronounce that to be false which is demonstrated.

Now here we find the Catholic Encyclopedia using a private 1615 letter to try to undermine a papal decree issued a year later. But worse, these encyclicals always twist Bellarmine's words to make it look like a dogma for the future of the Catholic church. What Bellarmine said was Galileo had no proof in the PRESENT TENSE, but look how the Encyclopedia made it look like he was talking in the future tense.

Final PROOF that Catholic Encyclopedias since 1913 can deceive even the elect, note Bellarmine's letter says: IF REAL PROOF BE FOUND THEN...' Now tell me that the writer of this item DOES NOT BASE HIS ARTICLE ON THE FACT THAT THE LOT OF THEM IN THE CHURCH BELIEVED PROOF HAD BEEN FOUND.

And on this basis, they conjured up a deception to try to undermine the fact that in 1616 a papal decree had found geocentrism as truth of scripture.

Second, as I just noted, the 1616 assessors report covered two propositions, but only one was evaluated as contrary to Scripture, namely the sun's rest and centrality. Current science happens to coincide on rejecting the sun's rest and centrality.

You mean only one defined as heresy!

(1) “That the sun is in the centre of the world and altogether immovable by local movement, was unanimously declared to be “foolish, philosophically absurd, and formally heretical, inasmuch as it expressly contradicts the declarations of Holy Scripture in many passages, according to the proper meaning of the language used, and the sense in which they have been expounded and understood by the Fathers and theologians.”

In red we see the term movement is QUALIFIED.

Here is one example:

“Then Josue spoke to the Lord, in the day that he delivered the Amorrhite in the sight of the children of Israel, and he said before them: Move not, O sun, toward Gabaon, nor thou, O moon, toward the valley of Ajalon. And the sun and the moon stood still... Is it not written in the book of the just [now lost]? So the sun stood still in the midst of the heaven, and hasted not to go down the space of one day. There was not before nor after so long a day, the Lord obeying the voice of a man, and fighting for Israel.” --- (Josue 10:12-13).
 
The MOVEMENT of the heresy then is the daily course of the sun, not the supposed movement of the sun you would like to give it to avoid that heresy.