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According to the Stanford encyclopedia (entry: Copernicus):

Pope Clement VII (r. 1523–1534) had reacted favorably to a talk about Copernicus’s theories, rewarding the speaker with a rare manuscript. There is no indication of how Pope Paul III, to whom On the Revolutions was dedicated reacted; however, a trusted advisor, Bartolomeo Spina of Pisa (1474–1546) intended to condemn it but fell ill and died before his plan was carried out (see Rosen, 1975). Thus, in 1600 there was no official Catholic position on the Copernican system, and it was certainly not a heresy. When Giordano Bruno (1548–1600) was burned at the stake as a heretic, it had nothing to do with his writings in support of Copernican cosmology, and this is clearly shown in Finocchiaro’s reconstruction of the accusations against Bruno (see also Blumenberg’s part 3, chapter 5, titled “Not a Martyr for Copernicanism: Giordano Bruno”).

The presented argument is based on the fact (Thus, in 1600…) that there is no formal decision reached against the heliocentric system. However, heliocentrism runs counter to the Aristotelian system and in the next few decades we see the ban of Kepler’s (1621), Copernicus’ (1616) and Galilei’s works (1633), on top of personal excommunication, during two different popes.

The distinction between mathematical, i.e. having to do with tools in calculation, and physics describing the actual cosmological state of affairs seems also to be an issue. According to Grant:

Only at a much later date, when it became evident that this work of Copernicus was not intended for mathematicians alone; when it became clear that the blow to the geocentric and anthropocentric Universe was deadly; when certain of its metaphysical and religious implications were developed in the writings of Giordano Bruno, only then did the old world react and attempt to suppress the new ideas of the universe by the condemnation of Copernicus in 1616 and of Galileo in 1632.”

Grant E., In Defense of the Earth's Centrality and Immobility: Scholastic Reaction to Copernicanism in the Seventeenth Century, American Philosophical Society, Vol. 74, Part 4, 1984.

I therefore wonder if – on the contrary - the opposite may be true, namely that there was a great deal of opposition to the heliocentric system both long before and after 1600.

Edit:Let me mention this is leading up to the burning of Giordano Bruno, and the sentence in the Stanford encyclopedia: ”When Giordano Bruno (1548–1600) was burned at the stake as a heretic, it had nothing to do with his writings in support of Copernican cosmology.” I believe it did.

I suggest – fully accepting that Bruna most likely was a pompous pain in the ass, likely to make enemies wherever he found an audience, on top of misunderstanding Copernicus’ system, and that there was no formal ban on Heliocentrism - that the Church was not only biased, but extremely biased, against it since it implied that Aristotle was completely wrong on a central issue in his teaching. The interest from the church that is sometimes reported might have been due to the mathematical or calculation aspect of astronomy. There is no other way to e.g. explain the inserted introduction in Copernicus’ De revolutionibus.

Also, I don’t believe cardinal Bellarmine, mentioned below, ever had a completely open mind on the subject. He was being careful in his earlier mention that there was no proof of Heliocentrism. The issue of proof in the Vatican year 1600 is a mixture of logical scientific and theological arguments.

On the contrary, he personally ordered Galileo 16 years later, 1616 “to abstain completely from teaching or defending this doctrine and opinion or from discussing it... to abandon completely... the opinion that the sun stands still at the center of the world and the earth moves, and henceforth not to hold, teach, or defend it in any way whatever, either orally or in writing.” (Wikipedia entry: Heliocentrism).

Edit 2 I just learned that the letter where Ballarmine express an open mind of heliocentrism is dated April 4 1615, a year before he express a very solid view against it.

I believe that Bruno - or opened up for - the connection between ideas from the reformation and the Copernican system, and that the political, theological and scientific issues became connected in way that made the issue red hot. It was probably not so hot before Bruno and I can offer that the Church’s opposition to Heliocentrism was growing during the period, and therefore perhaps somewhat less before his work was known.

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    The absence of evidence, far from being evidence of existence, is actually evidence of absence. Live with it. – Pieter Geerkens Aug 4 at 21:42
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The opinion of the Church on heliocentrism was not officially stated by 1600. This means that there was no Church opinion. People, including cardinals and popes could have their own opinion, and these opinions varied. You can read in Wikipedia and elsewhere how this official opinion was gradually formed. At the time of the process of Galileo, Copernican system was not officially prohibited, but it was required that it is represented as a "mathematical hypothesis", not the "description of reality", until there is a conclusive proof. (This point of view was stated by cardinal Bellarmine, so it is not completely clear whether this can be called the official opinion of the church.)

Galileo thought that he had a proof, and this (and other things) led to a conflict with the Church.

In fact Galileo's principal "proof" was wrong, by the way. Copernicus book was initially censored (some sentences removed, and a foreword added), but eventually it was placed in the Index of prohibited books in 1616. So one cannot say that there was a definite "Church opinion" in 1600.

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    The sentence "Copernicus book was initially censored, but finally it was placed in the Index of prohibited books in 1616" is worded in a very confusing way. What is it trying to say? My understanding is that "initially censored" was the same as being "in the Index of prohibited books". Are you claiming otherwise? Noting that they are the same, or perhaps that they aren;t the same? i can make neither head nor tail of the sentence. – Pieter Geerkens Aug 7 at 22:09
  • @Peter Gerkins: No, your understanding is incorrect. By "censored" I mean that several phrases were removed, and a foreword was added, explaining that heliocentrism is a mathematical hypothesis rather then description of "how the things are". – Alex Aug 8 at 0:16
  • I now read that " on All Heresies, published in Venice in 1590, specified that it is a heresy to “assert that the Holy Spirit is the soul of the world, as taught by Peter Abelard.” (Deciani, 1590, 236)" which Bruno did reg. the anima mundi. From theologie-naturwissenschaften.de/en/… – Mikael Jensen Aug 9 at 17:53
  • The fundamental problem of the Galileo Myth is that while Galileo was a very great scientist, he wasn't a very good one. He made major advances, but was terribly sloppy -- as noted, he supported the Copernician theory which had already been proven wrong by observation (orbits are not circular, so Copernicus couldn't reproduce planetary motions at all well). He had more than a small tendency to claim credit that wasn't all his, and he was a rather nasty character, personally. This means that the science is often window dressing for a fight about other things. – Mark Olson Aug 10 at 0:36

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