You're right, no Pope can change the Mass essentially, and Paul VI was not a Pope.
That's circular logic.
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Yet, it is within a true Pope's power to introduce a new rite of Mass
This is only accurate if you qualify the statement and say that the "new rite" is essentially the same as the previous rites. No pope has the power to introduce a brand new,
substantially different from Apostolic times, rite.
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and even make changes to the canon (as St. Gregory the Great did when he introduced the Pater into the canon)
The Pater is not part of the canon, so he didn't change the canon.
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provided they do not change the essence of the rite, yes? As a true Pope can make any changes he desires provided, only being limited by Tradition itself.
The parameters of Tradition and non-essential changes are VERY BIG parameters. So when you say a pope can do "anything he desires" that's quasi-contradictory. It would be like taking your car to the paint shop and saying, "You can paint anything you want, in any style, but I only want my bumper painted red to match the rest of my car." It's a stupid statement because you say "anything" but then define this word to mean something very specific.
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Because these changes were made, in an effort to change the essence of the rite itself, is proof positive that Paul VI could not have been a legitimate Pope.
Again, circular logic.
1. A pope has no authority to change the essential parts of the mass.
2. Paul VI changed the essential parts of the mass.
3. Therefore, such changes are illegal and without authority.
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Inserting the idea that he's illegitimate, AS A POPE, makes no sense, because
it's his act that's illegitimate, not his papacy.
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If you want to argue that he's not the pope
based on 10,000 other reasons, then ok. But simply because a pope issued an illegal order doesn't mean he loses his entire authority.