Not only can we provide examples, they have been common knowledge for decades.
Before you make silly demands like this, you should at least take a cursory look around.
I'm not very impressed by the wiki link you provided.
It is basically a series of descriptions of various theories of the decline and fall. They are categorized under four heads. I.Decay owing to general malaise, II.Monocausal decay, III.Catastrophic collapse, IV.Transformation.
I.This includes Gibbon; Vegetius; Arnold J. Toynbee and James Burke; Michael Rostovtzeff, Ludwig von Mises, and Bruce Bartlett; Joseph Tainter; Adrian Goldsworthy. A very impressive list of thinkers. To make your mental picture of this subject as complete and accurate as possible, you would have to study every one of these authors.
But not a single one invalidates Gibbon. There may be differences of emphasis; these authors fill out the picture, they flesh out the details, but they do not paint an entirely different picture.
For example, Toynbee and Burke, and their idea "that the Roman Empire itself was a rotten system from its inception, and that the entire Imperial era was one of steady decay of institutions founded in Republican times." I certainly can believe that a process like this was at work.
But at the same time, there could be a parallel process, such as "a loss of civic virtue among the Roman citizens, in which they gradually entrusted the role of defending the Empire to barbarian mercenaries who eventually turned on them, with Christianity contributing to this shift by making the populace less interested in the worldly here-and-now, because it was willing to wait for the rewards of heaven." That is how Gibbon's idea is described, and I honestly do not understand how these ideas conflict. In fact, they harmonize with each other.
You do realize there is nothing new in the idea described as originating from Toynbee and Burke? It sounds a lot like the republican ideology of Machiavelli. Of course, we have to discard him, because his books are even older than Gibbon's (you guys are so prejudiced). But I have to point out that Machiavelli says very similar things, how Rome was doomed by the loss of republican virtues, the centuries of corruption, and so on.
And all of this compliments Gibbon. I see Christianity as a by-product of a dying society, the dream of a once free republic, who became a victim of her own military successes, and the strange gods from foreign lands that came with these conquests (strange gods like Jesus). Now enslaved to an emperor of their own making, these humiliated people dreamed of a spiritual freedom that they could no longer enjoy on the plane of reality. Jesus was the avatar of this dream, and Paul was his prophet.
II.Disease... Environmental degradation... Lead poisoning. Various theories are described under this heading. I think we can dismiss the theory of "monocausal decay" out of hand. Of course, the authors who study these specific physical factors, like environmental degradation, they have to be read. All such physical factors are critical to a more complete understanding, but they are not the end of the story.
The way I see it, every society faces certain challenges, threats, or limitations of a physical nature. A vigorous society, like a free republic, will find a way to overcome these obstacles. Imperial Rome, weakened by a preoccupation with the other world (caused by a religion that they themselves created), just lost the energy to keep going.
Man uses certain physical techniques to help him overcome the perils of nature, and once Christianity became established, the knowledge of these techniques fell into decline. The civil engineering of the Romans was very advanced, and to support this fact I draw your attention to the aqueduct, which I've heard still functions to this day. But in the middle ages, people could barely feed themselves, let alone remove their own waste according to the proper methods or get consistently sanitary water. It's as if they lost interest in the physical plane of reality. I wonder why?
III.J. B. Bury; Peter Heather; Bryan Ward-Perkins.
Once again, I do not see how this theory of "catastrophic collapse" contradicts Gibbon in any way. Of course natural catastrophes contributed to the fall, and Gibbon is explicit about this. At one point, he tries to calculate the death toll of a particularly brutal cycle of famine, disease, and war in Gaul, I think; his estimate is one third to one fourth of the population.
If Gibbon made an assertion like this, and he was wrong in a significant way (say it was more like one twentieth or less), then I would be more willing to lend you ear. As it is, I am beginning to suspect that there is some ulterior motive, or some hidden prejudice, behind your rejection of Gibbon.
By the way, the factual accuracy of Gibbon seems to be supported by your own wiki source: "J.B. Bury's main difference from Gibbon lay in his interpretation of facts, rather than disputing any facts." In other words, he does not dispute Gibbon's facts, because his facts are accurate.
But apparently, you guys know better than J.B. Bury. You can't cite any specific facts to convince me of your superior knowledge, so I am inclined to think this arrogant sense of superiority is due to reflexive prejudice.
IV.Henri Pirenne; Lucien Musset; Peter Brown.
There is certainly an element of truth to this "transformation" hypothesis. What often appears as a short, sharp shock, sometimes appears from a more detached perspective to be a gradual continuity. Once again, this is nothing but a slight elaboration of emphasis.
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In conclusion, I have come to detect a hidden prejudice behind your rejection of Gibbon. No specific mistakes of Gibbon are cited. I increasingly get the feeling that you reject Gibbon, not because of some flaw in his method, but because you disagree with his conclusions. If his conclusions were more in line with your preconceived beliefs, then you would be more forgiving.
2 + 2 = 4. This fact is true, has always been true, and will always be true. It is true in the year of our lord 2012, just as it was true in 1776.