Do you understand the term "synthesis?" I am not one of those who discounts the critical importance of Christianity in the founding of our civilization. However, Christianity was only one of the roots. The other was ancient Greek civilization, as modified by Rome.
I would never claim that medieval civilization owed much of anything to Mohammed as a person, or to Islam as a religion. However it really does owe a lot to Islamic civilization, which was based on the older Greek and Persian civilizations. The Arabs created little, but they were very effective at combining the elements they found in new and better ways.
One significant reason why the High Middle Ages took off when they did was the infiltration of new Greek works or in some cases better translations. These came from the Moslems, mostly thru Spain, or in some cases Sicily. The Church, which had always had a high regard for Greek philosophy, was faced with the task of figuring out how to fit these new (to them) texts and the ideas they contained into the edifice of Christian theology. This great mental challenge took many decades to be acomplished and created great controversy and was a huge stimulus to intellectual life.
The fact that medieval civilization was greatly influenced by contact with what was at the time the much higher Islamic civilization is not a new or PC idea, although it may be exaggerated by some for that reason. Recognition of this by Western historians goes back for many centuries.
I think you may be confusing a couple of ideas. One is the Afrocentric idea that the Greeks (and therefore Western civ) somehow "stole" technology from Africans and that therefore Western civ is invalid. The other is that all civilizations are influenced by other ideas with which they come in contact.
The second is true, the first is ludicrous. Very few civilizations have arisen in isolated areas. Cross-fertilization of ideas seems to be essential to the development of advanced civilizations. That some of these ideas were transmitted from Islamic cultures to Western cultures is not an insult to the West.
Healthy cultures are willing to absorb good ideas, whatever their source. It's like the English language, which never saw a word it couldn't absorb. Compare this healthy attitude to that of the French, who are trying desperately (and unsuccessfully) to keep their language "pure." Which language is thriving and which is losing influence?
Much of the decline of Islam is based on its isolating itself and rejecting outside influences, as the French language has done, only much more so.
Western culture is the English language of cultures. It thrives on the free and open market of ideas, not rejecting some because they are from outside its bounds.
With regards to Greek democracy, does Europe take more after that or the Germanic freeman? (Didn't both cultures have people provide for their own weapons - maybe they have a common source?)
A book I read part of about the Holy Roman Empire stated that the division between Ancient and Modern history is Charlemagne's being crowned as Emperor in Rome. It was written a hundred years ago, so I don't know if that was the common perception at the time and we've only been neglecting it. Do you know of any dividing events in Islamic history, or other parts of the world?
I'm just asking questions. =)