Thought I'd throw in a couple of points:
The expansion of Christianity in the early centuries was nothing short of epidemic, and not to do with Greek philosophy, which had yet to make an impact on doctrinal thinking. By AD60 there was a sizeable community in Rome, and within a hundred years of Golgotha there were Christian communities in every corner of the empire.
A significant factor in the spread was the (relative) ease and safety of travel within the empire itself, and with just common Greek or Latin, one could be understood from Scotland to Asia Minor, from the Steppes to the deserts of North Africa. There is no question that the free movement within the frontiers enabled athe rapid spread of the gospel.
Persecutions were invariably local and sporadic, until the 3rd century when they became more widespread and pursued with greater vigour. One of the biggest was initiated by the Alexandrian Greeks who, by that time, had come to recognise Christianity as a rival philosophical system. What annoyed them, as Celcus' writings indicate, was that anyone could become a Christian, you didn't need to be highly educated - this conflicted with the view that salvation belonged to the intellectual elite, that religion was an intellectual pursuit.
A major, if not the major factor, in the uptake of Christianity was its morality, not its philosophy, and this was why it was embraced by the poor, the women, etc.
Christian social programmes were the talk of the empire. By the 2nd century the community in Rome alone was looking after over 1500 widows and orphans, the sick and the destitute - who otherwise would be left to fend for themselves or die. Everyone was taught to read and write, so that soon 'educated slaves' became a desirable commodity, invariably educated within Christian communities. Likewise Christians rose in the Roman hierarchy because they were educated and because of their moral character.
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The point regarding Greek philosphy is to remember that a higher truth does not displace the lower, but incorporates it. The 'problems' of Platonic philosophy, for example, found a solution in the JudeoChristian philosophy of creation which saw the world as essentially good, and not evil.
The unfortunate and intractable dualism of Platonic thinking still permeates Christian thought however, most evidently with regard to the soul as something extrinsic to the body - in JudeoChristian thought the soul does not inhabit the body, which it will discard at death, the body IS the soul, manifest in a corporeal mode of being.
Once this is understood, vistas of Christian anthropology, a vision of the nature of 'being-ness' (the 'esse' of the Scholastics), blossoms in its full magisterial and theophanic promise - and to my mind, a vision without equal.
Thomas