There are two preliminary matters I must dispose of before I can address this question in earnest. The first is the school of thought which holds that in fact there never was any such person as Jesus. One of the more elaborate versions of this theory, I gather, is that Jesus was a fictional creation of Josephus, the historian most famous for his eyewitness account of the of the losing side of the Jewish rebellion against Rome in 70 A.D. The short answer to this idea is that Jesus is about as well attested in ancient history as anyone gets. The long answer is that the Classical world did not have much realistic prose fiction. The stories about the mythic figures often compared to Jesus, such as Bacchus and Osiris and Mithras, all happened "once upon a time," outside secular history. The closest approach to an ancient historical novel I can think of, the Aeneid, is a poem about a royal exile who lived in the misty past. The Gospels, on the other hand, are rather flat prose accounts about the life of a carpenter who was born in the reign of Augustus Caesar and executed about 30 years later by a Roman official named Pontius Pilate. When people in the Classical world made stuff up, they did not make up stuff like this.
The other impediment to understanding the results of Jesus' life is the theory which arose in the late nineteenth century that Jesus is not responsible for Christianity. The idea was that the Gospels were "very late and very Greek," that is, written at least sixty years after the events they purport to describe by people of Greek culture who did not understand the Jewish Jesus and his environment. This approach to the New Testament seems to be ineradicable from seminaries, though in fact scholars in the classical languages no longer take it seriously. (Neither has it held up very well to archeology, but that's another story.) The Oxford scholar in Classics, Robin Lane Fox, author of "Pagans and Christians" and "The Unauthorized Version," is at best agnostic about Christianity, but he has no patience with the notion that Jesus was just a typical Palestinian hill-preacher who paid a rather severe penalty for preaching without a permit. As Paul Johnson remarked in his "History of Christianity," a Jesus who did not say and do extraordinary things does not explain Christianity. If you want a real lip-smacking anti-Christian diatribe, you should read "Jesus the Magician" by the Columbia University classicist, Morton Smith. He argues that of course Jesus claimed to be the Messiah and to be a god and that his immediate followers believed within days of his execution that he had literally risen from the dead. Thus, Dr. Smith triumphantly concludes, all these people were crackers. Well, maybe they were. But if so, it was their lunacy that gave all later history a unique twist, one that would never have happened without Jesus and his idiosyncratic ways.
So let us imagine an alternative Christmas night about 2000 years ago. Rumors of the end of the age, of a miracle child, spread among shepherds of Judea. They gather on a cold, clear night to watch the stars, expectant of wonders. One by one, they all fall asleep, and the night passes without incident. A few weeks later, some Persian astrologers pass through the area and pay a courtesy call on King Herod. They assure him, inaccurately, that his reign will be long and glorious. They continue on to Egypt, to the Library of Alexandria, where they host several well-attended colloquia on Indian mathematics. History continues undeflected.
For most of the first three centuries of its existence, Christianity was an underground religion. It was sufficiently obscure that you have to hunt through Classical sources even to find criticisms of it. Its absence during this period would have made a difference, I suspect, chiefly to Judaism. The process of canonical and doctrinal synthesis that occurred in Jewish culture after the destruction of the Temple in 70 A.D. was driven, at least to some degree, by the desire to sort Judaism out from Christianity. While the Torah would probably have been preserved much as we know it today, it is not at all clear that anything like the Talmud would have been compiled. Rather than rabbinical Judaism, the result would have been a Judaism of local "temples" and syncretizing theology, not unlike Zoroastrianism. This sort of thing was always threatening to happen in pre- Talmudic Judaism, as the still-surviving Samaritans illustrate. Without the Temple and with no aggressive ideological threat from a proselytizing competitor, Judaism could well have faded into the general background of Middle Eastern religion.
In the later stages of Roman imperial history, the implications of the absence of Christianity become more dramatic. The late Classical world was moving toward monotheism as surely as physics today is moving toward a united field theory (many people think that both ideas are delusional). Science and systematic philosophy were not forgotten, but they had ceased to be persuasive to the educated. People at all levels of society were ready for revelation, for the coincidence of this world and the next. Oswald Spengler calls this cultural mode "the Second Religiousness." It is a lifeless but fervent return to the naive religiousness that colors the early life of a civilized culture. Arnold Toynbee says that the victory of a "mystery religion" is a necessary feature of the late history of every civilization. The problem with late Roman history has always been that Christianity should not have been the victor in this contest. It should not even have been a contestant. "Pagans and Christians," cited above, is in fact an attempt to show that the Christianization of the Roman Empire was an accident resulting from the victory of Constantine in the civil wars of the early fourth century.
The victor should have been something called "astral piety." The theoretical basis of this is the Neoplatonism that became fashionable in the third century. Plato had held that there was an intelligible world, a world of ideas, behind the world of experience. This world could be approached, even to the One Absolute Idea which gave meaning to the whole, by philosophical reflection. The Neoplatonists in the decadent final centuries of Plato's civilization were interested in the steps, the levels of being that stood between the everyday world and Plato's One. These levels were associated with the Classical gods, with the stars of astrology, with the crystal sphere within crystal sphere described by Ptolemy's astronomy and supported by Aristotle's physics. The Neoplatonists were also interested in direct, ecstatic experience of the One. Thus this somewhat academic system came into contact with popular Gnosticism. Gnosticism, the belief that ultimate reality is accessible to an elite holding secret knowledge, appeared about the same time as Christianity and was the chief danger to Christian orthodoxy in the murky religious underground of the first and second centuries. It practice, it was a faith of magicians and wonder-workers and private revelations, a sort of shamanism for city-folk. It gave life to the old gods again. This was the vital force that made the astral piety of Diocletian a mass phenomenon. Even after Constantine ended the persecution of Christianity, it made a vigorous reappearance as the state cult supported by the emperor Julian the Apostate. To this day, it has been the chief constituent of the "hermetic underground" which peeps into the light of day from time to time in Western history. A history without Christianity is one in which this underground becomes the surface.
The Roman Empire itself, one suspects, would have trundled to its doom in much the way it did no matter which mystery religion had government support. (One can imagine the man who would have been Saint Augustine, for instance, playing very much the same role for the state's Neoplatonic Church as he did for the Church of Christ. He was always temperamentally better suited to Manichaeanism than he was to Christianity.) The end of Roman history was the beginning of Byzantine history. This development was occasioned partly by the division of the empire into eastern and western halves for administrative convenience, but it also reflected real differences between the spirit of the weary and depopulated West, in contrast to that of the vibrant and creative East.
Surprisingly, it is easy to imagine a Byzantine Empire without Christianity. The divisions we make in late antique history between East and West are really somewhat artificial. Byzantium and the Sassanid Persian Empire were in many ways part of the same culture. This has long been recognized in their politics. Byzantium adopted Persian court ceremonial, eastern liturgical practices, even much of their eastern enemy's military technique. Both were theocracies supported by feudal magnates. Both professed intricate versions of monotheism. The only real difference was that the western half of this culture area had been ruled by the alien Roman Empire for several centuries. Without Christianity, much of the friction between Byzantium and Persia would have been eased. Intermarriage between important families in each empire would have been greatly facilitated, for instance. They might, conceivably, have evolved toward the same cult. Indeed, without the centralizing effect of continuous warfare, one can imagine the both of them disarticulating into a single "family of nations" like Europe or (for most of its history) India.
The really interesting question is what would have happened to Islam. In medieval Europe, Islam was considered simply a Christian heresy, and in fact Islam did absorb a quite remarkable amount of slightly-garbled christology, just as it did much of Judaism. Spengler suggests that the best way to look on Islam is as a Reformation, as a movement to simplify and reinvigorate the common religious life of the Middle East. My own reading of the Koran suggests that "Islam," of a sort, would have been possible even if Christianity were non-existent and Judaism were fading into a folk religion. The energizing principle found in the Koran is that every people has its hour, its book and its prophet. In the seventh century, Mohammed said that the hour of the Arab people had come. Their hour would have come, one suspects, even if the religion he was simplifying had nothing to say about the Persons of the Hypostatic Union, but was quite eloquent about the energies of the Neoplatonic Archons. The big difference would have been in the international environment. In the late sixth and early seventh centuries, Byzantium and Persia had gone through the equivalent of a world war. Persia had finally disintegrated, but the whole region was exhausted. More important, the provinces of the Byzantine Empire bordering Arabia hated Byzantium, because the central government kept imposing ever finer definitions of Christian doctrine to which all local Churches had to submit. When the Muslims came, much of the Middle East considered them to be liberators.
It is probably true that Christianity is more likely than most religions to generate the "odium theologicum." Christian theology is historical; it is simply drawing the implications from history. Neoplatonic theology, on the other hand, is more like mathematics; facts are irrelevant. On the whole, history starts more fistfights than arguments about pure abstractions. In the politically more pluralistic Middle East which would have obtained without Christianity, the Muslims might have had to deal only with small kingdoms, but the inhabitants of these places would not have been so disaffected by the doctrinal preoccupations of their rulers. The Muslim advance would been slower, its victories more ambiguous. It is unlikely that it would have reached Spain and Sicily by the eighth century, if at all. The unchristian West would have been left to develop in peace.
Every culture in its youth is intensely religious. The organizational proclivities of the West would have ensured that something like the hierarchical church we know from history, with its penchants for rarified definitions of doctrine and precocious bureaucratization, would probably have happened no matter what the content of the religion of the Springtime had been. Again surprisingly, we do not have to imagine what a Neoplatonic Church would have looked like, since one existed in the twelfth and thirteenth century. The Albigensian Church, centered in the Provencal region of France, was just such a church. It was not even Christian in any serious sense, since it denied (with the Muslims) that Jesus had ever been crucified. Their religion was one of sophisticated myth, not of stubborn history. They believed in reincarnation. They had their own hierarchy, a set of their own sacraments, their own sacred books. (If you believe some people, they also had the Holy Grail, but that is another story.) With the Gnostics, they held that the God of the Old Testament was the devil. With the Manicheans, they held that matter was evil. Reproduction was an indulgence granted to those members of their community who, through social circumstance, simply had to have children. They promoted birth control and nonreproductive varieties of sex. (If you are interested in a remarkable speculation about what would have happened if they had not been totally destroyed in the Albigensian Crusade of the thirteen century, read Theodore Roszak's insufficiently appreciated novel, "Flicker.")
What they did not have, anymore than did Julian the Apostate's Neoplatonic cult, was any notion of "standing guard" on the state. Why should they? In St. Augustine's theology, progress is both possible and desirable in history. God loves the world, and calls men to repair the damage they have done to it. In the Gnostic view of things, on the other hand, the world is the devil's kingdom. The true God had nothing to do with creating it. The only improvement this world can look forward to is destruction. The idea of "the two swords," that church and state are different social powers even when they support each other, is one of the persistent themes in Western history. It is a necessary corollary to the fact that the Church is pursuing its own vision of the good. The state is necessary, the state is even a good thing in itself. However, it has its natural limits. Without Christianity, one suspects, the state would have been as omnipotent in political theory as it is in China and Islam.
What the spirit of the Neoplatonic Church would have been like at the emotional level, we can only speculate. There is only one day in the calendar that has never been Christianized, that preserves the pre-Christian spirit of Old Europe. That day is Halloween. There would have been nothing in the heritage from late antiquity to change this. In the Neoplatonic scheme of things, individual human beings are only flickering hints of a transcendent One. In some forms of Gnosticism, I gather, the mass of mankind are considered soulless cattle. Whatever else a non-Christian West might have produced, it would not have produced anything like a theory of human rights. Slavery might have become rare in Europe for economic reasons, but it would have been less likely to die out.
Arguably, Neoplatonic Europe would not have produced anything like science, either. Whatever else you may say about Christianity, it is certainly a very anthropocentric religion. Its theory of history is wholly man-centered. It adherents are predisposed to find the universe friendly, understandable, the product of a great Mind not wholly unlike their own minds. It is a religion of Incarnation, one which respects matter. (The art of a Neoplatonic West would almost certainly have been overwhelmingly nonrepresentational, like that of Islam.) It is also a religion of history, which means that it respects particular facts even when there is no theory for them. The Benedictine physicist Stanley Jaki has argued throughout a long career (see, for instance, his "Savior of Science") that science could not have occurred if Western culture did not implicitly assume, even when it explicitly denied, a metaphysics something like that of St. Thomas Aquinas. Aquinas was what is known as a "moderate Realist." That is, he thought that abstract ideas were real and could be investigated, but that they could be investigated only through the senses. Both in politics and natural philosophy, he espoused the principle of subsidiarity. In politics, this means that a higher level of government should not interfere with a lower one if the lower one is capable of handling a given question. In natural philosophy, it means that you don't have to understand everything before you can understand something. There is a passage in the "Summa Theologica" in which the Angelic Doctor explains that Scripture and the world are separate spheres, each of which must be understood in its own terms. This passage has been called the "declaration of independence" of science. If Christianity had never existed, that declaration might never have been issued.
Perhaps Fr. Jaki overstates the case. A Neoplatonic West would in some ways have been even more fitted to pursue science than a Christian one. The real difference between Western science and that of China is not Francis Bacon, but Pythagoras. Modern science began in the late Renaissance along with the Neoplatonic revival of that era. The roll of great scientists who have been inspired chiefly by pure number, by the elegance of order, would include people from Kepler to Heisenberg and beyond. On the other hand, one suspects that something would have been lost if the historical cast to Western thought were missing, an almost sure loss if Christianity had never existed. There would have been no Darwinism, for instance. Quite possibly astronomy would suffered, since that science is so much connected with calendrical concerns. Let us cut the baby in half, and say that something like science would have appeared, but that it would have developed less evenly, and would have been harder to adapt to engineering purposes.
Although the missionary impulse has played an important part in all the dealings the West has had with the world up to the present day, quite likely the West's unique desire to explore the whole world would still have been operative even if the West had not been Christian. (Other societies, notably those of Polynesia, seem to have the same impulse to travel and settle as far as their technology allows. Others, such as Hindu India, positively forbade oceanic travel.) A non-Christian West would have felt less impulse to remake societies in its own image. One can easily imagine prolonged relations of trade and border wars between the first European outposts in the Caribbean and the Aztec hegemony, since the Europeans would not have felt any special horror at Aztec religious practices. But if the West met the rest of the world with less presumption, it would also have met it with less charity.
There is little ground for this speculation, but I think that we should be pleased if we never know just what the West would have become had it never become Christian. A shadow of it may have been manifest in Carthage, or at least in Carthage as described in G.K. Chesterton's "The Everlasting Man." It would have been altogether a darker, more rigid, more ruthless civilization. The real choice in ethics, it has long seemed to me, is not between Christianity and liberalism, but between Jesus and Nietzsche. Had the shepherds slept soundly that night, we would be living in Nietzsche's world.