Ian Morris, in his popularizing history book Why the West Rules--For Now had a very good run down of this and the many ways that the idea of Greece and Rome as the fount of civilization is pretty absurd when looked at carefully. I will summarize the points as best I can into four points:
It treats Greece and Rome as somehow originators rather than profoundly influenced by outside forces (also as a single unite but we will leave that aside) or, worse yet, as some stage in the "progress of civilization" that starts in Egypt, then Babylon, then Rome, etc. But Greek culture was profoundly influenced by its neighbors that were often richer, older, and more sophisticated. For example, every Greece art 101 class will trace the descent of Greek statuary from the kouroi statuary of the sixth century BCE (to anchor your time frame, the Battle of Marathon was in 490 BCE) and how those statues were in turn from Egyptian predecessors. Likewise, the practice of bas relief is clearly influenced by Near Eastern predecessors. There are certainly regional variations, but that was not unique to Greece, and you would not confuse the reliefs at Karatepe with those at Nineveh. This went far beyond artistic practice, as Martin West's East Face of Helicon demonstrated the influence of near eastern literature, mythology and cultural practice was profound in Greece.
A point that I would not be surprised drives medievalists up a wall, it completely ignores the thousand year period between the sack of Rome and Lorenzo Valla. If "western culture" is defined by, say, Greek democracy then where was the Greek democracy in the court of Philip the Fair? There are certainly some literary survivals, the Aeneid and Ovid were always popular, but virtually the entire corpus of Greek literature was lost except a few Latin translations, and many of the Latin authors we consider exemplars of the Western ideal were basically ignored (Livy, for example). So what you are left with is this millennium long hole, a misguided detour on the glorious march from Sophocles to Shakespeare.
It really profoundly underrates just how weird ancient world was to modern eyes. This is something that more modern depictions of the ancient world like HBO's Rome have done a good job with, but there is a real disconnect between the classical ideal as shaped by the Renaissance and what the classical world actually was. I think statues are another good example to use: when we look at a Roman marble statue and a Renaissance statue we are tempted to think "aha, the similarity!", but that initial reaction is pretty superficial. First, most famously, is the issue of classical Roman statues against pure white Renaissance, as the Renaissance sculptors may have thought they were imitating a classical ideal, but that ideal existed almost entirely in their own heads. It goes beyond superficial aesthetics and into the social function of art as well, as there is a temptation to when looking at a Roman statue like the Capitoline Venus to find the artistic intent of the individual creator as you would with a statue of Michelangelo, but what you don't see is that there are just a bunch of those statues, some with variations (particularly in the face) but basically identical. The whole social function and conception of art was radically different (ed: cf Cuomo Technology and Culture in Greek and Roman Antiquity). This goes to literature as well, there is a great book called The Shock of the Ancient by Larry Norman that points out that, despite the stereotype of ancient vs modern as being stodgy traditionalists vs freethinking visionaries, the flow of classical texts into the courts of early modern Europe was actually pretty destabilizing, and many of the people arguing against the absolutist tendencies of Louis XIV were using these profoundly strange ancient texts to make their point.
Finally, and this is the point I feel is the most important, it completely ignores what most of the Greek and Roman world were. Most people under the Roman empire lived in the east, most art and literature were produced in the east, most of those lovely statues were made in the east, and most of the direct cultural survivals survived in the east. The architectural form of bazaars and suqs are pretty clear descendants of the Roman market, the Turkish bath is built like a Roman bath, the domes of the mosque are the real inheritor of classical temples, not the western European church. To say that the West descends from Greece and Rome is a claim of cultural ownership, to say that the true descendants of the glories of the past are the ones who live in what were insignificant outlying provinces, not the actual beating heart of the empire.
The consensus is that the idea of "Western Civilization" itself is incredibly problematic, and drawing connections between modern "western" cultures and ancient "western" cultures is possible, but you have to be really careful and do good history. That is, you need to make an effort to include the nuances and contradictions within the narrative. The textbook I'm using right now for my class, Grafton and Bell's The West: A New History, puts it succinctly: "There has never been a single, unified, easily defined place called 'the west'.....Even so, there is something we can call 'the West.' It is a web of societies, centered in Europe and its extensions, loosely linked by shared and interacting histories. These histories incorporate debts to other societies around the world and the results of conflicts both internal and global." Pretty broad, eh?
In other words, you can talk about "Western Civiliation," you just have to be careful. About what? Careful that you don't make too strong of a connection where there really isn't one. Rome didn't control all of what we now call "the West", and controlled places that we'd now mostly exclude from "the West." Islam is often excluded or even set up as a juxtaposition to "the West", yet Islamic thinkers were instrumental in carrying on Greco-Roman traditions of science and philosophy after major changes in the Empire. The Greeks, who used to be held up as the "western" standard, the founders of the humanism and democracy that defines the modern West, are being seen more as they really were: an extremely xenophobic, misognynist, slave society that had a highly restricted, if democratic, government. The bottom line is our society hardly looks anything like ancient Rome or Greece; virtually no one alive today would be super comfortable, or super safe, if somehow dropped into those far more brutal, far more segregated, ancient societies.
Perhaps the biggest problem is the way the history of the west was--and still is by some people--used for a political agenda. The original purpose of western civ classes was to create a narrative for the non-communist world after the first world war, to indoctrinate, more or less, America's young people into a proud historical tradition. This is bunk, if you take my previous point: the United States isn't really the inheritor of any Roman or Greek tradition, unless you're talking about the small (albeit important) influences of Roman Law, or representative government (we did call it the "senate" after all). Even worse, some people made it into a race thing, the idea that the ancient Greeks and Romans were "white" in the sense that modern white people are "white," and this is just ridiculously anachronistic (see my previous post from a few years ago on the history of race).
Anyway, all this is to say is that the consensus is that it's problematic. Many historians specializing in Europe will tell you that it's still incredibly important to teach the history of "the West" and will point to the various things we do inherit and the ways in which we can teach it properly; many historians of non-western history point to our global/international society and (rightly, I think) express the need to teach history surveys beyond Europe. In this day and age, many departments only get to force students to take one history class, and more and more are siding with World History. That's more reflective on the consensus than any argument among European historians.
Edit: Source: Check out Gilbert Allardyce, "The Rise and Fall of the Western Civilization Course," AHR 1982. It's old but has a decent history of the course.
I've seen a lot of this too, which leads me to a follow up question. When/where did the idea of a "Western civilisation" begin?
I know the criticism I've seen of the idea of Rome/Greece being the origins is rooted in the idea that there isn't really a "Western civilisation" that has any kind of clear path from then until now. That makes sense to me, but also is very wrapped up in my politics. Not sure where these ideas originated from. Does someone know?
This is a huge and complex question, so my response will be of necessity limited in scope to two main points in reply.
I think there is broad consensus that the West owes a great deal to both Hellenic and Roman culture, not least because the church (in the West) assumed much of the mantle of Roman institutionalism ( see Peter Brown's work for a more detailed discussion) and reproduced it after the end of the Roman period (6th c). And what remained of the literary and scientific tradition of the Helleno-Roman world was to some extent preserved in monasteries across Western Europe, such that it formed the basis of a "Western" intellectual tradition, especially after the so -called rediscovery of Aristotle in the 12th c. and extending thereafter (but Islamic scholarship also drew from these traditions so it is incorrect to think that such ideas "belonged" to the West).
The real confusion is the idea that Roman and Greek civilization were themselves "Western," which is generally understood to be false, or at least greatly exaggerated. For example, insofar as the basis of both was the polis, this was very much a characteristic of Eastern (= middle Eastern) modes of social and political organization. In western Europe, the city was essentially an import from the East, introduced through Hellenic colonies (as in Sicily), or later as part of Roman expansion. We have no better evidence for the foreignness of the city to Western thinking than the fact that cities largely disappeared in the West after the fall of Roman power and didn't really emerge again with any size for centuries (the Italian peninsula being an important exception). In cultural terms, Rome itself was at a western extreme of an axis of learning that extended through what is today southern Turkey and the middle east and into Persia. The great centres of Christian learning, for example, were in what is today the middle east (e.g. Egypt, Israel, and Syria) and Turkey. And many of the modalities that defined Hellenic and Roman life, while completely foreign to the indigenous inhabitants of Western Europe, would have been very familiar to the people living in the Eastern part of the Empire and beyond.
So a simplistic way of thinking about it is that the Roman empire "easternized" western europe, and, as a part of that very process, bequeathed a historical tradition that would later "westernize" Rome by bringing it within a way of thinking about western civilization.
Sorry, that's not the most complete answer, but maybe it's a start.
Follow up question to this: could someone please unpack the development of the concept of "Western civilization" in popular historical discourse? How does scholarship deal with this term and to what extent does it engage with or criticize the notion?
