Let me start this essay on a post-modernist post-modernistically by stating that Lyotard isn't the easiest philosopher to understand. He is very French and very pretentious, and he can bounce around, dropping names and spinning theories out of the air, and it becomes very hard to follow until, at some point, he makes a succinct and insightful comment that can crystallize much of the modern world.
In his essay collection The Inhuman, in an essay entitled "Time Today", first published in 1987, he writes (surrounded by pages of the incomprehensible):
In the name of the same motif, that of 'overcoming metaphysics', Carnap on the one hand and Heidegger on the other cut Western philosophy in two, logical positivism and poetic ontologie.
Boy howdy, that might not seem like a succinct and insightful comment, but it really is. While traditional metaphysics believed that diverse phenomena, including both moral, social and physical systems could be talked about with some of the same terminology and concepts, this has been separated in the 20th century, into "analytical" philosophy and "continental" philosophy. There is no overarching metaphysical structure for the world. The only options available are a "serious business" "scientific" description of the world that maximizes the extraction of resources, or there is a "poetic" description of the world where feelings and ideas can only be understood hermeneutically, with no outsider ordering permitted.
For example: take a train. We can either describe that train in terms of its dimensions, route number, passengers carried per year, the model number of the train, and all the many "objective, neutral point-of-view" things that wikipedia loves putting into infoboxes. And don't get me wrong, I like and find useful those infoboxes. But in our "logical positivist" philosophy, the infobox is all we have. On the other hand, our "poetic ontologie" about the train trip will involve impenetrable prose filled with jargon describing the magical realistic nature of the train moving across the landscape, and how the train is just one part of an experience that is fused, in a way that can not be judged or integrated from an outside perspective, into a personal story. Depending on our perspective, the mythos of personal experience, seen through lenses of gender and ethnicity, might be liberating or creepy, but it is also nothing that will open itself up to outside discourse. Because the only discourse possible is about the objective facts we can establish about the train.
This is not only the philosophical landscape I find myself in, but the physical landscape I find myself in: I live in a landscape of six lane highways, of giant utility grids, of multinational corporations turning each town into a clone of the next, of fossil fuel dependency, of anonimity---or else the landscape is "the great outdoors", little niches cut off and preserved in the distance, where people can "escape" to commune with nature, in a way that ranges from the naive to the (again, creepy) "blood and soil" concepts of people who lionize a small town existence that no longer exists. A way of relating to the world around me that is not part of one of those worldviews---extractive rationality or "poetic" irrationality"--is hard for me to find.
I could find many more examples. There are many autocracies that base themselves around extractive and exploitive technologies, while also embracing the idea of mystical ethnic unity as the basis of the state. Some of these autocracies have been creating a lot of problems lately.
And finally, we reach the bosom of all that we hold dear, the internet. Much of what I read on the internet falls into one of these two categories: either the driest and most undebatable of facts, which can be helpful when I really need to know how many isotopes of tin there are or what year the first airport in New Zealand opened; or I read things that are impressionistic, vague and poetic description of experiences or dreams that are both above and below criticism because they exist just as a subjective experience that is protected by a sentimental wall, and that perhaps I can never understand because I do not share the gender or ethnicity or general life experience of the writer. So there is, with this two-fold division, nothing to debate, because either everything is "objective facts" from a "neutral point of view", or it is a personal experience, beyond reproach, beyond analysis, beyond discussion, because I do not share the experience.
Although it is always more complicated, and this is based on a single line, written over 30 years ago by a philosopher not known for his clarity, I agree with Lyotard's statement. Or at least, I agree that it is a statement worth considering. Western philosophy was indeed cut cleanly in two, and I feel it personally because I don't know where to go next.