Post-modernism, is something that does not have truth to it. Post modernism does not believe morality is objective. It's a lie, to trick young college kids, into thinking there is no such thing as "absolute truth". Many students are victims of these typical sophomoric "arguments". However, they don't stand up once you actually study them.
While I agree with the notion that much of reality is subjective, the rejection of any objective truth is problematic. This is most true when discussing math, but proves to be practically true in the sciences as well. While the perception of reality varies from one individual to another, there are many questions for which there exists only one correct answer.
The majority of subfields in mathematics are entirely objective, and based on incontrovertible logical proofs: the entire field is reliant on objective truth. For example, the following facts are true no matter who or what you are:
There is no REAL number x such that x^2+1=0
The area of a circle of radius r is πr^2
Therefore, if postmodernism can be defined by the nonexistence of objective truth, then it cannot account for mathematics.
Moving onto the physical world (specifically, physics), I will begin by acknowledging that all science is an approximation of reality. However, within physics, it is an extremely close approximation. This means that while quantitative may always be approximate, qualitative statements are not.
For example, while it's possible to protest Newton's laws as a way of viewing the word, it is possible to predict whether or not a cannon ball fired at a given trajectory will be observed to hit its intended target with great precision. Sticking with this example, the ability to test the theories in the real world allows us to prove that a specific model is NOT true if it fails to predict an outcome. Even more precisely, if a cannon ball were to hit a target, it would be hard to argue that it hadn't. Those who argue that the cannon ball having hit the target is subjective should have no problem standing in a cannon ball's expected path (you can choose to report this post, but I ask you: was the content OBJECTIVELY objectionable?)
While that last statement is an obvious joke, it brings me to my final point: we are able to rely on our physical models being qualitatively accurate/true. In fact, scientific facts are the basis behind much of human invention. Indeed, it seems hypocritical to argue that there is no objective truth on semiconductor devices whose construction was reliant on the accuracy of physical models.
Postmodernism may or may not be muddled in how the philosophical branch grows out of the aesthetic and literary approaches. Postmodernism may or may not be supported by demonstrable tenets. Postmodernism may or may not be founded on intuitively accessible a priori assumptions. Postmodernism may or may not be supported by proponents who can construct valid arguments.
Postmodernism is not, in and of itself, a breach of the rules of logic.
The fields of philosophy are full of ideas that are supportable to various degrees, primarily depending on the skills of the particular philosophers who argue for or against the propositions in question.
Janetsanders733 indicates that much of what she objects to in postmodernism is the belief that there is no objective morality. I do not see any evidence for any objective morality, regardless of how much I see poorly supported insistence that it exists. More to the point, I see disagreement on every possible moral question. I take that to indicate the absence of an objectively discernible, or even universally definable morality.
Other than the now there is no truth. Everything else is a good guess. "Higher ideas" like "morality", "ethics",... Are in my opinion worth thinking about (especially because they influence people including yourself so strongly) but they have no objective existence unlike for instance "chair" or "piece of wood" and even here depending on how people talk about it they will think about and relate towards these concepts differently.
Some try to cite neuroscience in order to save the existence of truth, but that doesn't work. Here's why. Yes, certain neurochemistries have a strong tendency to correlate with certain feelings or how people relate to concepts such as ethics and morality. Yet these inner feelings are only given meaning and value based on how we think about them, which yes evidence suggests will also be composed of chemical processes but the moment you start thinking about that you are using those same chemical processes since you are conceptualizing and so still have not found any objective answers. Not everyone relates to the same feeling in the same way and opinions vary very widely on how to assign meaning to feelings. Some cultures tend to stress happiness as the be all end all, others warn the dangers of too much happiness. And indeed it's possible to think of these in terms of "it would be better to be sad, it's more meaningful" so in the end you can't find any objectivity. Even mental illness (though the same would go for physical illness) is not objectively bad, though I'm not saying I would like to be ill, just that it is a possible point of view to want and accept these things, or even just some of these things. And especially with regards to mental illness one can imagine alternative histories and societies where what we consider normal is called "disorder" (drapetomania) and we consider disorder is called "normal" (ADHD may be a boon in hunter gatherer societies and some cultures treat symptoms of what we'd call psychosis by raising the person to be a shahman).
People have been inventing, uninventing, affirming, and negating various ways of thinking since the beginning of time and will continue to do so in the future. And I wouldn't have it any other way, life would get boring if we just settled on a single set of concepts and narratives for the rest of time.