Postmodernism wants to say that there is no truth. That 2 things can both be right in the same way and manner at the same time. That you can be right that there is no God and that I can be right that there is a God. One is your truth one is my truth but there is no universal truth. The problem is they are building this on things that require truth as a foundation, namely logic and words.

If one thing can be true in one way, and the opposite can be true at the same time, well then what is to stop words from changing meaning? If you call something a chair under postmodernism, you could mean an elephant. But if this is true, than their very words in which they use to describe and argue for their position, are either meaningless, and thus their position is still not proven, or else they(the words) themselves disprove their very position.

It is as if they built a building where nothing goes anywhere or has any real purpose, and yet they built it on top of a traditional foundation. If the building was truly to be a postmodern building, then even the foundation and parts must be postmodern.

Thus postmodernism is shown to not be true by the fact that they can only argue for their case while using elements that in themselves disprove their own case.