That is a question I have pondered for about twenty years. The seeds for Postmodern thought were laid in the late nineteenth century and cultivated by Nietzche an those who followed his philosophical thought. As a cultural phenomena, however, Postmodernism did not enter the mainstream until the 1950s via the arts and in the 1960s through music. I remember a Devo song entitled "Post Post Modern Man" that was released in 1990. Devo was a pioneer in New Wave music in the 1970s. They were perhaps the first band to utilize the synthesizer in their music. Devo was ahead of the curve once again when it came to asking what comes after Postmodern thought.
Some of Postmodernism more well-known tenets were "spiritual, not religious" and no established truth that holds for everyone. To a degree, these concepts are still around in Western culture, and probably will always be in some form or fashion. Even in Postmodernism's heyday, Modernism still managed to exert influence as a philosophy. Postmodernism, however, seems to have expended its energy and is now coasting slowly to irrelevance. First, the "spiritual, not religious" idea is not some new concept dreamed up by Postmodernism. This idea has been around from time immemorial. What has happened is that the pendulum has begun to swing back in the other direction. People have realized that being spiritual at the expense of being religious really offers an empty sack that is not satisfying in their lives. People are orderly creatures who desire structure and discipline. Generic spiritualism fails to ultimately deliver this order. In a like manner, the idea that truth is relative has been shown to be less than satisfying. An orderly civilization just cannot exist or function without an established set of rules, laws and truths that apply to everyone and are upheld by everyone.
So if Postmodernism is spent, what shall replace it as the reigning philosophy? This question has been debated for several years now. Some argue for Scientific (Critical) Realism, Pseudo-modernism or Metamodernism. In many ways, Scientific Realism is just a rebranded Modernism with absolute truth challenging Postmodernism relative truth. Pseudo-modernism derives from the instant access the Internet offers as regards to knowledge, information and communication. Alan Kirby argues that this ultimately leads to a triteness and a shallowness that is exemplified in Reality TV. Metamodernism is a term coined by Timotheus Vermeulen and Robin van der Akker that argues for a third way beyond the competing Modern and Postmodern philosophies. There is a fourth possibility, what I call, for lack of a better term, Post-postmodernism. There is a real reaction to the blandness of Postmodernism and the triteness of Reality TV that upholds such concepts as specificity, values and authenticity.
It is too early to tell which of these competing philosophies will become the dominant viewpoint among people. Perhaps it will be a strange mixture of the four, which would in some ways be so Postmodern in its synergy. Personally, I hope the Post-postmodern philosophy wins the day as it offers the best strain of thought that reacts to the limitations of Postmodernism. A healthy dose of Scientific Realism would be nice in the Post-postmodern mix, too. We shall have to wait and see what the philosophical future holds.
Until then, enjoy a little Devo: Post Post Modern Man