Viewed in its chronological relation to postmodernity, hypermodernity has two senses:
1 – hypermodernity is postmodernity intensified and reworked by the digital revolution
2 – hypermodernity is postmodernity intensified and reworked by the Idea, sublated in the Concept.
If we examine Lyotard’s philosophical evolution, LIBIDINAL ECONOMY is postmodern, but THE DIFFEREND is hypermodern. Paradoxically THE POSTMODERN CONDITION is between the two, as in this book he replies to accusations of relativism and to the threat of the digital by reworking his earlier position, sublating it by means of the semiotic turn and the Kantian Idea.
Going back a little in time, we can look at Lyotard’s JUST GAMING, which was published in the same year (1979) as THE POSTMODERN CONDITION but which records a series of conversations dating from 1977-1978. We can see that here Lyotard is explicitly replying to accusations of relativism, and so of « postmodernism » in the sense it has acquired for most people today.
Lyotard’s answer is to give an alternate definition of postmodernism that incorporates Ideas. He later gave up on the term « postmodernism » as his definition lost out, and he proposed the term « re-writing », a perpetual non-historical questioning and inchoation, in its place. With this expression, he is able to retain elements of postmodernism, notably its pluralism, but reject its relativism.
This is why I am willing to play with the term « hyper-modernism » as it captures the two senses of « hyper-« :
1 (historical, hyper- = post-post-) – the intensification, acceleration of tendencies at work in postmodernism
2 (ahistorical, atemporal, hyper- = re-) – the appeal to another dimension (or more), the multiplication of dimensions.
Note: I am indebted to a conversation with Burton Fisher for helping me to clarify my ideas on this subject.