Derrida lays many of his presuppositions out in a hard but very important essay called 'Structure, Sign and Play' in the Discourse of the Human Sciences. You can tell what it is going to be like from the title! The argument goes as follows:
1. Western thought and language have always had a fixed centre in absolute truth. This places limits on what it is possible to think or believe. It provides a foundation for being (ie what we are), and for knowing (ie how we think). Absolute truth provides certainties.
2. However Derrida’s underlying assumption (which this essay does not explore) is that there is no God in the equation to guarantee such absolutes, and hence ideas about certainty are now ruptured. He concludes that any idea of a fixed centre was only a structure of power imposed on us by our past or by institutions of society, and does not in reality exist at all.
3. Hence for Derrida there is no ultimate reality, no God outside the system to which everyone and everything relates. Instead the only relationships that we can know are within the system of the world which Derrida calls discourses. For him ultimate reality is only a series of these discourses.
4. Because there is no fixed centre, there should no longer be any limits on what it is possible to think or believe. We should literally be able to think anything. We can be playful and flexible about the way we think, when we realise that “truth” and “falsehood” are simply wrong distinctions to make. Indeed they are just a destructive and harmful manifestation of that power structure.
5. Therefore we must stop considering everything in life, culture and thought in relation to absolute truth. To not do so is, for Derrida, oppressive and immoral.
A few more points if you want to think a bit further (but these aren’t vital to the argument!):
6. Derrida says that history is traditionally thought to be determined by Being. In other words God guarantees history There was a beginning and there is an end to which we are working. Most human optimism for Derrida springs from this fact. The whole of science for example is based on the fact that true things are there to be discovered and worked towards.
7. However this idea of history is what stops people thinking radical new thoughts because the assumptions we pick up from history are oppressive. But the fact that people can and do think radical new thoughts is seen to deny this oppressive version of history, and, of course, any absolute Being behind history.
8. Derrida’s ideal of play or flexibility therefore completely denies the possibility of absolutes or of God.