(response to a request to describe what I think Laruelle’s “one good idea” actually is)
Laruelle’s thinking sets off from a description of the decision schema, which he claims characterises “philosophy” in general: you split the world into representation (“transcendental”) and represented (“immanence”), posit a necessary relationship – of correlation or exchangeability – between the two, and reflect that relationship within the representation. That closes the loop of “auto-position”: your posit is necessary, because it posits its own necessity. (It’s a bit like Bible-bashers quoting 2 Timothy 3:16 at you as proof that the Bible is true). The representation then appears as “sufficient”, because it controls on its own terms the relationship between itself and that which it represents.
Laruelle’s Good Idea is that you can “suspend” that schema, by substituting a different posit: the relationship between any representation and the Real is unilateral and non-representable, so you can’t reflect that relationship in a self-authorising, sufficient way. That then changes the status of philosophical “decisions”: they no longer have the status of contending claims to sufficient truth, but are instead instances of a particular structure of thought that can be analysed in a non-decisional way on the basis of this alternative posit.
This is where it ought to get interesting, but doesn’t. Laruelle stipulates that a non-philosophical “theory” or “science” of philosophy should exist, but what he actually comes up with largely consists of repeating that stipulation.
In a lot of ways Laruelle’s development is similar to Richard Rorty’s. You start with “Philosophy and the Mirror of Nature”, which basically shows how lots of different philosophies try to close the loop of auto-position and how that never really works. That then leads into a generalised anti-foundationalism, the aporias of which Rorty tries to escape by turning to an account of philosophies as “final vocabularies” amenable to liberal-ironist unfinalising and mutation. The end-point is a congenial liberalism, concerned for the suffering of hurt and humiliated victims, and bearing a vague accusation against philosophy that it has turned aside, in its love of abstraction which is really a kind of delusional self-love, from the interests of suffering humanity and needs to be resubordinated to those interests.