Discussing Meillassoux in my Speculative Philosophy course. We just came out of three sessions on Latour and Harman's take on him and we're still full of that atmosphere. Latour's principle of irreduction (1.1.1 in Irréductions) says that nothing is either reducible or irreducible to anything else in itself. That means that it is neither the case that in itself each thing is one thing and not another thing - a world of arche-atoms - nor that there is a blob of interconnections or intercorrelations that is all-pervasive - a world of an arche-blobject postulated by monists like Horgan. Instauration (bringing things about) is what produces both individuation (irreduction) and connections (correlations) and it ought to pay the cost of transport both to bring things apart and to connect them together (to make them sui generis and to make them reducible).
Consider the two branches of metaphysics of the subjectivity that Meillassoux seems to be unhappy with - because they fail to take seriously the facticity of correlation. One goes from the correlation we have found (with correlationism, or with the so-called Copernican revolution) to the idea that there is nothing beyond that correlation, something akin to claim that to be is to be in this correlation (say, to be is to be mediated). The other goes from this correlation we have found to the idea that there is nothing beyond a correlation, the world is a world of correlations (in the form of prehensions or proofs of force), something akin to say to be is to be in a correlation.
Now, Meillassoux's rejection of those alternatives could share the spirit that drives Latour's principle of irreduction. But of course it goes in a very different direction as he makes room for no process as prior but simply a world of (absolute) contingencies. Still, there are no atomic correlations and no blob correlation. Any correlation we engage with - and maybe we are bound to engage in one - is out of our own risk (our own second creation, maybe) because everything including our (home) correlation is contingent. In other words, we ought to pay the cost of transport both to postulate a privileged correlation with the world or to consider a world of correlations (or even to consider an über-reality that brings together all correlations in a cubist or fragmentalist image as Kit Fine suggests). Correlations are not absolute, Meillassoux insists. They ought to be brought about and paid for. The emerging picture of contingencies is somehow interestingly close to the idea that nothing is in itself reducible or irreducible to anything else.