Badiou says that “being is inconsistent multiplicity.” As an advocate of immanence, unlike Heidegger, he doesn’t think that there is an ontological difference between Being and beings. As a matter of fact, he altogether refuses that there is such a thing as Being transcending the multiple beings, or beings as inconsistent multiplicities. To understand where Badiou is coming from we only need to look at his critique of Heidegger’s equation of being in the world and being towards death. For Badiou there is no such thing as being in the world, because for him there is not one world but multiple worlds and consequently being in the world as being towards death is a rather impoverished idea doomed to result in the mistaken assumption that consciousness of human finitude is self-consciousness.
I don't pretend to have worked out Badiou's schema but read a bit online (Dr Wiki!). He opposes Cantor's collection of infinity--there is no One, no perfect ontology. Yet he upholds set theory via Zermelo's axioms. Not just a typical materialist-nominalist, ala Quine. Maybe sort of conceptualist in a way (IMHE). There is an element of constructivism .
Some varieties of neo-platonism upheld immanence (rather than transcendent Being), as in....Reason manifests itself in nature, somehow.
Politically speaking though, Jan's probably right. He definitely looks like a Red. How the PoMos relate their abstract theory to the far-leftist politics remains a bit mysterious.
Assume Justice existed, as a platonic Universal of a sort. Would Justice (whatever It is) consider say ...Bill Gates, corporate execs of all types, or Ayn Randians above Marx or marxists (even corrupt, violent ones) ..or Hegel? And where would Heidegger stand?
Marx's implicit conception of Justice (of the overthrow of finance capitalism by the proletariat in brief) in fact sounds rather similar to the political ideas of the Republic (though Plato's Guardians are.... party members, not merely ..workers). I wager Marx had a well-thumbed copy of the Republic (as does Badiou, supposedly).
So far as I am aware, MH does not address the issue of distributive justice. I have not studied Rawls enough to comment on him.
All I recall from my ethics class is that "greatest good for the greatest number" conflicts with appeals to basic human rights. And apart from existing traditions, there does not seem to be much to offer.
I'm listening to Harvard prof Michael Sandel on Justice, and his question re "greatest good for the greatest number" is: If two people need kidneys, one a heart, another a gall bladder and a fifth a liver, is it OK to kill a healthy human to harvest their organs to save five?
Utilitarianism of any sort I would rarely defend, and it generally runs into problems as the one above, or runaway trolley cars, etc--ie, could we kill a few innocents to make life better for all? The utilitarian, whether rule or act, would seem obligated to say yes. The rule utilitarian who says, "No, there are other rules", usually resorts to quasi-theology/Plato, Kant, Rawls etc.
Rawlsian justice via some type of social contract may be a bit superior, but still problematic (I have scrawled a few things on ToJ on my humble site, including compare and contrast with marxistas). One, like...still depends on like a state force (and police) to enforce.
That said, at times platonic conceptions of Justice--or Kant, but IMHE Kant's categorical Imperative is still crypto-consequentialist (ie, utilitarian)-- seem nearly plausible, like....in regard to great villains and tyrants. OR, say, a Judge or prosecutor in a small town who lies to win cases, even if ...the citizens know and approve--rather trite, TV-drama like scenario often milked by screenwriters. But still somewhat interesting. However I couldn't easily prove to you why I think Justice holds (though we know it when it's gone).
Heidegger's with his mentor Nietzsche I believe in regard to ..democracy and justice--which is to say anti-democracy, and..."history is written by the victors."