There's a really excellent new post by Adam Robbert at knowledge-ecology, joining in the pluralism debate. His musings moved me to fabricate the following:
I don't think that there are X kinds of pluralism; however, the word is clearly being used in a few different ways and this is causing some confusion. Here's my initial (and rather sleepy, 1 am) attempt at a disentanglement:
(1) Metaphysical pluralism in the sense of Leibniz, Whitehead and von Uexküll (if he's read metaphysically). That is, there exists a vast plurality of beings; every being has its own perspective on existence; there is no über-being that contains or determines all other beings; i.e. there is no universe but rather a pluriverse.
This basic tenet is common to many of the 'pluralisms' under discussion. In fact the above is probably unproblematic within this debate; I don't think that this is what anyone's disagreeing with.
(2) Pluralism as it's understood in political philosophy. This is complicated; to name but a few pluralists in this sense: Harold Laski, Isaiah Berlin, Robert Dahl, William Connolly, Chantal Mouffe... Many different ideas here. To some extent political pluralism responds to the basic fact that there are many different identities and ways of living and that these have to co-exist somehow; this problem is particularly acute in heterogeneous, multicultural, modern, liberal democratic societies, etc. etc. Pluralists embrace this diversity, argue for its virtue and try to think through ways of living together in this pluralistic condition.
(3) Bruno Latour's modal pluralism is a metaphysical pluralism in another sense: he argues not just for a plurality of beings but for the plurality of being itself ‒ that is, there are many ways of being; being is itself pluralistic. To be is to persist in being somehow but there are many ways of achieving that persistence (these ways are irreducible to the achievements of individual entities) and, so, being is pluralistic.
Bruno is not the first to come up with this basic idea (see Souriau, Simondon, Deleuze, etc.) but his is a striking and unusually sophisticated example of the genre.
(4) The order that I list the three above meanings (or circumstances) of 'pluralism' is not accidental. Latour's modal, metaphysical pluralism is also a kind of political pluralism; it would be well termed 'value pluralism writ-metaphysical.' There is his mode of politics [pol], of course, but the entire project is a matter of detecting, evaluating and re-instituting values. It is as much a political as a metaphysical pluralism in this sense. And so, at risk of gross oversimplification, we can say that (4) fundamentally differs from (1) because it passes through (2) and (3). It is a far deeper pluralism that places far greater demands on us, should we follow its lead.
Levi subscribes to (1) ‒ pluralism in the sense of umwelten ‒ but has seemingly little time for the others. He can thus pursue a scientistic, modernist pluralism (I'm not even sure he'd disagree with those adjectives at this point) that is a metaphysical but not political; a metaphysics that is pluralistic with regard to beings (1) but monistic with regard to being (3) and which endorses a disqualificatory attitude towards ontology and a politics of speaking truth to ignorance and irrationality.
Myself, I disagree with many of Latour's arguments but I follow him all the way to (4). My preferred understanding of his pluralism (i.e. an interpretation that is creative but, I hope, a fair translation of his texts) is summarised here. Politically, I understand it to be an agonistic pluralism much like that of Chantal Mouffe but extended to a metaphysical level through the modes philosophy.
My understanding of Isabelle Stengers' philosophy is that it is broadly compatible with the above also, perhaps with some differing nuances and emphases compared to Bruno but mostly on the same page, as they say.
Both, it seems to me, are committed to a pluralism that goes beyond cosmography (1) and enters into cosmopolitics (4). Their pluralisms are not disinterested or neutral, they are committed and committing ‒ that is, they commit us to certain ways of being with each other. They offer us not just a 'picture' of existence, framed as a multiplicity, but offer suggestions for living.