Since this chapter is about the size of a small book, my intention here is not to rehearse its main arguments (although it’s almost never my intention to begin with), but to attempt to highlight some of its most provocative (on my view) ideas in light of the already raised issues of realism/anti-realism in general and the discussion of so-called Kantian Paradigm in particular. I will confess immediately that having read my share of later Heidegger and having heard my share of philosophical smirks about it (“Can you hear the call of Being right now?”) I still don’t get much of what Heidegger is talking about, or, I should qualify this statement, I don’t think I get much of what Heidegger is talking about, regardless of many moments of profound philosophical excitement that accompanied my readings of later Heidegger. Having said that, I must then confess that my discussion of Braver’s chapter will not be (since it simply cannot be) a probing investigation along the lines of “Did Braver get Heidegger right?” for two reasons: 1) I don’t know enough about later Heidegger interpretation field to claim any sort of expertise and, most importantly, 2) probing is ultimately a rather boring exercise…
As tempting as it is to begin at the beginning of the chapter, I think a better way to appreciate the real shift from previous discussion is to cite a small section closer to the end of the chapter:
We have to remember that meaning doesn’t come from us and that we cannot control it, since even those decisions to control are themselves determined by how things present themselves, and that the sustaining traditions represent a groundless ground, that is, they cannot be given ultimate rational justifications. Once we understand these features, we realize that we are immersed in rhythms that guide and support us, supplying us with “those paths and relations in which birth and death, disaster and blessing, victory and disgrace, endurance and decline acquire the shape of destiny for human being. The all-governing expanse of this open relational context is the world of this historical people.” […] This is the ethical side of epochal destiny: just as it gives us our way of thinking, so it gives us a way of dwelling, of being at home on this earth we were thrown into, of living with each other in families and communities, of celebrating festivals, worshipping gods, and facing death. [338-39]
I think it takes a bit of time to get to this point in the chapter (both physically and philosophically, if you will), but unless one has a slight idea of what exactly all of this means, one cannot really pretend to have understood Braver’s point about later Heidegger.
What is precisely the point of later Heidegger vis-a-vis the discussion of realism/anti-realism? I think the shortest version would be something like this: while early Heidegger (by his very own admission, although it’s not always wise to trust the authors themselves in such matters) still dealt with philosophical problems in terms of the Kantian Paradigm with its emphasis on the subject’s activity (whatever Heidegger’s own interpretation was), later Heidegger moves away from specifically Kantian version of active subjectivity and creates what Braver labels (appropriately) the Heideggerian Paradigm. Braver argues that Heidegger’s new conceptions of truth and Being inaugurate the next major phase in continental philosophy. 
Perhaps the single most important difference between Heidegger’s two phases is the way history permeates everything in the later work. 
This new position – “historical phenomenological ontology” – depends for the most part on Heidegger’s innovative understanding of truth as unconcealment (which my spellcheck refuses to accept as a real word). I am italicizing unconcealment possibly to the annoyance of some self-respecting Heideggerians since I am eager to emphasize what seems to be on the lips of anyone familiar with later Heidegger – it’s unconcealment this and unconcealment that, and Braver spends a lot of time and paper explaining exactly why unconcealment is essential (in the process, indeed, persistently unconcealing some of the later Heidegger’s most mysterious passages, sorry couldn’t resist).
What truth as unconcealment teaches us, seems to be the point, is that ultimately the traditional model of truth as correspondence (and therefore as correctness) is missing the mark and, some pages later, we find out that this missing of the mark does not come without a price in Heidegger’s discussion of technology and nihilism. However, the essential point of this new vision of truth is Heidegger’s transition from Kantian A5 Active Knower to a version of R5 Passive Knower (with a twist, of course). If the essential point of the Kantian Paradigm is that “the examination of anything else, including history, must start from the analysis of the structures of the self because it is these structures that constitute the rest,”  then the new Heideggerian Paradigm is all about “mutual interdependence” between Being and man.  Of many great formulation of this “mutual interdependence” my favorite is this: “We are the necessary site [of being/of thinking], but we do not control, constitute, or create this site; we depend entirely on the fact and character of Being’s approach.” 
What happens to the Kantian Paradigm then? On one hand, Braver writes quite explicitly, Heidegger continues the work he started in his early period, regardless of the Kehre, yet on the other hand, it seems that Heidegger must begin from scratch and free his thought from any remnants of Kant’s discussion of subjectivity and its constituting work: “the Heideggerian Paradigm is simulatenously close to and far from Kant, as appropriating his thought but also profoundly modifying it…”  Or, again, “rather than the subject opening and structuring a field of experience, Being maintains us in unconcealment, so we must examine this structure in order to stude Being and man, a new form of fundamental ontology.” 
The result of Heidegger’s reworking of the Kantian Paradigm is described in much detail, but is probably best captured in the notion of “Impersonal Conceptual Schemes,” admittedly a rather strange combination of words/senses, but according to Braver it works best to describe what Heidegger is up to. I am of couse skipping over some large chunks of text (and interesting discussions of, among many other things, epochs of Being, technology/enframing and more) here, but I think that as far as I am concerned, what is most interesting about this chapter is the way “ethics” makes it into the discussion of realism/antirealism as a consequence of Heidegger’s rethinking of the relationship between Being and humans. The passage I cited at the very beginning of this post present us with a rather intriguing ethical scenario of “attentive dwelling” and yet I wonder (possibly repeating myself) why only now we are talking about what is essentially a question that has to be prominently raised in every chapter, i.e. what sort of ethics does this or that version of realism/anti-realism scenario presents us with?
As I was writing and rewriting this admittedly short post on Chapter 6, I realized that I have basically reread the chapter again, thus all of my time went into trying to understand the subtleties of Heidegger’s (and Braver’s) discussion. So caught up I became in reading and rereading it that I almost forgot that we have tickets to the baseball game tonight and I must go fulfill my patriotic beer-drinking and hot-dog-eating duty. Thus I am going to leave this as it is and see if I can use comments as a way of continuing my engagement with this rich chapter.