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A Thing of This World‘s fourth chapter is dedicated to Nietzsche, a rather interesting choice, as Braver states from the very beginning of the chapter. Nietzsche’s big beef with realism is its psychological motivations “that cause people to find certain views persuasive” – if realism is a disease, so to speak, then what is the cure (if there’s one) or, more interestingly, what is the motivation behind the philosophical view of reality that is always assuredly there? Nietzsche’s response is simple: the motivation is weakness in the face of chaos and flux of becoming, realism is but an escapist fantasy, a support group for the weak (“Too overwhelmed with chaos, change and becoming are getting you down, have no friends and nowhere to go, join Realism Support Group this Wednesday”) In this sense, realism as a belief in the independent reality “out there” is akin to a religious outlook in its search for certainty and its way of dealing with the responsibility to create one’s own world. This “realism as religion” view is also confirmed, Braver writes, by the simple observation that “God is the oldest and obvious example of an independent reality issuing commands.”  Braver has a section on Nietzsche’s specific takes on “realism” and a section on “anti-realism” which one can easily acquaint oneself with – everything is splendidly compared and contrasted there. R5 Passive Knower and R1 Independent Reality are most obviously in trouble, and so is R2 Correspondence and R3 Uniqueness. R4 Bivalence is out of the question as Nietzsche often addresses the issue of “black-and-white thinking” that has overcome philosophy lately. R6 Realism of the Subject with its belief in a core, atomistic self is surely a myth aimed to help us deal with whatever it is that we are so need to deal with.
A discussion of Nietzsche’s anti-realism then takes a large chunk of the chapter. It opens with a repetition of the formula:
Realism is the belief system the weak resort to in order to escape the stress of internal and external conflict and flux, as well as the responsibility of choice and creation forced on them by these conditions. The strong, however, embrace and even celebrate these conditions; they accept that the world is of their own making, and, at the highest, take control of this process. [121-22]
So Nietzsche then is all about A5 Active Knower (like Kant) because the belief in “things” as pre-existing uninterpreted reality is unfounded, and serves the same purpose of supporting the weak and their fear of unreality. It is also all about A1 Mind Dependence, even if something like “noumena” does exist, it is of no interest to us and therefore the notion is refuted and rejected.
A6 Multiple Selves is where Braver thinks Nietzsche really advances anti-realist agenda:
Whereas Hegel gathers up the temporally spread but logically linked phases of the subject and reality into a limited, rationally structured totality, Nietzsche scatters an irreconcilable multiplicity of power-hungry drives. 
Nietzsche does the above in two moves/innovations that Braver shortly describes as following:
1) Niezsche extends the Empirical Directive and inserts the self into the world by identifying it with the body – there is no longer anything like a noumenal or transcendental self (no soul, no spirit, none of the left-over Christian superstitions). Anything resembling categories is explained in terms of evolution and nature, there is nothing transcendent or transcendental (“Keep moving, people, there’s nothing to see here”). Any stability is formed through reification and simplification – we need to survive and since only stable, self-identical objects can help us do so, we invent them.
2) Nietzsche disavows simplicity and stability – everything is complex and changing now. However, any change and adaptations are not rational as “the wills and drives are not debating each other in a mock United Nations.”  Apparent stability of anything is a mask, mostly a mask of “will to power.”
Nietzsche’s view of truth deserves our attention, argues Braver, because it is a rather peculiar one as Nietzsche redefines the very value of truth, of the true-false dichotomy. Braver identifies “pragmatic truth” and “corresponding truth” in multiple uses in Nietzsche’s text. The ultimate result is easy to guess: “The impossibility of correspondence frees us from attempted allegiance to reality, liberating us to create new views for the purpose of making a better life.”  Correspondence truth is making it impossible for us to use our creativity and blocks us from taking control by providing us with a number of fanciful doctrines that fascinate us but fail to provide for any better life. More than that, the insistence on univocal truth is bad for us, it closes off alternatives and oppresses us with its awesome but ultimately annoying (and certainly overbearing) rightness.
In opposition to supposedly descriptive realism (which it is not, of course, because mere description and correspondence are myths used to boss us around) and normative (prescriptive) realism (normativity here is based on the same sort of sources as the normativity of any religion – dogmatic propositions one has to embrace without questions/criticisms – for example, like a belief that we can talk about objects with any references to humans as in some versions of “speculative realism”) , we need normative anti-realism that helps us understand that values are our very own creation and we need to create better ones.
Once we understand that we were creating these ideals all along, we realize that we are not bound to the ascetic, anti-life values inherited from tradition; we can discard those to make more life-affirming ones. 
In order to do what we have to do, we let passive nihilism destroy the previous set of commands and then active nihilism can help us create better values. More perspectives, more ambivalence, less posturing claims of knowing the truth, less assholery of the educated and so on.
The rest of the chapter deals with possible issues with Nietzsche’s pronouncements and I honestly don’t really get most of it as it attempts to find inconsistencies and contradictions in Nietzsche (or at least attempts to critically evaluate his positions, or that’s what it reads like to me) right after the previous discussion told us exactly how little Nietzsche cared for that sort of philosophical exercise, so I’m going to let the readers take a look at it themselves. Much of it is subtle and sophisticated and I don’t have any sort of expertise here to evaluate it (especially the Step Six Physics section) and simply restating it seems superfluous since it’s a reading group after all.
My main question that sort of popped up here and there as I was reading the chapter dealt with possible political implications of both realism and anti-realism – what sort of politics would a realism of the weak solicit? what about an anti-realism of the strong? Multiple realists go about their realist ways avoiding issues of politics (“we are metaphysicians, not politicians!”), multiple anti-realists do the same – I wonder if it’s about that time in the book that we have at least attempted to raise the issue of political signification of realism/anti-realism dichotomy?