One from the Archives: Negativity

Although I’m working on other things at the moment (though very slowly, due to this rotten cold), it occurred to me that I’ve got a bunch of material lying around in my email account from various conversations I’ve had with terribly interesting individuals. Some of this is fairly easy just to copy and paste onto the blog, so there’s no good reason not to do so. I’m going to post them pretty much as is, and any necessary corrections or revisions will appear in ‘[…]’.

To start with, here’s something I wrote in response to a really excellent question from Alex Williams on my understanding of the relation between politics and negativity. It doesn’t really talk about politics much, but rather tries to disambiguate various ways in which the concept of negativity can be deployed philosophically. Hope you enjoy.

I haven’t read Benjamin Noys book on the matter, which I suspect I should, but I’m generally very skeptical of the way ‘negativity’ and ‘positivity’ get used in much of mainstream continental philosophical discourse. It’s one of my pet peeves actually, because it often ends up running together logical and metaphysical issues with metaphorics of affectivity (‘we must be positive’ or ‘we must be negative’, etc.). That said, I’ll try and disentangle the bits I think something can be said about as best as I can.

There’s basically three different registers in which talk of negativity is relevant: philosophy of logic, philosophy of subjectivity, and metaphysics. These overlap insofar as subjects can be conceived as necessarily having the capacity for reasoning (which is made explicit using logical vocabulary) and insofar as there are questions about the subjects place within reality (and the relation between logical and metaphysical structure more broadly). To understand the relations between these different ways of talking about negativity I’d like to trace a few historical debates running through Spinoza, Hegel, Deleuze, Heidegger, Sartre and Brandom.

Beginning with Spinoza, there is the famous principle that omnis determinatio est negatio – all determinations are fundamentally matter of negation, i.e., one characterises what something is (be it an individual mode or a general quality) by determining what it is not. Deleuze famously reads Spinoza contrary to this principle, and tries to develop his own metaphysics of ‘pure positivity’. This is not empty rhetoric, as we will come to see. The best way to understand this is to see the way this idea develops in Hegel’s philosophy of logic, which Brandom has done a good job of reconstructing and developing further. He picks out the notion of incompatibility as what is central to Hegel’s approach (which he takes to be synonymous with ‘determinate negation’ though I think this is perhaps an overstatement). Incompatibility is a relation that both propositions and concepts can stand in amongst themselves  (e.g., ‘My brother is upstairs’ and ‘My brother is out walking’ are incompatible, and the predicate concepts ‘…is red’ and ‘…is green’ are incompatible). Brandom’s idea is that Hegel takes the content of propositions and concepts to consist solely in their incompatibilities. This means one grasps the concept ‘…is red’ and the property of redness that it corresponds to by understanding what something being red excludes as a possibility.

Brandom elaborates this point by showing that one can derive inclusive differences between predicates from these exclusive differences. The property of being a car and the property of being red are distinct without being incompatible (i.e., it is possible for there to be red cars), which is an inclusive difference between them. Yet, this can be derived from the fact that they are incompatible with different things (e.g., there can be green cars, but not green and red things, at least, not in the same spatio-temporal areas). This means that the incompatibility relations between predicates let one produce complete Aristotelian hierarchies of genus and species, in which one has a series of distinct highest level genera containing mutually exclusive species. Brandom has also been trying to show how one can use these relations between concepts to generate incompatibility relations between propositions, which we can then use to derive inferential relations between them (e.g., ‘x is a dog’ implies ‘x is a mammal’, because everything that is incompatible with being a [mammal] is also incompatible with being a dog, but not vice versa). This is what Brandom takes Hegel’s discussion of ‘mediation’ to be about. Regardless, Brandom shows how Hegel provides a conception of determination, or difference, which is based on a specific form of negativity, namely, incompatibility (or opposition), from which he derives more ordinary forms of difference, namely, distinction (or diversity). Indeed, Brandom thinks that the logical role of negation (i.e., the ‘not’) is just to make explicit these forms of difference.

Now, Brandom has a notoriously non-metaphysical reading of Hegel, and I’m certainly opposed to this particular aspect of his reconstruction. Because of his strong conception of the identity of thought and Being, Hegel takes relations of incompatibility and inferential mediation to be genuinely constitutive of the structure of the world, to the extent that he thinks that the notion of contradiction (which is based on incompatibility) not only plays a motive role in the process of reasoning (e.g., by forcing us to revise our contradictory claims into synthetic unities), but also in the unfolding of nature (i.e., his infamous discussions of contradictions driving growth in living things and motion in bodies). Following Deleuze and others, I think that this is a very forced interpretation of the nature of change. However, we can still see in Hegel an important connection between this interpretation of the logic of difference and negation and the nature of subjectivity. Hegel’s conception of subjectivity is essentially rational (it is a development of Kant’s on this point), and thus must be able to navigate the relations of determinate negation and inferential mediation that structure the world. Thought involves negativity in a very crucial way for Hegel, which becomes even more crucial in dialectic as the highest form of thought. Contradiction plays a motive role in the process of reasoning insofar as it forces us to revise not only the propositions we take to be true but also the concepts which articulate their content. Dialectic is just the process wherein we allow the content of concepts to unfold by way of working out the contradictions of their simpler forms until they become more complex and determinate. Again, Hegel simply reads this into the structure of the world itself because of his commitment to the identity of Being and thought.

Heidegger’s contribution to the debate over negativity is his discussion of the Nothing, which then gets taken up by Sartre and Badiou amongst others. I’m currently writing a big bit of my conclusion on this and it’s relation to the philosophy of logic (in order to conclusively refute Carnap’s criticisms of Heidegger), but I’ll try not to go into too much detail. The important point to make is that although Hegel and Heidegger both hold that Being and Nothing are identical, what they mean by this is very different. For Hegel, the claim is what he calls a speculative proposition. It’s explicitly a transitional claim that will ultimately be superseded by others. This is obvious if one remembers that the Logic is just a matter of explicating the content of the concept of Being, reaching it’s culmination in the fully articulated Absolute Idea. Being thus turns out not to be empty of content after all, it’s simply that it initially appears to be devoid of content, and the claim that it is identical with Nothing makes this explicit, thereby beginning the dialectic of explication. For Heidegger, the claim is not transitional at all. Heidegger thinks that the concept of Being has a very determinate and specific content, and that this is identical with the very determinate and specific content of the Nothing. The definite article is very important here. Hegel’s notion of Nothing is a general concept (i.e., nothingness) that applies to a plurality of nothings, whereas Heidegger is talking about a unique Nothing. He’s talking about the structure of the world as distinct from it’s contents, which for him is the structure of Dasein’s temporal projection of a world, or what he calls Temporalitat in Basic Problems of Phenomenology.

Leaving aside the specifics of Heidegger’s account of Being and its relation to time, the important thing is to get clear about this relationship between nothingness and negation. Nothingness is a fundamentally quantificational notion. It’s about there being a specific number of something that functions as a limit-case in relation to all other numbers, namely, zero. It is a limit-case insofar as it can be opposed to all other numerical possibilities (i.e., to there being something). It is thus in a sense the negation of the fact that there is something. We have nothings when we have what I call empty states-of-affairs. There is no milk in the fridge, no money in my bank account, and no resistance to capital. These are all relatively empty states-of-affairs, as they are absences of specific things. Heidegger’s Nothing is unique insofar as it is the limit-case of limit-cases. It is the absolutely empty state-of-affairs, or an unqualified absence of things. I think Heidegger is onto something when he equates Being and Nothing, insofar as it provides a way of defining Being as the unified structure of entities as such and as a whole (or the structure of reality), which in principle excludes onto-theology, insofar as Being is not. This means that there is interesting work to be done here regarding the metaphysical status of the Nothing, Nothingness, and its relation to negation, and so that there is an interesting debate to be had with figures like Badiou, who interprets a lot of this by way of the empty set, which is both singular (the Nothing) and general (Nothingness) insofar as all specific nothings are identical to it due to the axiom of extensionality. However, such debates presuppose getting clear about the relationship between thought and Being, and thus the relationship between logic and metaphysics. It is in this space that the various permutations of these themes we see coming out of Hegel and Heidegger (e.g., Sartre, Badiou, Laruelle, Ray) come into play.

I’ve made my own views about the relation between thought and Being, and logic and metaphysics particularly, very clear elsewhere. My position can be usefully contrasted with some of these successor positions. Beginning with Sartre, I think that his appropriations of both Hegel and Heidegger are terribly shallow. He does not appreciate the importance of incompatibility for Hegel, nor the notion of inference, and so develops a rather trite phenomenology of negation in which we trace the distinctions, or inclusive differences, between the concrete particulars we experience, rather than the rich connections between the general concepts that describe them. He does not appreciate the importance of the Nothing in Heidegger, abandoning it in favour of a metaphysics of Nothingness that he derives from his uninspired phenomenology of contrasts. He thus rejects both the resources that Hegel provides for developing an interesting account of thought, and the resources Heidegger provides for developing an interesting account of Being, and on top of this completely fails to circumscribe the methodological issues surrounding the relationship between thought and Being. He simply treats thought as one mode of Being (the for-itself) in terms of which the other principle mode of Being (the in-itself) is to be understood. True, the early Heidegger did this too, but he at least tried to provide an interesting argument for it, rather than just stumbling straight into ‘phenomenological-ontology’. Moreover, he is less interesting than Heidegger insofar as he interprets this mode of Being as having a kind of causal efficacy disconnected from that of the in-itself. This is the vulgar Kantianism I described [elsewhere]. In order to make room for this metaphysically inflected notion of freedom he turns the subject into a Nothingness, a transcendence removed from the causal order of the in-itself. As you can tell, I think that this is one huge motherfucking step back in every respect.

I don’t really understand Badiou well enough on these points. I suspect that he doesn’t follow Hegel in grasping the importance of incompatibility, as his whole model of predication in terms of set-theory is purely extensional. This would ally him with Sartre on the question of negation. But his use of extensionality to combine Heidegger and Sartre’s notions of Nothing and Nothingness (in the empty set) is potentially more interesting. It certainly requires more attention on my part. Nonetheless, I still think that his whole approach vis-a-vis the relation of thought and Being, the situation of the subject within the natural order, and the connection to freedom and sufficient reason is way too Sartrean. Even if he has a conception of the subject which is less individualistic than the early Sartre (and maybe even more Hegelian and subtle than the later Sartre) he still conceives of it in terms of nothingnesses and supplements to the causal order.

Ray’s fusion of Laruelle and Badiou in Nihil Unbound is more subtle and interesting, precisely because it explicitly severs it from the Sartrean influence and its rejection of sufficient reason. This isn’t to say that it explicitly champions sufficient reason, although there is certainly an interesting relation between it and determination-in-the-last instance, but Ray is clear in his critique of the Badiouian account of the Event and in his support for the scientific process of comprehending nature. Indeed, his use of the Laruellian notion of unilateral duality as non-dialectical negativity and the Badiouian notion of the void as Being-Nothing can be seen as trying to produce a minimalist ontology that circumscribes the relation between thought as the scientific process through which nature is comprehended and Being as that both that which it comprehends and is. Unilateral duality is thoughts ability to think its own inability to assimilate the Real insofar as it is determined by it in the last instance, and Being-Nothing is the world as limit-case of scientific comprehension, the Real as evacuated of all content, or as what is common to all stages of the indefinite process through which scientific thought attempts to grasp it. It’s an interesting approach, though I think it ultimately can’t go anywhere, because it’s Laruellian elements are neither sufficiently detailed in their account of the transcendental structure of thought (decision is a weak schema of philosophical thought) nor able to support anything like the positive metaphysics of extinction Ray tries to develop at the end of the book. Nonetheless, it avoids vulgar Kantianism and tries to genuinely think through the relation between thought and Being.

My own position has a certain similarity to Ray’s use of unilateral duality, but it is much less hostile to transcendental philosophy in its authentic Kantian form. I’m happy to provide detailed analyses of the structure of thought, and use these to demonstrate the relationship between the structure of thought and the structure of Being (my transcendental realism). This leads to a conception of the relationship between thought and Being in which while it is true that subjective domain is distinct from the natural domain only from its own perspective (the difference between the normative and the natural is itself a (unilateral) normative difference), this does not foreclose either the possibility of adequately describing either domain, at least, not in the way Laruelle’s position does. I end up with a position in which we can describe the formal structure of thought, and this enables us to describe the formal structure of Being (e.g., to make explicit our pre-ontological understanding of it), even if its real structure is in excess of this. The question that I’ve left open is whether or not the Real can be completely grasped by the scientific cognition of the world. I tend to agree with Ray that it is an indefinite process, but I think that we need much better arguments to demonstrate this.

This is where I see Deleuze coming in, insofar as his critique of Hegel demonstrates that we must understand the way in which the Real is actually determined (or internally differentiated) cannot be understood in terms of negation, but must be understood in terms supplied by differential calculus. This is what underwrites Deleuze’s claim that a lack in the concept is an excess in the Idea. Hegel may have shown that the way reason (or what Deleuze simply calls representation) tracks the determinate structure of naturenecessarily involves a certain form of negativity, but this is perfectly compatible with the determinate (sub-representational) structure of nature being in excess of all such forms of negativity (and thus purely positive). This is not a trite appeal to something like Ereignis or Differance, which refuses to provide a positive metaphysics of the excess of reality, but is grounded in a detailed account of the nature of the sub-representational. To explain this more would require going into a great deal more detail though [(watch this space)].

Returning to the question of the relation between negativity and politics then, here’s my conclusion. Negativity has nothing to do with the proper metaphysical circumscription of the natural, including the manifestation of the cultural within nature. If it has any role, it’s in our understanding of the structure of thought itself, and thus if it has any political role it’s going to be in our understanding of the structure of political thought and action, or political reason. Leaving all appeals to affective negativity (e.g., the psychologically transformative power of depression, the aesthetically transformative power of black metal, etc) aside, which I think are reasonably spurious and certainly unrelated to the important issues at hand, the one issue to which an understanding of rational negativity can perhaps make a contribution is the nature of critique. I’ve written some basic things about my understanding of critique before, but I see it as a fairly broad phenomenon. I haven’t done much further work on it, but I’m increasingly coming to see that the sensible aspects of Hegel’s account of dialectic (and their relation to the classic socratic method of dialectic) is an aspect of the account of critique, and that here the role of negation (which is to be understood logically) is very important. The Hegelian idea that we can not only criticise concepts (as opposed to sets of propositions) but use this process of criticism to develop more positive and determinate positions that incorporate the insights of those we surpass, is a very powerful one. This needs to be analysed in more detail, but its clear that in order for this to work, the logical role of negativity here needs to be totally dissociated from any associations with aggressive or reactionary affective negativity. Critique is not about destroying one’s opponents, but playing off of their positions in the process of seeking truth.

Published by


Appropriate descriptors: (neo)rationalist, left-accelerationist, socratic wanderer, heretical Platonist, computational Kantian, minimalist-Hegelian, heterodox Foucauldian, dialectical insurgent, conceptual mercenary, philosopher of fortune.

3 thoughts on “One from the Archives: Negativity”

  1. Wonderful post Pete, as usual. I would like to ask you about your brief exegesis on Badiou. You claim the following:

    “I suspect that he doesn’t follow Hegel in grasping the importance of incompatibility, as his whole model of predication in terms of set-theory is purely extensional.”

    Can you explain why an extensional approach would miss the importance of incompatibility? The axiom of extensionality (AOE) simply states that a set will be different to another if and only if there is an element of one that isn’t an element of the other. This leaves it open that there might be some elements that both share, or none. And the same holds for inclusion: something that does not belong to a set might nevertheless be a part of it (what he calls ‘exrescences’), and something that is not a part can be an element (what he calls ‘singularities’).

    On any account, it seems to me that both inclusive and exclusive differences can be accounted for, and neither would have an ontological prerogative. Indeed, since the AOE distinguishes by the mere exclusion of one element in one of two sets, it’s scope is invariably more general than inclusive or exclusive differences. For it could easily be that two sets share nothing, or that they share some elements, or that they are parts-elements of each other.

    Great post!

    1. Hi Dan,

      The point is that incompatibility is an intrinsically *modal* notion, and thus is intensional rather than extensional. If propositions P and Q are incompatible, then it’s *impossible* for P&Q to be true, and if predicates F and G are incompatible, then it’s *impossible* for Fa&Ga to be true. This means that characterising the content of predicates in terms of incompatibilities is different from categorising them as sets, insofar as the latter are defined by the members they actually have. This is what it is for them to be extensional, rather than intensional.

      So, on the one hand, the set of lions is different from the set of lions there would be under certain specified counterfactual conditions (or if you prefer, in some possible world), and the set of creatures with hearts and the set of creatures with kidneys are identical because they have exactly the same members. An intensional characterisation of the predicates ‘…is a lion’, ‘…is a creature with a heart’, and ‘…is a creature with kidneys’ would behave differently, allowing us to talk about possible lions, and to distinguish creatures qua possessing hearts from the same creatures qua possessing kidneys.

      Now, of course, it’s possible to try and build intensional semantics out of extensional components. This is just what possible world semantics (in it’s various forms) aims to do. However, I would argue that this never gets you truly intrinsic modal features of things, but tends to just derive them extrinsically from an expanded actuality (i.e., an actuality that now includes whatever possible worlds that there are).

      I can’t comment on how this stuff on modality relates to Badiou in any detail. I know the third volume of B&E is supposed to deal with modal logic, so I suppose we’ll see how it goes. However, I doubt he’ll be able to provide the sort of intrinsic account of modality that a neo-Spinozist like me is looking for 🙂

  2. hi pete
    you said that there are basically three registers where negativity plays a relevant role: philosophy of logic, philosophy of subjectivity, and metaphysics. I think you forgot about ethics.
    Second, it is probably worthwhile to note that at the end (much later to the work on Spinoza) Deleuze came up with positive negativity, emphasizing thereby the latter. The problematics “solved” by that is not a minor one (at least, it outlines the direction where to look for a solution).
    It is impossible to define anything in a positive manner without implying “violence” (involving the problem of justification), or to deny potentiality/virtuality. Here we meet also the central problem of idealism/materialism.
    I think the only thing possible is to describe conditions, which is nothing else than to lean to negativity. That does not mean that everything or even just a particular identifiable thing is “negated”. The principle of positive negativity is just to withhold any attempt of a positive definite fixation.
    This argument easily applies to any of the flavors of philosophy you discussed. And I don’t think as well that it fits to your three registers (which could be separated anyway only in a rush of a structural idealism…)

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s