Lacan, Zizek, Badiou: Why Sellars Matters in These Debates?

LACAN, BADIOU, ZIZEK:

Why Sellars Matters In These Debates?

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As a response to my last post about Zizek's claims to realism, and my latest post on the theoretical cogency of psychoanalysis, I have been receiving some critical commentary, all roughly along the same lines. Characteristically, by my friends Levi Bryant, and Javier Urbina, all defend Lacan from my criticisms. As far as I can gauge, the main criticisms are that:

a) Lacan, and by extension Zizek, are not interested in a notion of the Real like that of philosophers. Therefore that the questions about realism raised by people like Meillassoux or Brassier, concerning our access to the in-itself, are not to be conflated with Lacan's own questions.

b) Badiou, similarly, has no analogous concept of the Real as impossible, but rather of Being as inconsistent, which is radically different, and should not be identified.

Levi wrote the following:

"You treated psychoanalytic practice in terms of knowledge, presupposing a set of transcendent criteria for evaluating it, missing the entire point that the psychoanaytic clinic is a site of evental truth and a truth-procedure for the analysand that undergoes it. The psychoanalytic clinic is not after *knowledge*, nor does the analyst *have knowledge*. The psychoanalytic clinic is after that which *escapes* knowledge and language. This is what the term "subject" means in psychoanalysis. Subject is precisely that which is in excess of any linguistic category and that through this excess generates a series of signifying effects as language strives to gentrify it."

In private, a friend wrote the following:

"Dear Daniel,

I just read your post on realism and your critique of Zizek which is very good and makes an excellent point about how Lacanians (and Zizek) in general are trying to enter into the debates started by the speculative realists/materialists/etc. I have a few questions though, I hope you don't my launching directly into criticism.

Perhaps the real -subject/object issues are not really the same between the Lacanians and, say, Brassier. This is one of those situations where the question already defines the answer. This is ultimately Zizek's error but I think you err precisely in taking him too seriously. To be specific, Lacan's Real occurs within an economy of the symbolic and imaginary: the barred subject faced with objet a does not correspond to those discussions of the real being addressed in realism, neither ontologically nor epistemologically. The legacy of structuralism is right here: the price we pay for the generation of semantic distribution is the alienation from the real.

Zizek's point precisely is that it is this precise exchange that is the real. I would disagree here with your paragraph that starts "put simply". If Zizek and other Lacanians want to argue that the rule is precisely a fracture within discourse itself (barred S <-> a) and that is what truth is: well obviously there is no real conversation to be had with Sellars, Brassier, etc. We are talking about different things.

Now we get to your brief comment about Badiou. I would say that the matheme does not touch the real in Badiou because there is no real. Being, yes. Truth, yes. Knowledge, yes. No real. What is more important is that despite all the differences between Badiou and the Lacanians, they share on this point that you are criticizing. That is: for Badiou the very possibility of ontology is rooted in the inaccesibility of the unity that underlies the Parmenidean condition in its original meaning: what is not one, is not. By arguing that the one is not, mathematics doesn't really "touch" the real. What it does is fully flesh out what is being "not one". This is a version, again, of Zizek's point, which locates being (if we want to call that "real") on its incapacity to be grasped "adequately" or "qua ens".

Having said this about Badiou, I want to empahsize again that I do not think there is a real in Badiou nor do I think that he can play any significant role in these discussions. The problem is that they talk past each other.

Let me know what you think of these brief reflections.

Hope you are well.

"

Despite the pertinence of these rejoinders, I think my original criticisms, if read carefully, anticipate these potential rebuttals, and show that nevertheless the indicated problems remain for these thinkers. But I thought I might use this as a way to clarify what I think is precisely at stake in the axis composed by Zizek, Lacan and Badiou, in spite of their differences.  Predictably, Hegel turns out to play a somewhat important role here.

I - Zizek and Lacan: Why it's not just a different question

As indicated above, the main problem both Levi and my friend indicated apropos my reading of Lacan and Zizek, is that I illegitimately import standards proper to the concept of the Real in contemporary realist debates, and which are enveloped by ontological and epistemological concerns, with Lacan's psychoanalytic concepts. Levi targets the residual concern with representation in my account; my other friend, in turn, simply indicated that the Real couldn't be thought of as pertaining to a mind-independent reality, and therefore couldn't be judged in accordance to standards set by philosophers in regards to that problematic. 

With regards to Lacan and Zizek, I think a few observations are in order. I certainly agree in that Lacan does not want to formulate his thinking about the Real in epistemological, or indeed ontological, terms. Nevertheless, I think it is important to distinguish between what an author says they are doing and what they effectively end up doing; or put differently, between what they want to say and what they commit themselves to saying. I recently wrote in more extensive length why I think that, in spite of Lacan's 'anti-philosophical' attempts to wrest the theory of desire that psychoanalysis produces away from classical ontologico-epistemological concerns, he ends up effectively cornered into a sort of methodological quandary, that results from the elision of representation. Finally, I think that this quandary demands, in spite of its protestations to the contrary, from us to read Lacan as moving within a philosophical register, which indeed implicitly relies on representation.

       With that said, I think that Lacan's account of the Real is certainly ambiguous: on the one hand, we have the structuralist adherence to the immanence of the signifier, and therefore of the articulation of desire between the imaginary and the symbolic. On the other hand, we have a conception of the Real as that which resists symbolization, and of the recalcitrance of Real desire to the order of the signifier. But how to attempt to give an account of this separation between the Real and the symbolic-imaginary, without thereby ontologizing desire, in its structural coupling between the barred subject and the Real object? My contention is that, beginning from Seminar XI onwards, Lacan begins to flirt with the idea that mathematization allows precisely for this kind of operation. On the one hand, as Russell had already noted, the matheme subtracts itself from the order of the symbolic, because it is not inherently meaningful. Thus, we cannot 'translate' mathematical formulas or their syntactical composition into ontological, or epistemological terms. Of course, for Lacan, this is precisely a crucial requirement in dislodging psychoanalysis from (ego)-psychology, which continues to reify the subject as an individual, and which must therefore tacitly remain encumbered in the imaginary-symbolic envelopment of the signifier, and of the symptom. 

What the matheme offers, in turn, is a non-translatable formal ideography recalcitrant to such operations. But the question then becomes about how we can distinguish between the Real of the mathematic inscription, and that of the Real phenomenon or 'Real desire' that psychoanalysis is in the process of providing a theory of. And my claim is that this forces Lacan, and consequently Zizek, into a methodological quandary. On the one hand, it is clear that he cannot avow for the separation between Real inscription and Real phenomenon without reactivating the distinction between representing and represented, signifier and signified, that marks epistemological discourse. On the other hand, it seems clear that if psychoanalysis is to be a theory of desire, rather than just another phantasy, circulating around its own proper impossible object, the formalizations it carries out and the claims it makes about desire cannot be identical to the Real desire that the analyst is set to deal with in practice. This is because if we conflate the generality of the statements/formulas with the analytic transference with the analysand, then the theoretical practice that psychoanalysis embodies, and the clinical practice, become conflated. But short of accounting for this separation, it renders suspect the theoretical status of psychoanalysis, purporting to have done away with representation.

So the question becomes: what is the relation between these three crucial levels:

a) The Real of desire, in its structural coupling between the barred subject, and the object-cause.

b) The claims of psychoanalysis, that are still formulated by way of the signifier.

c) The formulas of psychoanalysis, that formalize the structures described by those claims.

And I think here is where Lacan must tacitly rely on both an ontologization of Real desire, on the one hand, and an epistemological account of the relation between the claims that psychoanalysis makes, the formulas it produces, and the Real phenomena that these claims describe. For the matheme would be truly 'meaningless', and couldn't count as a formalization of anything, unless psychoanalytic discourse and claims held a prerogative when describing the general structure of desire. But what sets this prerogative for psychoanalysis, considering that Lacan insists that there is no 'meta-language', and that, like structuralism demands, the signifier does never reach out onto things, but defers invariably to other signifiers, eliding any representationalism? And by the same token, how are we to understand the difference between the formal reality of desire and the subject, which 'slides through the signifying chains' tethered to the formal vacuity of the impossible object, and the formalization of psychoanalytic claims? My position is then that although Lacan wants to say that 'Real desire' preconditions its objectification in discourse, it is actually the objectification of desire in psychoanalytic discourse which conditions the reification of desire as Real, and the matheme as adequate to its formalization. These are the relevant passages from my paper, which begin by a statement from Lacan, and which the reader should obviate in case they have read the paper in the past, or if they so wish to forward to the conclusions:

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"There is a fundamental ambiguity in the use we make of the word 'desire'. Sometimes we objectify it- and we have to do so, if only to talk about it. On the contrary sometimes we locate it as the primitive term, in relation to any objectification." (S2, pp. 225) This ambiguity is not trivial whatsoever. For if desire must be objectified in order to be spoken about, in what sense is it any different than any of the other terms that philosophers or scientists purportedly use to describe phenomena of all kinds, desire included? How are we to understand the claim that desire is simultaneously of the order of signifier and that which conditions any objectification whatsoever? How to address the Real of the libidinal subject and the Real of the object if, like Zizek insists, "There is no ontology of the Real: the very field of ontology, of the positive order of Being the Real are mutually exclusive: The Real is the immanent blockage or impediment of the order of being, what makes the order of Being inconsistent..." (LTN; Pg. 958). 

         This problem is particularly acute: Lacan insists that desire cannot be ontologised. But then what is it that psychoanalytic theory is doing when they 'objectify' desire "if only to speak of it"? How could such an act constitute anything but the making of an ontological valence? Despite his precautions, by flattening the symbolically enveloped epistemological relation between knowing individual and known object into the relation between the Real of the unconscious subject and the impossible object, Lacan seems to be effectively ontologizing the relation between the desire and its object-cause. The deflection of the transcendental relation between words and things at the level of the symbolic is coupled to a reification of the relation between the desiring subject and desired object, at the point where the Real of both becomes indiscernible. The Real of desire appears thereby as the ontologization of the relation between the Real subject and the Real object, as the distinction between them becomes a nullity. Desire as precondition for symbolic-ideal objectification is the reification of the transcendental correlation between subject and object, by reducing it to a formal difference allegedly intractable by conceptual means. For psychoanalysis to be a theory of desire, it's symbolically enveloped statements must conditioned by Real desire, rather than statements being the condition for mere 'talk' about the Real. For the latter would merely duplicate the philosophical 'myths' in question.


        Yet to claim that desire is not just one more signifier in the commerce of the symbolic, but rather the enabling condition for signification and objectivation, is once again to reactivate the relation between signifier and signified, only this time in terms of desire as Real precondition for objects understood as linguistically individuated posits.  In other words, although Lacan has done away with the transcendental relation of reference at the level of the symbolic, he still depends on such connection between the Real of desire, in its formal vacuity suspended in the subject-object polarity, as the condition of possibility for the symbolic individuation of the signifier. This is to covertly ontologise desire as an Aristotelian 'first mover', as the 'ground of being', as Ineffable Being stripped even of the honor of the name. And since symbolic objectification occurs on condition of the Real unobjectifiable cause, it follows that even the theory of desire, that psychoanalysis purports to advance, is conditioned on separation between the claims and formulas about desire, and desire itself.  In other words, if Lacan claims that the objectification of desire relates to a pre-objectified desire, then he has reactivated the referential relation between signifier and signified, sign and referent, in the dichotomy between objectual desire-for-us and unobjectifiable desire-in-itself. This surrenders Lacan to a bizarre, libidinal paradox of Kantianism. But to do that he must once again rehabilitate not just the ontological valence of desire as such, but the epistemological valence of the relation between desire's objectification in language and the depths of the desire that it bridges us to in the act of theorizing it, that is, in the making of claims and formulas that express it or which are about it. It is impossible to understand Lacan's claim that desire is a 'precondition' for its objectification unless one reenacts this philosophical cunning of the original psychoanalytic coup against philosophy and science. 

...
First, a possible answer is to leave it open that psychoanalysis may gain traction with respect to Real desire, via the objectification of the signifier. That is, the signifier might grant access to desire as an unknowable, unobjectifiable, but nevertheless thinkable condition of possibility for signification (a variety of 'weak correlationism'[1]). Under this light, Lacan's account of desire as Real precondition begins to startlingly resemble the minimal realism of Heidegger, for whom the opaqueness of the Earth qua unobjectifiable being stands as necessarily refractory to the variegated structure of Worldhood, with its populating entities and individuations at the ontic level. Real desire would be the proto-ontological motor conditioning, ironically, the merely ontic register of being and the symbolic investment of symptoms. The early Lacan seems to indicate this much when he claims in a rather cryptic passage: "Desire... is the desire for nothing namable... this desire lies at the origin of every variety of animation. If being were only what it is there wouldn't be room to talk about it. Being comes into existence as an exact function of this lack." (SII, pp 223). This is the direction in which the later Lacan, through his idea of the Real as that which resists symbolization, seems to have succumbed, as we shall see below[2].

          Alternatively, in this first re-philosophizing scenario, the structure of desire remains epistemically accessible without residue, but confined to the signifying order, in which case Lacan is involved in a bizarre structuralist parody of textual idealism. Yet as we surmised above, this cannot be done, strictly speaking, without a qualitative distinction that vitiates the structural uniformity of the signifier. In other words, it requires a qualitative distinction within the order of the signifier, a typology that sets those signs which map the structure of desire from those which are merely within the libidinal commerce of phantasy, and so those which are theorized by the former in expressing their conditions of possibility. Both options in this scenario rehabilitate the philosophical spooks that Lacan took to have demoted, at the price of reactivating the possibility of a special kind of reference or relation between signifiers, apart from the articulation of the four discourses, and with it one must accept the neutral possibility of attaining the status of a 'meta-language' to save psychoanalytic theory from itself.

        The second alternative, foreclosing the explanatory purchase on desire, and leaving the exteriority of Real desire unthinkable, shuns the status of psychoanalysis as a theory and surrenders it to a sophistic endeavor marking its internal contradiction (a variety of strong correlationism). This is the tragedy that we surmised above, when showing that psychoanalysis couldn't even surrender its rights to knowledge if it fully relinquishes its epistemic vocation, and the possibility of distinguishing between Real desire and its theorization. For in this scenario, the Lacanian edifice ends up undermining itself, rendering the conceptual endeavor it pursues into utter incoherence, the knowledge of desire undermining its theorization, and the theorization of desire undermining the possibility of knowledge of it[3].


         As we suggested above, however, Lacan seems to have progressively realized that he couldn't do without explaining how a theory of Real desire relies on such a conceptual envelopment, as evinced in a particularly telling passage: "[Our] conception of the concept implies that the concept is always established in an approach that is not unrelated to that which is imposed on us, as a form, by infinitesimal calculus. Indeed, if the concept is modeled on an approach to the reality that the concept has been created to apprehend, it is only by a leap a passage to the limit, that it manages to realize itself. We are then required to say in what respect- under what form of finite quantity, I would say- the conceptual elaboration known as the unconscious may be carried out." (SXI: pp. 19) The metaphor is that of an asymptotic approach to the Real via the matheme, forever removed from the concept's touch.

            Yet at this point, signaling both the beginning of a mathematical obsession and that of a poetic escape, Lacan begins to opt for the first horn of the dilemma and to surrender psychoanalysis to what appears under all lights to be a re-philosophizing of its fundamental task, along with the valence of knowing. A passion for the purity of formalization and the inscription, which begins sliding down to the notion that the matheme is closest to the Real. The matheme becomes the receptacle of a pure transmission, insofar as formalization subtracts writing from its conceptual envelopment, prizing it free from any semblance of meaning or intention. This is why, for Lacan, "The mathematical formalization of signifierness runs counter to meaning." (SXX, pp. 93) The matheme is said to be closest to the Real insofar as it formalizes while symbolizing nothing: it has a Real status insofar as it cannot be positivized in a representation. The Real subtracts itself from all positive content and all imaginary-symbolic envelopments; it is delivered only to the pure act of transmission, the transference of the analyst's intervention which opens the promise for the traversal of the phantasy. Just like the subject, there can be thus no theoretical knowledge of the Real: the latter cannot be totalized or unified by a predicate, or thought of consistently through definable properties. Therefore, it cannot be qualitatively determined so as to be tractable conceptually: "If there is a notion of the real, it is extremely complex and, because of this, incomprehensible, it cannot be comprehended in a way that would make an All out of it."[4] What formalization enables, Lacan wants to say, is not a representation of desire and so of a knowledge about the Real, but rather an experience or 'act' with respect the Real, a possibility for transference in analysis: "Truth cannot convince, knowledge becomes act.[5]" (Ibid; Pg. 104)


          And yet, as we saw, as much as the matheme itself remains recalcitrant to the symbolic, it is just as true that Lacan cannot dispense of the task of deploying the matheme to formalize psychoanalytic concepts and structures. Lacan himself says that the formalization is the formalization of the signifier: of whatever is articulated through the signifier, psychoanalytic claims included. But if mathematics can operate to formalize psychoanalysis, this is because formalization operates over the concepts and claims that psychoanalysis deploys. But in order for psychoanalytic claims and concepts to be any more apt for the formalization which 'touches the Real' of desire, then the claims of psychoanalysis must be in some respect peculiarly related to the Real of the unconscious, or else the formalization would appear arbitrarily dependant on a discursive register. Yet the on what methodological grounds could we assess whether psychoanalytic enjoy this priority, if not epistemological or semantic?

         At this juncture, the claim that the matheme resists translation is merely to refuse to explain how it is that it functions as a formalization adequate to the statements of psychoanalysis, and which concern the Real as much as the symbolic or the imaginary. The matheme is said not to obey the norms of knowledge or enter into the rule of the symbolic, but at the same time is coordinated with a series of theoretical interpretations, granting it rights before the Real. But what grounds this proximity between the matheme and the Real, as regulated by psychoanalytic concepts? Without explaining this connection, psychoanalysis fails to adequately account for the relation between the practice of formalization and the theoretical statements which provide the semantic interpretation for the mathematical formulas. For the psychoanalyst needs not only the matheme which is recalcitrant to meaning, but a series of theoretical claims explaining how the matheme formalizes certain structures. Without this connection, any mathematical inscription cannot count as the formalization of anything, is truly 'meaningless', and there would be nothing to distinguish pure mathematical forms from Real psychic structures[6]. This would render psychoanalysis complicit with a kind of Pythagorean upsurge. Just like unobjectifiable desire was 'objectified' in theory only to speak of it, the Real non-translatability of the matheme is translated by psychoanalytic theory since, without such a theorization, the matheme could not stand for the formalization of anything whatsoever. The interesting paradox is therefore that although in order for the matheme to be non-translatable to any discursive register that operates under the symbolic it must, paradoxically, be able to be translated into the conceptual register of psychoanalysis, for the latter provides the interpretation without which, the abstract terms would fail to account for anything.


         What this evinces is that psychoanalysis ultimately is forced to speak of the Real ambiguously: in one sense it said to pertain to formalization in its untranslatable dimension, and in another to desire as the unobjectifiable condition for any discourse. It is precisely at this juncture that the unobjectifiable Real of desire, touched only in the act of transference, is mediated by a tacit separation from the matheme that ordains it, evincing a division that psychoanalysis ultimately cannot resolve.  Much like for Heidegger Being qua the unobjectifiable opaqueness of the Earth cannot be apprehended conceptually but must be delivered to the poetic word of the thinker and the act of the artist, the Real qua unobjectifiable opaqueness of desire cannot be known but must be delivered to the epistemic opaqueness of the matheme and the transference occasioned by the analyst in act. As Lacan puts it: "Mathematization alone reaches a real - and it is in that respect that it is compatible with our discourse, with analytic discourse- a real that has nothing to do with what traditional knowledge has served as a basis for, which is not what the latter believes it to be- namely, reality, but rather phantasy... The Real, I will say, is the mystery of the speaking body, the mystery of the unconscious." (SXX; pp. 131)


          However, the call for the bodily act signals also the inevitable moment of loss for explanation, the moment in which, no longer capable of separating the thought of the Real from the Real itself, one must surrender all theoretical pretences and en-act the traversal itself, a clinical pilgrimage before the inflections of the symptom through the lessons of formalization. The discursive access to knowing-that becomes delivered to the oblique efficacy of  non-discursive know-how. This is how we should coordinate these two seemingly disparate statements from Lacan: "There is some rapport of being that cannot be known" (SXX, pp. 119, TM), and "If analysis rests on a presumption, it is that knowledge about [subjective] truth can be constituted on the basis of its experience" (Ibid, pp. 91). The impossibility of a knowledge of being is but the obverse of the possibility of knowing how to speak in bringing about the transference. Or as Badiou formulates it: "The paradoxical position of Lacan concerning truth is that there is no knowledge of truth, but finally there is a psychoanalytic knowledge concerning this absence of knowledge. This is the great paradox of the unconscious...a subject can have an experience of its proper Real only in the form of an act." (Badiou, 2010)

       The levels must be clearly demarcated: the analytic transference enjoins the traversal of the phantasy and is supported by the formalization of the symbolic by the matheme. But as we have seen, the operation of formalization which demarcates the positions and structures is in turn supported by the conceptual register of psychoanalytic theory itself. Lacan can thus claim that: "It is in the very act of speaking that makes this formalization, this ideal meta-language, ex-sist." (SXX, Ibid; pp 119) The two Reals glare forth in their unresolved difference: the pure form of the mathematic inscription, recalcitrant to incorporation within the symbolic order of language, and Real of desire in the passage to the pure act that deposes all representational knowledge, where the traversal of the phantasy takes place. As Badiou stresses: "This act is like a cut in language and also a cut in the ordinary representation of the world- a representation which is imaginary. So the act suddenly isolates the Real from its normal collection to the imaginary and symbolic orders." (Badiou, 2010).

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    I encourage readers to take a look at the rest of the paper, since there I develop my reading and case in much more thorough fashion. 

With regards to Badiou, I think that he basically appropriates the structuralist move that Lacan makes apropos psychoanalysis into a philosophical register. Thus, the matheme is, for Badiou, adequate to the thinking of being qua being, because it resists translation into transcendental terms, thereby refusing envelopment by 'bourgeois epistemology'. The latter, as one does well to note, remains encumbered in the "third dogma of empiricism" that distinguishes between form and content, and which thereby conditions all forms of 'naturalist' epistemology and ontology, even still in the case of Quine. But Badiou goes further than this, because he avows explicitly the extensional core of set-theory to resist intensionality, which for him is what remains of Aristotelian essences in mathematized logic. Thus, the mathematization of being allows him to subtract the latter from the One, or render it 'inconsistent', insofar as it refuses any qualitative determination. This works to simultaneously deflate the (Kantian and post-Kantian) transcendental problematic of the distinction between thought and reality, or form and content, in favor of an immanent ontology of the pure multiple, and later a phenomenology with a 'subjectless object'. Yet the price to be paid for this liquidation of 'empirical content' is an ontological reification of form or ideality, which results in an endorsement of a form of the Parmenidean thesis according to which being and thinking are one and the same. And at this juncture, Lacan and Badiou meet again: in conversation, Badiou told me that precisely because one cannot distinguish between mathematic inscription and being-in-itself, the matheme is 'closest to the Real'. 

   But in my estimation, if epistemic indiscernibility ensues as a criterion for ontological identity, then short of rendering possible a materialism, Badiou has reified, like Plato and Hegel before him, the intelligible at the price of eviscerating sensibility and content. This is the invariable result that obtains when one folds the epistemic into the ontological, or logic and metaphysics, as Hegel shows. Nevertheless, if one cannot distinguish between our thought or inscriptions about being and being as such, then we yield a form of Platonist idealism, which becomes difficult to differentiate from Pythagoreanism. Indeed, in conversation with Luke Fraser and Ray Brassier, I have become increasingly convinced that, in spite of his extraordinary advances in Logics of Worlds, the fundamental problem in Badiou continues to be the articulation between mathematical and non-mathematical situations, so as to avoid reifying mathematics ontologically (like he claims from the start).

   Yet whereas in B&E the articulation between the ontological and non-ontological was tantamount to the distinction between the mathematical and non-mathematical, where the latter was theorized through the former by a process of analogy (like Lyotard, Deleuze, and others claimed), in LOW Badiou proceeds to give a mathematical formalization of the consistency of Worlds, or non-ontological situations, so that the crucial connection then becomes the articulation between set-theoretical ontology, and category-theoretical phenomenology. In spite of these advances, I believe that the fundamental question about the relation between the mathematical and the non-mathematical remains, and forced him into a quandary not unlike that of Lacan. That is, if Badiou wants to claim there is such a thing as non-mathematical reality, not of the order of being, but rather the 'unthinkable' or 'unknowable' by cognitive means, then he has committed himself to a form of correlationism. I am afraid this is the position that one would have to draw if the claim that Badiou is simply 'not concerned with the Real' in any sense analogous to that proper to transcendental philosophers holds. But if Badiou wants to eviscerate any notion of inscription-independent reality altogether, as Hegel does, then he has effectively endorsed a form of Pythagoreanism, where all situations, ontological and non-ontological, must be mathematized. It is the latter which, I think, ultimately must be Badiou's position, in spite of his ambiguous proviso that the claim that ontology is set-theory is a claim about discourse, and not about the world.

Now, the reason why I think Sellars is important for these discussions, and where I think some crucial cross-breeding can be done, is that he proposes to reconcile nominalism about semantics, with realism about ontology. He thus proposes to offer an account that, like structuralism, does not appeal to a relation between words-things to flesh out semantic proprieties, in turn offering a full blown inferentialist semantics, while at the same time advocating a process ontology of his own. I am currently working on a paper explaining how precisely this works, and what I think is most valuable about this strategy; but the basic idea I would like to extirpate from it is the following one:

We can agree with Badiou in that materialism, indeed philosophy, requires the rehabilitation of the Platonic axis between truth and doxa, in order to stave off the (neo)-sophistic conflation of the former into the latter. But I think it is also important to understand Badiou's work as operating on the second crucial Platonic axis distinguishing between reality and appearance, in terms of the intelligible and the sensible. I think that Badiou, like Plato and Hegel, proposes to identify reality or 'being' with intelligibility, and demote sensibility to appearance or doxa. In the three philosophers, what we obtain is a trivialization of sensibility as that which is not real, at the price of reifying ideality ontologically, in order to save rationalism from the phenomenological reification of being as an irrational Otherness, only tractable by poetic-practical means.

The Sellarsian alternative proposes, in turn, rather to insist on the reality of appearances, while rendering this reality fully intelligible, while refusing to reify ideality metaphysically. We can understand the ontological valence of appearances, as part of objective reality, without thereby forcing us into separating, in dualist spirits, between the ideal and the real.  Now, this is not to say all reality is sensible, which is the panpsychist hypothesis. Rather, it means that sensibility can be both a) ontologically investigated, and b) that it conditions our knowledge about the external world. Realism obtains precisely by refusing the ontological reification of the sensible or the intelligible, while recognizing the logical irreducibility of the intelligible, while its causal reducibility. The trick then consists in finding out a way of preserving a positive role for sensibility to anchor us to the mind-independent world, without thereby render it ubiquitous. And this requires, in turn, that we distinguish between the semantic-epistemic conditions under which we can talk and adjudicate claims about the real, and the positive metaphysical claims that result once we have cleared up our semantics. Finally, Sellars will propose to think of the connection between language and the world in terms of a non-semantic relation or 'picturing' which, developing on the work of Wittgenstein, seeks to establish how second-order isomorphy obtains between matter-of-factual claims qua 'natural linguistic objects' and real objects and events in the world. 

     The details here are complex, as ever with Sellars, but the major result is that in persisting on the Kantian methodological distinction between reasons and causes, while refusing their metaphysical separation, we can understand how while there is an ontological priority of the logical on the natural (without proper evolutionary conditions sapience wouldn't obtain), there is an epistemological priority of the natural on the logical (only sapient creatures who inhabit the logical space of reasons can adjudicate claims, and undertake normative statuses required for knowledge). In short, the Sellarsian alternative proposes to preserve the distinction between form and content, in the name of a revisionary naturalism, that avoids reifying intelligibility at the price of evacuating sensibility (idealism: Plato, Hegel, Badiou), or reifying sensibility at the price of demolition intellection (Bergson, Deleuze...).

      I think here some crucial work can be done in tandem with both psychoanalysis and Badiou. The former integrate a thinking of how libidinal structures are both causally and normatively constitutively binding the Real practices and transference, and the symbolic. The latter provides a formal account of change relative to structural conditions by modeling truth on generic sets, defusing the romantic exuberance tethered to creation 'ex nihilo', which including post-Kuhnean approaches reifying change and discontinuity in the way of instrumentalizing science. Incidentally, this is also a fertile ground to assimilate insight by people such as Ladyman and Ross, who further the case against instrumentalist approaches by insisting that discontinuity at the level of content in scientific theories is underwritten by continuity at the level of form. I think if can sort out the pragmatics with the semantics here we can integrate both approaches beyond the strict axiomatics of mathematical Platonist approaches, while opening the playing field for a discussion of not only traditional epistemic practices governed by standard proprieties of inference, but all sorts of intricate articulations. In a larger scheme, I am looking to amplify the Brandomian project of integrating pragmatics with semantics, with the Badiouean project of providing a synoptic ontology-phenomenology adequate to the articulation of different thought procedures. 

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