Axioms and Theorems of a Fictional Melanesian Ontology

Mountain Ok/Telefolmin Shield

Mountain Ok/Telefolmin Shield

Axioms and Theorems of A Fictional Melanesian Ontology

Disclaimer: The following makes no attempt to be a definitive statement about the ontologies of Melanesian societies. It is but a philo-fiction produced from the collision of Western philosophical idioms with concepts and ideas drawn from the available ethnographic literature on Melanesia.


1.     There are no distinctions between flows and objects.

2.     Everything is a container and contents and contains itself.

3.     Since everything is a container, everything has holes. These holes are the entrance and exit points of flows/objects.

4.     Everything is implicitly analogous to everything else (cf. Wagner 1977). This may be through inversion, scaling, subdivision and segmentation, or homeomorphism (continuous transformation).

5.     Relations are given and multiple, discrete terms or units are produced (ibid.).

6.     While relations “partialize” persons into an open multiplicity of object-flows, unit-definitions rely on dyadic distinctions (self/other, male/female). (Cf. Strathern 1988).

7.     The whole replicates the structure of the part. General part-whole equivalence and substitutability. (cf. Wagner 1986).

8.     Everything has growth-potential, but only if there can be differentiation.

9.     Everything is implicitly androgynous (cf. Gell 1999).


1.     According to axioms (2), (5), (8), Melanesian ontology forms a fractal topology of self-containment in which everything is implicitly identical.

2.     According to axioms (1), (3), (4), (7), persons are composites of flows and objects.

3.     According to theorems (1) and (2), the structure of persons must be identical to the structure of the universe, even as social life consists of deliberate acts of differentiation.

4.     By axiom (8) and theorem (3), social life consists in growing, but it is threatened by its own implicit presuppositions of fractal non-differentiation.

5.     By axiom (9) and theorem (1), gender relations are formally symmetrical. Although they may be empirically asymmetrical.

6.     By axiom (6) and theorem (1), dualistic distinctions degenerate back into identities, by the very fact of producing (analogical) relations.

Looking Ahead

Structures of Transformation (From D’Arcy Thompson)

Structures of Transformation (From D’Arcy Thompson)

I have been recently trying to explore to what degree Levi-Strauss’s method of structural anthropology, more specifically his structural study of myths, can be incorporated into a Laruellian or Non-Philosophical framework. I think the set of formal analogies or isomorphisms one can come up with respect to the two theories is convincing, but at this point, I need to determine to what degree these comparisons add up to some kind of substantial theoretical discovery, rather than just a mere comparative enterprise or even the kind of disciplinary eclecticism that Non-Philosophy can appear to be.

First, the correspondences: according to Laruelle, Philosophy involves the attempt to move from the two the one, and misunderstands the immanence of the One as a form of synthesis. Philosophy is only the recombination of the original analytic divisions it makes in thought and thus internal to the activity of thinking, “missing” the autonomy of the One’s independent reality. It continually repeats this gesture so long as it cannot develop a thinking that is in line with the independence of the Real from thought or its essential “impossibility” with regards to the ruses of synthetic recombination.

Levi-Strauss also affirms that the structure of myth is one of mediation and that it attempts to move from the two to the one. It is clear too, from his analysis of the Oedipus myth, that this is not only about moving from two terms to one term which unifies the two, but also about moving from “the one” and “the two” each as the two terms to be unified. This corresponds to Laruelle’s assertion that philosophy aims to “mix” Being and Other. Also, Levi-Strauss had one foot in science and the other in mythology as the discourse on signification, as is evidenced by his claim that the science of myth would be a sort of “myth of myth.” Levi-Strauss gestures to something like a “unified theory” in the Laruellian sense.

The comparison only really links the terms if it is justifiable at the level of content, i.e if mythology and philosophy can actually be assimilated. This is what I attempted to do in my Masters thesis, in which I attempted to begin to develop a transcendental logic of mythology, building off of Husserl’s genetic phenomenology. I needed to develop a transcendental logic of mythology because Laruelle’s claims about mediation apply to the transcendental mediation that philosophy effects between Thought and Being and is not simply a repudiation of all discursive mediation in general.

This project can be taken up through analyzing how “mythic thought” in Levi-Strauss’s terms encodes propositions, and I took as my starting point the attempt to make Levi-Strauss’ claim that it does so explicit. I rejected a directly Kantian approach for the same reason Husserl does, for it does not show the conditions of possibility of logic but assumes the legitimacy of Aristotle’s term logic at the beginning. This is the same problem with many contemporary transcendental accounts that simply accept the current results of science: the latter can be used as “clues,” but the specific form of evidence that applies to logical formations needs to itself be clarified and built up only from the structures of immanent manifestation.

However, this thesis was clearly an experiment more than a goal, for I am not ultimately interested in simply a transcendental logic but a thinking rooted in a Real irreducible to logic, which is how Laruelle proceeds: this is the only way to achieve an anthropological and mytho-poetic thinking that would be both “materialist” and rooted in something like science.  

 But my thesis led me to the next problem: psychologism. Levi-Strauss aims to do two things that are antinomical philosophically: first, show mythic thought to be encodable in the form of propositions and to enact logical operations; second, to show that its patterning is in line with that of natural forms and objects. The second thesis contravenes the first since natural events and objects do not possess the specific “normativity” of logical values, i.e they reduce to the de jure relations of logical inference to de facto accounts of what occurs. In addition, the conceptuality of “naturalism” has come under attack in anthropology itself, and there is a desire to liberate a whole field of “conceptual worlds” irreducible to the very concept of “nature.”

My framework would then be productive in conceiving the latter as relatively autonomous transcendentals, preserving their irreducibility to western categories, and mythology would be a direct entrance point to these transcendental worlds, and we would have a method at least somewhat developed to study mythologies in just this way (Levi-Strauss’s). I have an inkling that Laruelle has already implicitly solved the problem of psychologism, but this needs to be made explicit, without falling into the philosophical traps of much of the epistemology that Laruelle has warned against.

The splotches on the feline’s coat

As much names

As Names of the Father

A thought which admits no reduction

A history by weaving

Blocks of time, absences as eros

Traces as features, logics

Still animal, feathered


On our way to divinization

It is the soil which bears this fruit

An underground constellation

A decaying crystal, a micro-scope

It was the Jesuits who first came, who

Wanted to look and force our confession

Their deceitful appearance did not defame, 

And were born from them

A horror unnamed

It is the beautiful who remain

The beautiful who are our gods

The beautiful who do not lie

For ever and ever

     The Logos of the World and Its Anthropological and Non-Philosophical Critique

totemic operator.jpg

The Logos of the World and Its Anthropological and Non-Philosophical Critique

A hypothesis: the existing state of affairs, as one of capitalist globalization, poses the eminently logical question of the universal and particular, of classification and relation. Capitalism, perhaps like all social formations, and perhaps like all ideologies, gives itself as universal – its figures of humanness (“homo economicus”) and its paradigms of rationality, present themselves erroneously as timeless, and its norms appear as “common sense.” The critique of capitalism traditionally (and of other logics like patriarchy, heteronormativity, etc.) expose this universality as a particularity, while the sublation of such a critique is the dialectical affirmation of the universality of such a contradiction itself. The question of the capital-form and the question of the contemporary world-form are thus implicated as a question of the logos, dialectical or not, of particular and universal.

What exactly is the world’s “form”? In part: the abstractions of the commodity-form and money-form. Such abstractions effect a process of deterritorialization, annihilating traditional particularisms, stable identities, and personal images. They replace the qualitative logics and codings of pre-capitalist formations with decodings carried by a minimal and informatic code. At the same time, capitalism, according to its modality of social reproduction, reterritorializes, and today particularism is the prime technique of ideological reterritorialization, in the production of egoic and personal images.

The predominance of the type. The subject of Capital today is not merely a wage-laborer; it is a dehumanized ensemble of information-capital at every moment, beyond the limits of the work day, employed or unemployed. The ensemble of information-capital is what allows statistical algorithms to construct the average consumer-producer. We must all be identities, person-types, indexable as certain kinds of consumers and creators of categorizable information capital. The world-form as a logic of particular and universal is as much one of classification and identity (it is taxonomical). In all of this the phenomenal role of exposure and hyper-visibility in the constant availability of indexable personhood, the ideology of pure transparency, the “culmination” of the metaphysics of presence.

Globalization is capitalism in its most quasi-universalistic dimension, especially post-1989, where nothing explicitly poses as a veritable counter-force while Capital extends extensively and intensively (universal because everywhere, we still know it is but one social formation, quasi-universal). The homology between Capital and World as auto-positional form is in analogy with the homology between Logos and Society (realizing in another way the isomorphism between social classification and logical taxonomy, cf. Durkheim and Mauss On Primitive Classification). Abstractive deterritorialization and reterritorialization on one side, the logic of particular, universal, and type on the other: in truth, they form a complex. Yet the logos here is characteristically twisted for “the World” is the name of the auto-positional complex, and logos is already both its logic and its term: only a deeper form of what Non-Philosophy calls mixture and to be treated according to a scientific symptomatology.

Our theoretical solution is not an anti-logic but a “non-logic”: a unilateralization by generic humanity, by a Real foreclosed to Logic, although logic must be identical with it in the last instance. What can we do with “globalization” if not to push it forward towards a globality that would determined by this kind of humanity, a generic uni-versality prior to predication? Against the quasi-universalization of globalizing Capital, a materialistic uni-versality of generic humanness: globality-without-globalization. Finally, a genuine thinking from the human according to a scientific and empirical anthropology, this time freed from Western humanism, and also from the equally European obsession with the logos of identity.

It is to the credit of ontological anthropology to have paved the way to a truly matrixial and variational approach to human ontologies in their broadest dimension, and to a symmetrization that places “Greco-Judaic thought” as nothing but a human variant  Such a relational matrix, however, poses the eminently logical problem, this time, of the status of relation: we are dealing with both the logic of class and the logic of relation (cf. Levi-Strauss The Elementary Structures of Kinship) even as we would free ourselves from the aporias of relativism: we now see “relativism” as itself a Western schema, we now see the relativity of “Culture” itself.

However, ontological anthropology fails when the matrix of relation is confused with an ontology of relation. The Relation is the Philosophical fantasy of synthesis and world-form, the logic of logic as logos, evidenced in the over-inflation of the concept of “relationality”": is this not the ideology and utopian ideal of connectivity? The usage of (world-)logic according to an immanent style of thinking starts, in contrast, from the non-logical and non-relational core of the human-in-human as a materialist theoretical praxis. Underdetermining according to an axiom of separation from the world-form, the matrix of relation is reduced to a tool of modelization.

Let us subvert the logos of the universal and particular and replace it with the complicity of the singular and the uni-versal (dialectical singularity is here a useful model): this is the paradigm of the generic. Indifferent to philosophical decision and to the arbitrariness of the World, we see the synthetic conjunction of the particular and the universal, as well as the (cor-)relations of relationality, as relative-absolute. Relative first and foremost as part of a relational matrix, a system of variants, and absolute as Philosophy and philosophical synthesis, we employ the latter as a modelization of the capacities of a human-in-human prior to predication. Separated and opposed to the capitalization of both identity and relation, but not without making use of its logics (are these not the transcendental masks of the human?), the non-philosophical subject emerges as a thinking in accordance with humanity.




Neuronal sub-ensemble, to chase fragmentation
In hyphenated nouns, and indo-european grammar
Like a last migration, to a last side of the head
Not cracking

And a whole set of sorely male warriors
Chasing after a whole set of tenderously vacuous priests
A singing without end
A glory too little

Chasing fragmentation
And a dispersal that would lead to joy
Of an earth and terra firma
Or rather terra nullius
On which to rest
and hyperspace


Air is absence

The crevices of Being

For the Nuer it is kwoth

For me a name I don't recall


There are little pockets of time


Convex while the heart is concave


Transfer and translation

Metaphor and subtention

Building blocks of thought

Without space


I awake to the timeless inanimate

Another metaphor

Another "little death"

Note on A Philosophical Over-Determination of Non-Philosophy

Note on A Philosophical Over-Determination of Non-Philosophy

Much discussion of the reception of non-philosophy involves the role of ‘abstraction’ in its axiomatic framework. At the same time, non-philosophy speaks incessantly of the immanence of the lived (more precisely, the lived-without-life). These two ‘sides’ of non-philosophy have seemed irreconcilable and have raised a new antinomy. This antinomy can be resolved via a re-initiation of non-philosophy itself, taking the antinomy to indicate a philosophical resistance and normalization. The antinomy is a form of philosophical decision that works in either direction and is based on a traditional concrete/abstract dyad.  The romanticist privileges and re-doubles the concrete as mediation, the theoreticist the abstract. From the standpoint of a hallucinatory appearance of non-philosophy, both trajectories appear as "deviations" from an ideal "correct stance" or orthodoxy.

In the case of the romanticist trajectory, the primacy of the lived submits the axiomatic as means for auto-position, whereby the axiomatic will ultimately merely “reflect” the lived, carrying it forth, “expressing” as what is most genuine and precious, and so as a "truth of the Real". In this way, the lived will in fact be double transcendence or mediation, governing the relation between it and 'the axioms,' that is, as authentic, romantic, genuineness of the mere use of axioms to represent and defend authentic life. What is lost here is the lived-without-life in so far as the lived will degenerate into Life when it aims to circumscribe the axioms as modes of re-flection of authenticity.

For the theoreticist trajectory, abstraction here is taken as a sufficient way of determining the Real, if it can be “intensified” far enough. This ultimately becomes dialectical and it is held that the Real is grasped once abstraction is sufficient to account for itself, a direct form of philosophical sufficiency. This is what occurs in Ray Brassier's work and it misses the abstract-without-abstraction

This antinomy clearly arises from a philosophical decision and overdetermination in philosophy, which we can think of as the concrete-abstract dyad. In the romanticist case, the concrete is the doubled term, occurring twice. In the theoreticist, the abstract. In both cases, this dyad is mediatized by transcendental mediation, either as reflection/authentic expression (and so a "truth of the real"), or dialectical self-thinking ("closing the circle"). Its resolution is in the given-without-givenness, taking this is an axiom, but an axiom-without-axiomatization. The ‘romantic’ and the ‘abstract’/’scientific’ can be thought as in-identity since, depending on the occasion, the Real can be modeled both by phenomenological, religious, and spiritual materials, as well as by philosophies-of-science or epistemo-logies. The Real is in fact indifferent to the oppositions between 'the spiritual' and 'the abstract' as they appear in doxa. 

Divine hypnosis!

If only a word, as archaic, could suffice

To think currents so contemporary

Washings over so heinous

Memories so tongue tied


Divinity is in-tensity,

But it is also flow, oscillation,


Sacred liminality


The knife bleeds sharply

Because “life is suffering”

And it is always a coming

Without be-coming, not knowing

Where, or wherefrom


The divine is the aurora of the morning

The dawning of time-space

Which speaks to you

From withdrawal


It is the closure of midnight

The change of seasons

Which will only last so long

Before the sun bursts.

Some Aphorisms on a Thought In-Art

Some Aphorisms on A Thought In-Art

  1. There can be no phenomenology of the lived, unless of course it would be a lived phenomenology. Phenomenology is the closest philosophy has come to a certain fusion with the lived. If art is to become life, so is philosophy. But it cannot have Life. There is no Life. We are dead inside.
  2. The passive synthesis of the sense-field (something like time) is the closest we can get to immanence, in "consciousness" that is. Its realization is art and music. In musical hypnosis, in incessant repetition, temporal melding, desire binds itself to the real, maybe also to consciousness. Thought is moved by art.  
  3. A thought that is in-art is a moving thought. It moves with sense. Sense-uality. 
  4. There is nothing left of Life. It has become demanded of us. The disciplined ascetic has shown himself as the true revolutionary of history.
  5. Art is a mystical state. Or it is meaningless. 
  6. The immanence of the lived, of the phenomenon, is not a plenum. It is a chasm. And this chasm is always the chasm of the Crisis. The chasm of the Crisis moves thought.
  7. Thought is thought when it is unthought.
  8. It, I, you move. But we are not seen...




Someone awoke

It was a typographical error

Potentially, in-group-in-fusion coordination


And there was a fever

Pulsing like a room

And some of us were happy


Lightning struck,

Like heaven had shed its ancient

Modules, that we had grown bored of


But we needed them in person

Because we needed you

The digital christ whose name

We are now on the point of remembering


A singled-out resurrecting

Of bodies without feelings

and Bodies without brains



Here is truth: there is no spectacle that descends on the world

Because there is no world, which we would submit to our descension

There is a we, however.


This is we on the cusp of memory

The point where memory curls around

And froths a bit at the tip

Just so you can touch it

Maybe even “observe” it


It is the kind of thing where you only care about the future

You only care about the future.

Towards A Badiousian Dialectics

Preliminary Notes Towards A Badiousian Dialectics

For a while the idea of doing what Reinhold or Fichte tried to do to Kant, but to Badiou, has appealed to me: that is, a more "systematic" and unified rendering of the most key philosophical developments of Badiou's system.  It is not necessarily that I wish to subscribe to such a system, and whatever system I would create would not be able to "cover" the diversity and transformations of a thinker's oeuvre. The project would unavoidably produce its own philosophy, and even then not something I would necessarily wish to take up. But I believe this kind of formalization has its own kind of intrinsic interest, especially when it comes to discerning key philosophical problematics and logics. I also thus leave the text in acknowledgment of the full possibility of internal errors.

  • The Two is the thinking and inteligibility of the separation between the one and the void.
  • The Two as movement, retroactively constructs this separation.
  • The separation that The Two performs is the sole relation between the one and the void, thus their connection.
  • This separation-connection is not constituted by the Two, for its condition of possibility is the material point of the Event
  • The Event is the aleatory encounter of the one and the void, where what is encountered is their impossible combination.
  • This impossible combination is nothing but the connection of their separation at the point of the un-thought.
  • After the Two has come into movement, it dialectizes the situation. The Two dialectizes the one by splitting it from within.  This is the consequence of the appearance of separation in a one, that is, in a local situation.
  • We can call this dialectization the split-one. It has two moments:  the one-as-one (also named “the State”) and the becoming-one-of-infinity that is the split-one’s essence. These two moments are in conflict. 
  • This conflict is the dialectical unity of the situation. It is nothing else but connection-separation as it appears in the one. 
  • In the split-one and in its dialectical unity, only one side - the becoming-one of infinity - represents this unity. The split-one has a certain asymmetry. 
  • The split-one is only truly a split-one when the one-as-one is thwarted by the positivity of the becoming-one of infinity. This is because the split-one is nothing but the fact that the one is not as one. The Two determines the one solely as separated-connected from the void.  
  • Though separation occurs as split-one, or in-a-one, it is global separation (or: truth is universal). This is because the one limits through the one-as-one, but the one-as-one has become the inessential.
  • Although the Two is an equalizing unity-of-difference - the connection-separation of the Two - there is ontological asymmetry. The globality of the split-one requires that the void be said to be, while the one be said to not be
  • This requires that the distinction of Being and non-being as asymmetrical does not exactly coincide with the connection-seperation of the Two. Otherwise Being and non-being would be the opening moment of a unity-of-difference indistinguishable from the Hegelian dialectic, and consequently non-aleatory and non-materialist. 
  • How then is the distinction between Being and non-Being thinkable, when thought is the Two as connection-separation? We will see that there is asymmetry through a self-mediation of The Two.
  • In order for ontology to be thought, it must be a unique form of the Two.  This difference in the Two is a Two-of-the-Two.
  • The Two-of-the-Two is the separation-connection of separation-connection. Seperation-connection is generic unity of absolute difference, or a unity which is nothing but the absoluteness of this difference. What would it mean to say that absolute difference was absolutely different from itself? It would mean it was absolute identity.
  • The Two-of-the-Two is the identity of the void and the one, the void-of-the-one (it is also the one-of-the-void, or appearance). And the sublation of difference in this identity is ontological assymetry.  The Two-of-the-Two performs the non-being of the one.  Or: the non-being of the one is the-void-of-the-one.
  • The affirmation of the Being of multiplicity cannot be dialectically inferred from the Two. It is specific to ontology’s real forms of practice. The concept of the Two-of-the-Two is only the elaboration of the possibility of ontology.
  • Ontology’s existence is necessary for thought, but its coming into being is aleatory (like any Two).
  • Ontology as Two-of-the-Two cannot itself think the Two. Though thinking is The Two, this does not mean that a Two-of-the-Two would be a self-thinking.
  • The Two-of-the-Two annihilates the one in the void-of-the-one. Without a one there can be no split-one, and so the Two cannot act as thought. While remaining thought, its thought is eliminated for it. It is unconscious thought.
  • How then is the Two itself thinkable? There is only the void and the one, and the Two which thinks their separation. The Two cannot think itself, so that which thinks the Two is either the one or the void. But only the Two is thought, so the only solution is that the Two be deployed as one or void.
  • If the Two were deployed as void, it would mean the Two was no-where, for the one is localization. We have as yet of yet no evidence that the human being can be no-where. 
  • if the Two is going to come to our knowledge and be thought, it must then be deployed as one. We will call the one-of-the-Two philosophy.
  • Philosophy would not be the Two "in-itself." It is the one of the Two, or Two as one. Nor is it the Two of-the-Two as for-itself self-thinking, for the Two-of-the-Two is unconscious thought.
  • Nor is philosophy the one-as-one (the state). The one-as-one is a moment of the Two as split-one, not as one. Or put differently, it is one-as-one not the-Two-as-one. If philosophy exists, it is not ideology.
  • However, if philosophy is a one (the one-of-the-Two) philosophy finds itself “caught between” the two one-moments in the split-one, the one-as-one and the becoming-one of infinity. In order to think the Two it must “ally” itself with that which represents it, the becoming-one of infinity in the split-one.
  • The next installment will broach the operations of this “allying” through establishing a concept of subjectivity


Badiou and A Typology of Truths

Badiou and A Typology of Truths

One of the most common objections to Badiou is that his listing of the four truth procedures (science, love, art, politics) is arbitrary; why are there only these four? The reproach tends to come from one of two directions: either readers perceive no rigorous method proposed by Badiou in this enumeration, or they think that the arbitrariness of the four types follows from Badiou’s own concept of the radically subjective nature of truths.  

The result in both cases is to reduce Badiou’s enumeration to a mere personal proclivity, which often accompanies other claims about Badiou’s supposed authoritarian posturing.  However, rigorous philosophical method involves transcending ad hominem attacks and instead focusing on precise conceptual distinctions that are charitably drawn from the text itself.  

The two lines of criticism mentioned above can be repudiated by demarcating specifically the manner in which Badiou’s theory of truth develops at the dual level of empirical specificity and conceptual generality.  I propose a schematization of Badiou’s theory which he himself does not offer, but for which ample support can be found in First Manifesto For Philosophy, Being and Event, and Logics of Worlds.  

There are three “levels” in Badiou’s thinking of truth, moving from the most general notion of truth to the most specific.  

These are: 

  1. The concept of Truth (or Truth in general)
  2. The typology of truths (math, love, art, politics)
  3. Specific truths/truth procedures (Cantorian set theory, the Bolshevik Revolution, serialist music etc.)

The Concept of Truth or Truth in General

Badiou’s theory of Truth in general is most clearly explicated in First Manifesto For Philosophy. For Badiou, the concept of Truth is constructed in the unique space that is philosophy.  The concept of Truth is not in itself material, but rather a discursive, general concept abstracted from existent truths.  This is part of the sense in which truths “condition” philosophy, as Badiou says. Philosophy needs truths in order to determine what is most common to Truth, in the same way that one can only form a concept of “car” through the observation and analysis of real cars.

However, not all conditions are equal.  As Badiou explains in Being and Event, he essentially agrees with Heidegger that philosophy must be assigned its destination only on the basis of the ontological question, the question of Being. Given that Badiou, as is well known, equates math with ontology, this means that philosophy will have a privileged relation to mathematics as one of its conditions. What are the motivations for this move?

Let’s think about the impetus that runs through all of Badiou’s philosophy: the critique of relativism and his defense of universal truth. Now if Being and Event has a kind of culminating point it is the utilization of Cohen’s theory of generic sets.  If mathematics is ontology, and Cohen’s theory formalizes the indiscernible universality that belongs to any truth, then math assures that Truth has an ontological form. Thus, it is at least possible that Truth is not a fiction.  Math assures that there is a consistent, ontological form of Truth.  Truth, affirmed as  ontologically possible, then is to be conceptually and discursively “filled in” by the philosophical analysis of the specific truth procedures that would locally instantiate this form.  

The Typology of truths/Specific truth procedures

How do we move from the concept of Truth in general to the typology of the various kinds of truths? In order to explicate this move we have to already jump to the idea of the most specific truth procedures themselves. Our knowledge of specific truth procedures is radically empirical.  This is straightforwardly Badiou’s concept of the Event. Truths happen, as real occurrences in history.  As such, that there is this or that truth exists is an empirical matter.  There is no deduction of the existence of a truth, and this is in part why truths are subjective decisions and are “axiomatic.”

Does that mean there is no criteria as to what can count as a truth? No. The rejection of this point is what allows Badiou to elaborate a theory of truths as subjective decisions and to construct a systematic theory of the essence of Truth.

Again, we must refer to philosophy’s ontological assignment. For Badiou, mathematics formalizes and develops the ontological notion that Being is pure multiplicity and the one is not. However, outside of the purely ontological presentation of multiplicity, a dialectical contradiction between the one and the multiple can arise according to local conditions: this what he calls the Event.  Breaking the logical/linguistic unity of the oneness of the situation, the Event serves as the condition of there arising in said situation an indiscernible multiple, non-reducible to the language of the situation: i.e what would count, ontologically, as a truth. Thus, the Event is the condition for the local deployment of a particular truth which would instantiate the ontological form of Truth in general.

The possibility of truths thus rests on the existence of this dialectical contradiction between the one and the multiple, as well as the material consequences of the Event (the way the truth actually begins to change the situation in a readable way).  This is the objective criteria as to whether or not something can be a truth.

So why love, art, math, politics? 

Let us note the following.

1) The four categories are only adduced, and can only be adduced, because events of the corresponding character have actually taken place.  That is, if no love events had taken place, if no revolutionary art or politics, or no mathematical breakthroughs had ever happened, the adduction of these four categories would be impossible.

2) Each category is meant to point out qualitative similarities between various truth procedures which are brought together using the conceptual means provided by philosophy in its development of Truth in general.  Thus, love will correspond to the Two of the Event, art the relation between the one and the multiple (as staged in sensual form), math the thinking of the multiple-void itself, and politics the subtraction from the one (qua state apparatus).  


Badiou's Rationalistic Reabsorption of Heidegger

beautiful cezanne badiou heidegge rpost.jpg

Badiou’s Rationalistic Reabsorption of Heidegger

The principle contours of Badiou’s ontological thinking can be thought to involve an absorption of Heidegger, an absorption which rationalizes Heidegger and thus produces new consequences.  Science will be revalidated, and along with it, its essential historical corollary: the subject. Both terms, so deeply criticized by Heidegger, will be reaffirmed in a radical re-absorption of Heidegger himself.  

The absorption will occur on two levels: that of place and that of ontological difference.

One can conceive of the conceptual development of Heidegger’s work - from Being and Time up and through the later works - as a deepening meditation of the role of place in ontology.  If there is a connection between Heidegger’s thinking and his brief Nazi engagement, or between his thinking and a generally “archi-fascist” orientation (as Lacoue-Labarthe argued), then this comes down to his meditation on place.

What emerges in Being and Time is that the opening of authentic time is always at the same time the embrace and owning-up to a radical “thrownness” (gerworfenheit) of our being-there.  In other words, the modes in which Being opens itself up to me, such that I experience beings as beings, is always a transcendental condition.  I cannot deduce or divinely create Being, but it is the factical opening of the way things already are. If beings are to be revealed to me as beings, as being determined authentically by Being, this can only be the case if my being-there bursts open to its already-being-there.  

The key is to understand how this temporal ‘already,’ converts itself into the worldiness of place. The unity of time-space for Heidegger, is the unity of the ‘already’ and place.  What is ‘already’ is history, the set of social codes in which I find myself, as well as the language in which I think and dwell. This language, or social code, is where I dwell.  To be from Germany, for Heidegger, and to live in Germany, is to be part of German history, and to embrace such is to assert the distinctively German destiny. Here we see the Nazi engagement, or at least a fascistic-nationalist orientation, quite clearly.

How does Badiou absorb, yet subvert this concept of place, with the consequence in fact of converting a nationalist project into a universalist project? First we must understand the second transformation between Badiou and Heidegger: that which concerns ontological difference.

Heidegger is the inventor of the term “ontological difference,” but if we follow Heidegger in his 1929 work Kant and the Problem of Metaphysics, we can find the origin of the concept in Kant.

The idea is this: as opposed to the realist, metaphysical determination of beings from an absolute ground (what Heidegger calls “onto-theology”), beings can only be thought according to transcendental conditions. The transcendentality of these conditions means that they are only ever presuppositions of the opening of beings. For Kant, these conditions are the pure concepts of the Understanding and the forms of intuition in Sensibility. The first supplies the concept of an object in general, or representations thought according to necessary rules, such that what is experienced as nature is no subjective whim: it is a rule governed order that genuninely counts as Nature. The second limits the use of the former, ensuring that Nature is only ever given within the finite horizon of human thinking and experience.  

In his reading of Kant, Heidegger attempts to synthesize the two faculties in Kant’s concept of the Transcendental Imagination, using the latter as the ground for the unified whole of Dasein, which just is this finite opening of genuine Nature.  Yet this opening, as being a mere transcendental presupposition, ensures that there can be no reduction of the Being of Dasein to a being: there is no objectal ground of this opening of Nature, and Dasein is just this liminal point between Being and beings.  

The ontological difference explains why Heidegger will end up conceiving Being as itself Nothing. Being is no-thing, but beyond a mere word play, this means that the conditions of the opening of beings are in a sense inaccessible, because any opening of these conditions, requires the “invisible” presupposition of the conditions themselves.

The impossibility of reaching Being then becomes a kind of endless task for Dasein, it requires a “resoluteness” in a meditative waiting, a thinking of the “withdrawal” of Being; for this Nothing, though nothing, in some sense can still be felt, in its effects, through this quasi, anxiety-inducing, vanishing, presence.

This is the point at which Badiou makes the daring move: yes, Being is Nothing, but no, it cannot be felt: for Being is merely the empty set of mathematical set theory that formalizes the void.  For Badiou, Heidegger is inconsistent: if Being is Nothing, there cannot even be a mood which thinks it. Mathematics is moodless.  Yet this also means that the void can have no history, no patient awaiting, no promised archi-fascist, poetic revolution.  Put differently, Being is placeless.

So  what happens to place, now radically cut off from Being? Badiou nonetheless fully incorporates place into his system, making it the ground of the topological theory of what he calls "situations." Like Heidegger, situations are linguistic and their character is a kind of appearing: they are accessed according to phenomeno-logy. They are finite openings, yet presuppose a void of Being, which now, for Badiou, will be mathematically infinite. 

Following this reabsorption we rediscover science: for the science of Being is mathematics. And we rediscover its well-worn rational correlate: the subject. No longer the figure of technological domination, the subject is merely the fragmentary support, the reclaimed sub-jectum, of Truth.