Badiou’s **Prologue** is entitled: **Formal Presentation of the Absolute Place **(or Location).

Note: I am continuing my commentary on the Table of Contents to Badiou’s forthcoming book THE IMMANENCE OF TRUTHS, trying to anticipate some part of its content based on his prior published works and on his unpublished seminars.

This is an intriguing title as in his previous work Badiou has always ruled out the existence of such an “absolute place”. In his SECOND MANIFESTO FOR PHILOSOPHY he argues that the idea of a total multiplicity, or multiplicity of all multiplicities, is incoherent and thus is devoid of being.

There is not the localizing being of worlds and the localized being of objects. Nor is there the Universe as the absolute place of all there is (SECOND MANIFESTO, 30-31).

This non-existence of an absolute place is also a crucial part of his presentation of his difference with Deleuze. In his seminar on Politics Badiou contrasts his own thinking of the Void with Deleuze and Guattari’s thought of Chaos:

In any case, if the key concept is chaos then I stipulate philosophically that chaos does not exist, for beneath this unthinkable “there is”, outside of sense, unattainable, hides the figure of presence. Deleuze and Guattari try to maintain such a figure simply unbound to any allegiance to sense.

Let us examine their definition of chaos: “Chaos is defined not so much by its disorder

as by the infinite speed with which every form taking shape in it vanishes. It is a void that is not a nothingness but a virtual, containing all possible particles and drawing out all possible forms, which spring up only to disappear immediately, without consistency or reference, without consequence” (page 118, with a note citing Prigogine and StengersEntre le temps et l’éternité).Infinite speed of births and disappearances, which define chaos as a place of the virtual, i.e. as “a void that is not a nothingness”, chaos is presented as the absolute reservoir of possibles in an incessant movement of births and disappearances. Constant infinitesimal upsurge of all possibilities, chaos refers to an absolute place of all possibles, i.e. to a pure natural “there is” as absolute system of all virtualities deprived of any being. In contrast, although it is called a void by Deleuze and Guattari, I oppose to their definition of chaos, the residue, in my opinion non-existent, of a figure of presence, my own definition of the sutured being of the void. It is a questiion here of a fundamental philosophical choice, marked by a very sharp distinction between chaos and the void

(from the seminar Politics, academic year 1991-1992, course three entitled Deleuze 2).

The problem with Deleuze and Guattari’s plane of immanence, according to Badiou, is that it re-institutes a transcendence, in the form of a transcendent presence or absolute place, a totality of all possibles.

However, this thesis of the non-existence of an absolute place can be seen to be in tension with another thesis that Badiou develops in the** Introduction** to THE IMMANENCE OF TRUTHS, that of the “absolute ontological referent”, which he explains in the short text Toward A New Thinking of the Absolute.

Badiou’s objection to the concept of an absolute place is that it implicitly re-institutes a form of onto-theology. It posits as coherent the idea of a totality of all beings, which it treats as a presence, and so is yet another figure of transcendence. In the article “Toward a New Thinking of the Absolute” Badiou’s own version of the absolute ontological referent frees it from these residues of transcendence.

This absolute ontological referent is “V” the Universe of sets.

We shall conventionally call V, the letter V, which can be said to formalize the Vacuum, the great void, the place (truly inconsistent since non-multiple) of everything that can be constructed by means of axioms. What is metaphorically “in V” is what can respond to the axiomatic injunction of set theory. This means that V is in reality only the set of propositions that can be proved from the axioms of the theory. It is a being of language exclusively. It is customary to call such beings of language “classes.” We shall therefore say that V is the class of sets, but bear in mind that this is a theoretical entity that is unrepresentable, or without a referent, since it is precisely the place of the absolute referent.

V, the Universe of sets, a place that is inconsistent, a being exclusively of language (and so not a presence). It is the “place of the absolute referent”. The universe V is not thinkable as a coherent idea, but is only definable axiomatically. It is a “rational fiction in which all sets are thinkable”, but is not itself thinkable.

In conclusion, I do not endorse Badiou’s solution without seeing further arguments. For me it is even more onto-theological. But I do think he is on to something. In WHAT IS PHILOSOPHY? Deleuze and Guattari write:

“Concepts are events, but the plane is the horizon of events, the reservoir or reserve of purely conceptual events: not the relative horizon that functions as a limit, which changes with an observer and encloses observable states of affairs, but the absolute horizon, independent of any observer, which makes the event as concept independent of a visible state of affairs in which it is brought about”

(page 36).

Thanks for bringing it to the English readers of Badiou.

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thanks. There is one point of imprecision in your summary I think. Whereas Badiou writes that V is “the place (truly inconsistent since non-multiple) of everything that can be constructed by means of axioms. What is metaphorically “in V” is what can respond to the axiomatic injunction of set theory.” You then summarize this as “The universe V is not thinkable as a coherent idea, but is only definable axiomatically.” But this is too strong. To be axiomatically definable has a precise logico-mathematical meaning. Something is axiomatically defined if it is logically a primitive notion for which axioms are given. But this means that the objects so defined show up in the domain of discourse. For example, Hilbert’s geometry axiomatically defines points, lines, and planes. This means that points, lines, and planes are objects of the domain of discourse of that particular language. In other words, the variables of such languages range over these axiomatically defined objects. Similarly, set theory is a logical language whose variables range over sets; it defines the notion of set axiomatically. V, the set-theoretic universe does not show up as an entity in ZFC. So it is certainly not axiomatically defined. It is only from a model-theoretic meta-perspective that we can consider a mathematical object which would contain everything (sets and structure) that would be a model for the particular language we are considering. For example, we know that the set-theoretically defined object ‘the real plane’ is a model for the language of two-dimensional euclidean geometry. For set theory this is not that simple, since it is the strongest language out there, really. So there exists no stronger language to describe objects which are models for it. But by analogy, we do talk about something like that and name it ‘V’. But ‘V’ is certainly not axiomatically defined.

To my mind, the proximity that you detect between Badiou and Deleuze on these matters does depend on the conflation described above to some extent. Perhaps one can take it that Badiou’s philosophy of the higher infinite serves to clarify mathematically some Spinozist (and hence Deleuzian) themes. In fact, at his final seminar on monday this week, Badiou said as much himself, claiming that his recent work ends up confirming Spinoza’s idea that the absolute infinite has infinitely many attributes.

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Thanks for this contribution.

At this point of the argument what matters is that V not be a coherent object or place, in contrast to Badiou’s reading of Deleuze’s plane of immanence. Probably you would accept the reformulation that Vis only axiomatically prescriptible (rather than “definable). I was following Badiou’s terminology here:

“By saying that set theory constitutes an absolute reference, I am assuming that there exists a system of axioms, incompletely discovered as yet, which defnes the universe V, the rational fiction in which all sets are thinkable, and defnes it alone. In other words, no important, signifcant, useful property of sets will remain undecidable once we have been able to fully identify the axioms” (“Toward A New Thinking of the Absolute”, page 16).

The last sentence here defines what he means by “definable” in this context.

This is not to be pedantic, as I think you are highlighting an important point, but the “conflation”, if any, is not mine but Badiou’s (at least in this passage). Badiou tells us that the choice of universe is a decision, but that its delimitation is effectuated by the axioms, including axioms that we have yet to discover. So we seem to have two senses of definition here:

the mathematical one, and as you say Badiou’s arguments imply that V is not a definable object

the “ontological” one, that induces a non-objectal Universe from a set of axiomatic prescriptions.

Tell me what you think.

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