Reading Summary of Meditation 1 - a priori conditions for any possible ontology
Badiou's ontological schema in Being and Event commences by revisiting Plato's dialogue Parmenides. The dialogue demonstrates the "impasse" of ontology: "what presents itself is essentially multiple; what presents itself is essentially one." Or rather, persons experience the pure multiplicity of presentation (trees, ants, noses, beliefs, skin tone, cells, particles, etc.) while remaining convinced of its unity (the world). Perhaps the most puzzling of thoughts: Is being one or multiple? To posit being as one; is to say that what is not one, the multiple, is not. But presentation as such is multiple, thus Badiou ponders how one could have access to being outside of what is presented (the multiple). However, if the one is trumped by the multiple there are equally problematic conclusions; for instance, what presents itself is no longer significant. But how could this be? When one experiences the multiplicity of presentation, it is only ever this or that multiple. Multiples are always counted-as-one in structured presentation. Thus Badiou thunders forward: "We find ourselves on the brink of a decision, a decision to break with the arcana of the one and the multiple in which philosophy is born and buried, phoenix of its own sophistic consumption. This decision can take no other form than the following: the one is not."
Badiou has no desire to overthrow Lacan's positing that "there is Oneness," merely to note that the "there is" localizes being to the one. And since the one is not, the one must only be understood as operation. That is, as the count-as-one. The one is quite literally a number. "In sum: the multiple is the regime of presentation; the one, in respect to presentation, is an operational result; being is what presents (itself)." Thus being is neither one nor multiple. Before moving ahead, Badiou wants to make clear his terms. I will here consider the genealogy of the terms: situation, structure, inconsistent multiplicity, and consistent multiplicity.
Situation - “any presented multiplicity”; “the place of taking place”; "whatever the terms of the multiplicity in question"
Structure - a situation admitting its own count-as-one; "it is what prescribes, for a presented multiple, the regime of its count-as-one"; when something is counted-as-one in a situation it means it belongs to its structure
Inconsistent Multiplicity & Consistent Multiplicity - Considering presentation is multiple, and the multiple is the predicate of an operation (the count-as-one in structure); the multiple apparently is divided at this point (by the count). "...'multiple' is indeed said of presentation, in that it is retroactively apprehended as non-one as soon as being-one is a result. Yet 'multiple' is also said of the composition of the count, that is, the multiple as 'several ones' counted by the action of structure." Thus Badiou distinguishes inconsistent and consistent multiplicity. Inconsistent multiplicity is the "inertia" of presentation (think unthinkable). Consistent multiplicity is "that of number and the effect of structure" (think formal observation).
Return to Structure - "Structure is both what obliges is to consider, via retroaction, that presentation is a multiple (inconsistent) and what authorizes us, via anticipation, to compose the terms of presentation as units of a multiple (consistent). It is clearly recognizable that this distribution of obligation and authorization" makes the one-which is not- into a law."
Return to Situation - Badiou's assertion, which is significant, is that there "is nothing apart from situations." He proceeds: "Ontology, if it exists, is a situation." It is, as Badiou notes, the "wager" of his enterprise. What does it mean for ontology (the science of being qua being) to be a situation as so termed by Badiou? Essentially, that there "is no structure of being." But if ontology is a situation, it would still have to "admit" a count-as-one; that is a structure. But hasn't this lead us back to the necessity of the one and being. Badiou clarifies, "If the one is not, being solely the operation of the count, mustn't one admit that being is not one? And in this case, is it not subtracted from every count?" We shall read much more in future meditations about the subtractive, which is key to Badiou's schema.
The most significant adversaries to Badiou's schema are "ontologies of presence." Badiou writes, "To say that ontology is not a situation is to signify that being cannot be signified within a structured multiple, and that only experience situated beyond all structure will afford us an access to the veiling of being's presence." An ontology of presence, therefore, is the "exact contrary of [an ontology of] presentation." Thus Badiou moves forward "to oppose - to the temptation of presence - the rigor of the subtractive, in which being is said solely as that which cannot be supposed on the basis of any presence or experience."
It should be noted that the greatest venture in all of Being and Event is to resolve the "paradoxes" of ontology as a situation. In Meditation 1 Badiou sets the trajectory: "If there cannot be a presentation of being because being occurs in every presentation - and this is why it does not present itself - then there is one solution left for us: that the ontological situation be the presentation of presentation." Moreover, "...if an ontology is possible, that is, a presentation of presentation, then it is the situation of the pure multiple, of the multiple 'in-itself'." What Badiou is implying here is that ontology can only be the "theory of inconsistent multiplicites," it must be the science of "multiple qua multiple." Thus two "a priori requirements" are asserted for any possible ontology:
1. "The multiple from which ontology makes up its situation is composed solely of multiplicities. There is no one. In other words, every multiple is a multiple of multiples."
2. "The count-as-one is no more than the system of conditions through which the multiple can be recognized as multiple."
But what should be made of the "system of conditions" in thesis 2? As Badiou himself asks, "What is a law whose objects are implicit?" He clarifies, what ontology counts as one "is not 'a' multiple in the sense in which ontology would possess an explicit operator for the gathering-into-one of the multiple; a definition of the multiple-qua-one." As we will remember, if the multiple is gathered into one, "being is lost," because the one is not. Instead, what is needed is a system of conditions which would divide or count multiples (thus making inconsistent and consistent multiples, or rather prescribe and prohibit) implicitly (rather than explicitly). Badiou's answer to these questions is that "It is evidently a system of axioms." An axiom, you see, operates "on the basis of non-defined terms." That is, "This rule counts as one in the sense that the non-defined terms are nevertheless defined by their composition; it so happens that there is a de facto prohibition of every composition in which the rule is broken and a de facto prescription of everything which conforms to the rule. An explicit definition of what an axiom system counts as one, or counts as its object-ones, is never encountered." Because again, to define it is to count it as one, and being would be lost.
In the introduction to Being and Event Badiou makes his argumentative aim clear: "mathematics=ontology." This thesis which will be argued throughout both volumes of Being and Event (including Logics and Worlds), stands in opposition to the linguistic-turn (Wittgenstein and Carnap) in philosophy which makes language the ultimate horizon of the science of being qua being. For Badiou, of course, this mathematical return (missing since Hegel) excludes God. Badiou will utilize Cantor's "set-theory" as his ontological-mathematical-metaphorical structure. It should be noted however that Cantor himself did not preclude God from his system which we will see later in Meditation 3. Badiou's atheism is a significant obstacle for a theologian attempting to utilize his schema of the "Event" (which involves a radical envisioning of the subject and the nature of truth) for at least two reasons. First, Badiou's atheism is implicit in his ontological argumentation which is then deployed across is entire schema. Thus, so as to not simply pillage the philosopher for kernels of sophistry or turns of phrase, one should invest in Badiou's work to see if his general schema of "mathematics=ontology" necessarily precludes God. Secondly, Badiou's materialism is similarly problematic to the dualism which much of Christian thought has embraced. That is, an ontology of presentation over and against an ontology of presence must be examined, and decided upon. Can one affirm an ontology of presentation and keep their God? I shall be examining both questions intently as the research continues through Badiou's first three parts on Being.
Badiou's ontological schema in Being and Event commences by revisiting Plato's dialogue Parmenides. The dialogue demonstrates the "impasse" of ontology: "what presents itself is essentially multiple; what presents itself is essentially one." Or rather, persons experience the pure multiplicity of presentation (trees, ants, noses, beliefs, skin tone, cells, particles, etc.) while remaining convinced of its unity (the world). Perhaps the most puzzling of thoughts: Is being one or multiple? To posit being as one; is to say that what is not one, the multiple, is not. But presentation as such is multiple, thus Badiou ponders how one could have access to being outside of what is presented (the multiple). However, if the one is trumped by the multiple there are equally problematic conclusions; for instance, what presents itself is no longer significant. But how could this be? When one experiences the multiplicity of presentation, it is only ever this or that multiple. Multiples are always counted-as-one in structured presentation. Thus Badiou thunders forward: "We find ourselves on the brink of a decision, a decision to break with the arcana of the one and the multiple in which philosophy is born and buried, phoenix of its own sophistic consumption. This decision can take no other form than the following: the one is not."
Badiou has no desire to overthrow Lacan's positing that "there is Oneness," merely to note that the "there is" localizes being to the one. And since the one is not, the one must only be understood as operation. That is, as the count-as-one. The one is quite literally a number. "In sum: the multiple is the regime of presentation; the one, in respect to presentation, is an operational result; being is what presents (itself)." Thus being is neither one nor multiple. Before moving ahead, Badiou wants to make clear his terms. I will here consider the genealogy of the terms: situation, structure, inconsistent multiplicity, and consistent multiplicity.
Situation - “any presented multiplicity”; “the place of taking place”; "whatever the terms of the multiplicity in question"
Structure - a situation admitting its own count-as-one; "it is what prescribes, for a presented multiple, the regime of its count-as-one"; when something is counted-as-one in a situation it means it belongs to its structure
Inconsistent Multiplicity & Consistent Multiplicity - Considering presentation is multiple, and the multiple is the predicate of an operation (the count-as-one in structure); the multiple apparently is divided at this point (by the count). "...'multiple' is indeed said of presentation, in that it is retroactively apprehended as non-one as soon as being-one is a result. Yet 'multiple' is also said of the composition of the count, that is, the multiple as 'several ones' counted by the action of structure." Thus Badiou distinguishes inconsistent and consistent multiplicity. Inconsistent multiplicity is the "inertia" of presentation (think unthinkable). Consistent multiplicity is "that of number and the effect of structure" (think formal observation).
Return to Structure - "Structure is both what obliges is to consider, via retroaction, that presentation is a multiple (inconsistent) and what authorizes us, via anticipation, to compose the terms of presentation as units of a multiple (consistent). It is clearly recognizable that this distribution of obligation and authorization" makes the one-which is not- into a law."
Return to Situation - Badiou's assertion, which is significant, is that there "is nothing apart from situations." He proceeds: "Ontology, if it exists, is a situation." It is, as Badiou notes, the "wager" of his enterprise. What does it mean for ontology (the science of being qua being) to be a situation as so termed by Badiou? Essentially, that there "is no structure of being." But if ontology is a situation, it would still have to "admit" a count-as-one; that is a structure. But hasn't this lead us back to the necessity of the one and being. Badiou clarifies, "If the one is not, being solely the operation of the count, mustn't one admit that being is not one? And in this case, is it not subtracted from every count?" We shall read much more in future meditations about the subtractive, which is key to Badiou's schema.
The most significant adversaries to Badiou's schema are "ontologies of presence." Badiou writes, "To say that ontology is not a situation is to signify that being cannot be signified within a structured multiple, and that only experience situated beyond all structure will afford us an access to the veiling of being's presence." An ontology of presence, therefore, is the "exact contrary of [an ontology of] presentation." Thus Badiou moves forward "to oppose - to the temptation of presence - the rigor of the subtractive, in which being is said solely as that which cannot be supposed on the basis of any presence or experience."
It should be noted that the greatest venture in all of Being and Event is to resolve the "paradoxes" of ontology as a situation. In Meditation 1 Badiou sets the trajectory: "If there cannot be a presentation of being because being occurs in every presentation - and this is why it does not present itself - then there is one solution left for us: that the ontological situation be the presentation of presentation." Moreover, "...if an ontology is possible, that is, a presentation of presentation, then it is the situation of the pure multiple, of the multiple 'in-itself'." What Badiou is implying here is that ontology can only be the "theory of inconsistent multiplicites," it must be the science of "multiple qua multiple." Thus two "a priori requirements" are asserted for any possible ontology:
1. "The multiple from which ontology makes up its situation is composed solely of multiplicities. There is no one. In other words, every multiple is a multiple of multiples."
2. "The count-as-one is no more than the system of conditions through which the multiple can be recognized as multiple."
But what should be made of the "system of conditions" in thesis 2? As Badiou himself asks, "What is a law whose objects are implicit?" He clarifies, what ontology counts as one "is not 'a' multiple in the sense in which ontology would possess an explicit operator for the gathering-into-one of the multiple; a definition of the multiple-qua-one." As we will remember, if the multiple is gathered into one, "being is lost," because the one is not. Instead, what is needed is a system of conditions which would divide or count multiples (thus making inconsistent and consistent multiples, or rather prescribe and prohibit) implicitly (rather than explicitly). Badiou's answer to these questions is that "It is evidently a system of axioms." An axiom, you see, operates "on the basis of non-defined terms." That is, "This rule counts as one in the sense that the non-defined terms are nevertheless defined by their composition; it so happens that there is a de facto prohibition of every composition in which the rule is broken and a de facto prescription of everything which conforms to the rule. An explicit definition of what an axiom system counts as one, or counts as its object-ones, is never encountered." Because again, to define it is to count it as one, and being would be lost.
In the introduction to Being and Event Badiou makes his argumentative aim clear: "mathematics=ontology." This thesis which will be argued throughout both volumes of Being and Event (including Logics and Worlds), stands in opposition to the linguistic-turn (Wittgenstein and Carnap) in philosophy which makes language the ultimate horizon of the science of being qua being. For Badiou, of course, this mathematical return (missing since Hegel) excludes God. Badiou will utilize Cantor's "set-theory" as his ontological-mathematical-metaphorical structure. It should be noted however that Cantor himself did not preclude God from his system which we will see later in Meditation 3. Badiou's atheism is a significant obstacle for a theologian attempting to utilize his schema of the "Event" (which involves a radical envisioning of the subject and the nature of truth) for at least two reasons. First, Badiou's atheism is implicit in his ontological argumentation which is then deployed across is entire schema. Thus, so as to not simply pillage the philosopher for kernels of sophistry or turns of phrase, one should invest in Badiou's work to see if his general schema of "mathematics=ontology" necessarily precludes God. Secondly, Badiou's materialism is similarly problematic to the dualism which much of Christian thought has embraced. That is, an ontology of presentation over and against an ontology of presence must be examined, and decided upon. Can one affirm an ontology of presentation and keep their God? I shall be examining both questions intently as the research continues through Badiou's first three parts on Being.
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