Being and Event: The Point of Excess, Hegel's Logic, and the Name-of-the-Father (part 1 of 2, On Letters α and β)
Intro: On Writing “The Name-of-the-Father”
I normally choose not to use hyphens when writing out the term borrowed from Lacanian psychoanalysis, “the Name-of-the-Father”, because it looks precocious and it feels unnecessary; however, for the purpose of explaining and unifying the usage of Greek letters in Hegel-and-Badiou’s respective writings, I am obliged to include them here in the writing out of the term.
One can assume that the hyphens themselves carry out a clever function, that of putting several words together into a singularly understood and inscribed Word (“Name-of-the-Father”) that signifies a signifier for all the other signifiers, or a one-word for all the other multiple-word(s) which are also words that exist on their own, both alongside it and without it. Perhaps, then, the Name-of-the-Father is truly either “Lexicon”, “Language”, “Vocabulary”, “Dictionary”, or maybe even “Word-Bank”. Anything like that. But my personally-chosen approach to psychoanalysis is more emphatic about the future relationship of psychoanalysis to philosophy, and therefore, a primacy of the signified emerges over the signifier as the multiple of active agents which ought to be used for understanding both “existence” and “reality” simultaneously, if psychoanalysis is to possess any political usefulness at all.
First, examine this important passage from “Hegel’s Logic” (p. 113, Oxford University Press):
Is this not basically the same iteration as what Badiou terms “the theorem of the point of excess” in his conceptualization of Russell’s paradox?
Furthermore, one gets the impression from this comparison that the Greek letters used to write the theorems in Being and Event also possess properties unique to themselves, albeit only in relation to one another.
In conjunction with the concept of the Name-of-the-Father (Nom-du-Père), this observation finds its highest realization in philosophical principles derived from the grammatical mechanics of a written language. Examine the following passage from Being and Event (p. 87):
The resemblance to the concept of the Name-of-the-Father stricken here by the notation Alain Badiou uses in Being and Event, p(α), yields a linguistic analysis of the text that is indispensable for incorporating ideas from Hegel’s philosophy into a critique of psychoanalytic terminology that might have concretely political applications later on. Hegel’s philosophy, once it is finished giving its account of human history (which for him is also the history of philosophical progress throughout a living civilization), can commence with its more substantial and holistic analyses of logical thought, so as not to “give an inadequate conception of them”, as Hegel might put it.
However, Hegel wasn’t entirely “right”, was he? If human civilization had finally finished progressing philosophically, as Hegel hypothesized it ultimately would in a Napoleonic Europe, perhaps his Philosophy of Right would have been published a bit sooner, and democratic human rights would already have become universally granted to all without exception. We must consequently look towards more contemporary thinkers in our own present-day.
The Letters Themselves (α, β, γ, δ)
The philosophical or logical principle innate to α, then, is the “Abstract side” of logic, that of bare understanding. It is encountered in the very functioning of a “Name” so-called. This is a functioning that is simultaneously both different-from and identical-to that of a signifier, which in writing can take the form of either a word, a name, a title, a pronounceable character, a character that is never pronounced when reading (a notion of writing derived from the logical functionings of a given language’s various parts of speech, such as a comma or a semicolon), a symbol, a signal (a signified of the signifier that is unconscious), a part of speech (a signifier of the signified that is unconscious), or a void (either read-as-silence or a physical “space” between signifiers that separates them qua appearing as something-zero).
In other words, history is something understood a priori within any given dialogue as already-written, but it is not something that is capable of interpreting itself in the mere act of becoming-read. Unlike the logical functionings of particles of grammar and language, which lead the thinking subject towards the conceptual completion of speech by means of their internal mechanisms of (a seemingly Kantian) necessity (i.e, the rules of forming a complete sentence), historical exposition must avoid taking on any kind of subjectifying narrative if it is to remain as something objective and factual. In other words, already-written history is something that can be investigated, or even revised, if needed.
The condition of this intrinsic revisability is only that it must never become interpreted by means of its very own exposition. Otherwise history becomes more like a Netflix series (I’m thinking of The Dark Crystal: Age of Resistance) or something similar. This principle of historical exposition is continuously causing problems for the relatively nascent field of anthropology, for example, and causes even more problems for more contemporaneous (synchronic) fields such as law enforcement, forensics, and political legislation, which must always stay abreast of what is currently happening.
The side of logic Hegel called “Abstract”, that of mere understanding, is therefore highly duplicitous. The letter α only exists on its own, then, in the form of p(α), a letter “p” which alludes to Bertrand Russell’s paradox of set theory; this paradox states that a given set, written by Georg Cantor as λ(α) (source: Badiou, Being and Event, p. 42), can contain anything except itself (as an element). In other words, p(α) is identical to α, but qua set, it cannot include itself as an element, and this is not only a logical law for analytic philosophy, because it is also considered as a law of nature and a law of physics, so to speak, for any scientific ontology.
What is innate to β in Badiou’s theorems is what Hegel termed the “Dialectical” side of logic, or “negative reason”. This (β) is the argument whereby the distinction between belonging and inclusion is introduced by means of an other argument besides α, namely γ. It is called the “power-set axiom”, which states that if any set of any argument exists in the first place, it also belongs to a different set, designated as β, by means of its elements necessarily falling somehow into a relation with γ, another different set. The set of (all) multiples that actually exists, α, also founds the existence of the set of all multiples which can be inferred from α’s respective elements and subsets, that of β, solely and exclusively because of the inclusion of γ in α.
Inclusion relation: ⊂ (“included in”)
(source: https://lexique.netmath.ca/en/inclusion-relation/)
Membership relation: ∈ (“belongs to”, or, “is an element of”)
(source: https://lexique.netmath.ca/en/membership-relation/)
Universal quantifier: ∀ (“all”)
Existential quantifier: ∃ (“there exists”)
(source: https://lexique.netmath.ca/en/quantifier/)
(∀α)(∃β)[(∀γ)[(γ ∈ β) ↔ (γ ⊂ α)]]
“For all α there exists β, but only such that for all γ, γ belongs to β because γ is included in α.”
I will add two (rhetorical?) questions to accompany this information: is there any more perfect way of writing out the concept of Absolute Knowing in Hegel’s philosophy? Also, should the third “side” of logic perhaps precede the second “side” of logic if γ is more fundamental to constituting α than β is?
As these Greek letters in Badiou’s written theorems also serve as “moments” of logical entity (according to myself), then, we maybe get some crucial insight into the synchronic grammatical constitution of complete sentences, and the informational entropy which is generated from the understanding of the signified that is undertaken by the Lacanian (barred) subject in either reading any text or listening to spoken language. For example, in the formula of sexuation written (∃x)-(Φx), or, “there is One who is not submitted to the phallic function” (I am utilizing a hyphen as a minus-sign in place of the horizontal bar usually written over the top of “Φx”), we can glean that a sentence, even if it is grammatically correct, may also approach an infinite length in its being-articulated. A long list of names read aloud at a graduation ceremony or a veterans’ memorial service are examples of this formula as it can be applied to actual speech. The monologue of Leopold Bloom’s wife Molly in the last section of James Joyce’s novel Ulysses is an example of the formula as well, since it can also be applied to written/printed literature.
What this means for the interpretation of the theorem is that the Lacanian “little other” (in contradistinction to the big Other, “A”, in French, Autre), also called in English “object a” (in French, objet petit “a”), is an “other” α only in the form of γ. This applies directly and precisely to something that Jacques Lacan presented in the fifth year of his seminar (1957-1958), titled “Formations of the Unconscious”, on the interactions between messages and codes which are constitutive for the functioning of a metonymic object. This was called the two functions in a sequence of signifiers, which I interpreted to refer to the processes of “coding” and “re-coding”:
Since the properties of α are found in the functioning of a Name, it is far easier to make a list of the possibilities of the forms taken by α as they occur in writing than as they occur in speech, since speech frequently overlaps with the anarchic qualities of auditory perception in general. However, the properties of β complicate what is encountered in the written forms of α precisely because of the relationship that a Name necessarily bears to a metonymic object. The bare recognition of γ precedes any “Dialectical” understanding of language itself, insofar as a human child’s biological birth-event is a prerequisite of possessing any subjectivity in the first place. This further implies, of course, that language acquisition, as it relates to any bare understanding of language, begins at zero, at age zero, and possessing (a) zero understanding of anything. In this way, language becomes an immanent metaphor (immanent to our reality) for perception itself, since the “transcendental unity of apperception”, as Kant termed it in Critique of Pure Reason, must be forcibly synchronized with the fact of language’s existence; this is a fact which constantly asserts itself by means of languages’ practical usage in our real, social world of shared perceptions.
In turn, language not only codes and re-codes elements of α through the economics of discourse (via the real exchange of signifiers), but it also de-codes our sensory perception(s), and it does this by using Kantian cognition as a mediator, or as a kind of referee, of consciousness. Thus, the signification of a word is not the result of a unitarily understood signified; rather, signification is the result of multiple-signified(s) that are strictly unconscious, and move the forever-nascent subject towards ego-ideal formation, propelled by the cyclical economics of discourse in language acquisition. This specifically means the recognition (β) and identification (β’) of grammatical parts of speech as they present themselves in the usage of language (α), and how they interact with the Hegelian moments of logical entity through the multiplicity of γ.
Parts of speech (a signifier-of-the-signified that is unconscious): ego-ideal i(a) formation
While it may seem that because the ideal-ego, I(A), is located at the dead-end of the Lacanian graph of desire at the lowest left position, the formation of the ideal-ego must therefore be a more mature process that happens later on in language acquisition than the formation of the ego-ideal, it is perhaps more true to state that the ideal-ego originates for understanding from the blank image of the mother, i, a point which is located on the pre-Oedipal triangle between M and -φ. In this way, understanding proceeds apparently from nature, from Nature-proper, and not directly from the de-coding processes that cognition uses to mediate the self-same consciousness that cognition also necessarily inherits some duty towards interpreting.
Signals (a signified-of-the-signifier that is unconscious): ideal-ego I(A) formation
Negative reason, or the Dialectical side of logic, defaults here from a reliance on language and the logical/affective entanglement with grammatical parts of speech to a philosophical form of cognition experienced as something more primally universal than speech. It is therefore implicitly understood to exist prior to the appearance of the mother’s image, i, within the subject’s relationship to language. In this acquired sense of cognitive difference, it becomes possible to register the phallus (on the pre-Oedipal triangle) as something more like the mother’s α. The desire of the mother, which transforms the “I” into a grammatical part of speech which is always present within speech even without its appellation, originates from the metonymic object which can be located in any sequence of signifiers, and whenever δ’, a signifier of language which seemingly proceeds from Nature, is understood as the initial trigger or catalyst of the mother’s desire, an anxiety develops that is foundational for ideal-ego formation probably a while before ego-ideal formation is ever encountered.
