I Will Never Finish Your Book

you will never make sense even to yourself

Notes on ‘The One and the Multiple: a priori conditions of any possible ontology’

• Parmenides
  • Q: ‘what  presents itself is essentially multiple; what presents itself is essentially one
  • Leibniz: ‘What is not a being is not a being’
  • Problem: if being is one then what is not one (multiple) is not
    • Unacceptable conclusion: obviously what is presented to the senses is a multiple (I see trees and dogs and dirt and semen and shit and they all appear distinct; the confusion is in that all these things taken together ‘seem’ to be part of ‘one’ thing (i.e. ‘the world’))
      • In thought, we analyze particulars: things part of the multiple
  • For Badiou, presentation is multiple, and to accept ‘oneness’ as a conclusion here is to eradicate presentation which would then give us no access to being (how do we access being without the presentation of sense experience?)
  • ‘on the other hand…’ if we grant presentation (what a thing to grant!) then the multiple necessarily is (‘presentation’ as a technical term needs elaboration)
  • One as operation
    • ‘there is no one, only the count-as-one’
    • ‘one’ is a number (1); ‘one’ is not a presentation
      • ‘being’ is what presents itself
      • Situation = any presented multiplicity
        • What is ‘taking-place’ in a situation is the multiplicity
        • Structure = (general definition) when the ‘count-as-one’ operates on a situation
          • Thus, structure allows numbers to occur within the situation
          • To Badiou, every situation is structured (this remains to be seen)
          • Argument: (1) structure instantiates the count-as-one; (2) ‘being’ is the multiple; (3) ‘being’ is prior to structures (as they are not-yet); (C) the multiple is anterior to the one
            • Question: how does the ‘count-as-one’ occur from an unstructured, indeterminate (that of ‘being)? Answer: ‘one’ is an operator, a subject  uses the concept of ‘one’ and operates on the multiplicity in her picking out of a particular multiple, thus starts the ‘count’ and the structuring
              • Question: how does structure occur from the ‘count’? Answer: once we begin to count, we’ve begun to put things in an order (at first, simply, in a list of items).  Structure emerges when we further organize this list by criteria (categories, types, disciplines, subjects, object, etc.) thus the ‘counts’ instantiation of structure
              • We retroactively perceive the multiple because we know that the ‘count’ is a result of something
                • Result: the domain of the operation is not ‘one’ (in the sense of ‘the world’, or some ‘thing’), it is ‘multiple’ (operators work on the multiple) and it never generates in any presented structure a ‘one’.  Why? Because in presentation what is not one is necessarily multiple
                • In other words – when we start to ponder on the world, we immediately notice particulars and as part of our investigation, we attempt an organization of them in a veridical way. In noticing a particular, we’ve begun to ‘count’, and numbers appear (consider trying to make sense of your hand). When the count-as-one starts, we supposedly have indicated a ‘one’, or X, and we say of that ‘one’/X, “that is ‘one’/an (X)”.  Notice however, that we have predicated this ‘one’ with ‘that is-’ or ‘this is-”.  Now, notice how we were only able to recognize this after the fact (indicated by the “notice… that…”).  That we can only demonstrate this retrospectively indicates the ‘blindness’ of the ‘count-as-one’ or, rather, logico-mathematical investigation, towards what it is emerges from and how it was inaugurated.  It also indicates that of the ‘count’ there is no prior ‘oneness’ that makes the concept ‘one’ a referent to something essential (by virtue of the count-as-one bringing one to the scene not in ‘being’ but afterwards, in an operation).  Remember now, that the ‘count’ operates on (any) presentation and that presentation is structured in this way; also, what is not ‘one’ is necessarily ‘multiple’.  Therefore, presentation and its structure (a structure can notice several ‘ones’) are multiple.
• Two different ‘multiple’
  • (1) ‘pure’ presentation or ‘that-predicate-multiple’ (in its being apprehended as such retrospectively) – ‘the multiplicity of inertia’ (we’ll have to unpack ‘inertia’)
  • (2) multiple as ‘several-ones’ counted by the action of the structure (that action being the ‘count-as-one’) or composition which is that of number and structures’ effect – ‘the multiplicity of composition’
  • Technical terminology:
    • (1) = ‘inconsistent multiplicity’
    • (2) = ‘consistent multiplicity’
    • Situation = structured multiplicity (there are only ever situations)
      • Relative to (1) and (2); How?
      • “(the count-as-one)structure is both what obliges us to consider, via retroaction, that presentation is a multiple (inconsistent) and what authorizes us, via anticipation, to compose the terms of the presentation as units of a multiple (consistent)”
        • Obligation and authorization: bare minimum of a law
  • The Law of the Multiple = (is not) one
    • How one is-not – is it an operator (see above) and therefore, not a-thing
    • How one “is” – it “is” in the sense of it being a law: the law of the multiple
      • In one’s ‘not-being-there’ (in its being an operator), it is the law of any structured presentation in that it is the bare minimum for any structure/axiom/law/etc. – (note: the idea of ‘void’ and the ‘void set’ that clarifies its operating despite ‘not-being-there’)
      • Discourse on being qua being (Ontology)
        • (1) there is nothing apart from situations
        • (2) Ontology is a situation
        • (3) a situation is a presentation
        • (4) ‘being’ is included in what any presentation presents
        • (C1) ‘being qua being’ cannot be presented
        • (5) if (2) then it must admit a mode of the count-as-one, a structure (see above)
        • (6) if the one is not then being is not one
        • (C2) if (6) then being is subtracted from the count (i.e. is not operated on by the count-as-one)
        • (7) if (C2) then being is heterogeneous to the opposition of the one and the multiple
        • (C3) if (7) then, there is not structure to being
          • Question, if a situations are structured, then is it not the case that (2) is incorrect? Either this or, (2) and not(1)
          • Refutation of ‘Ontology is not a situation’
            • If ontology is not a situation then being is impossible to signified within a structured multiple
              •  …this is why I never finished your book…
      • fcuk logic, titzz

Related articles

• Alain Badiou: The Three Fundamental Logics of Negation (Hyper-Transcription) (dingpolitik.wordpress.com)
• TrOn: An Anatomical Ontology for the Beetle Tribolium castaneum (plosone.org)