From “Dictionary” at the end of Alain Badiou’s Being and Event (pages 498-526) CONDITIONS, SET OF CONDITIONS - We place ourselves in a quasi-complete situation (+). A set which belongs to this situation is a set of conditions, written ©, if: a. Ø belongs to ©, that is, the void is a situation, the ‘void condition’. b. There exists, on ©, a relation, written ⊂. π ⊂ π 2 reads ‘π 2 dominates π 1’. c. This relation is an order, inasmuch as if π 3 dominates π 2, and π 2 dominates π 1, then π 3 dominates π 1. d. Two conditions are said to be compatible if they are dominated by the same third condition. If this is not the case they are incompatible. e. Every condition is dominated by two conditions which are incompatible between themselves. - Conditions provide both the material for a generic set (+), and information on that set. Order, compatibility, etc., are structures of information (they are more precise, coherent amongst themselves, etc.). - Conditions are the ontological schema of enquiries (+). CONSTRUCTIVIST THOUGHT - The constructivist orientation of thought (+) places itself under the jurisdiction of language. It only admits as existent those pats of a situation which are explicitly nameable. It thereby masters the excess (+) of inclusion (+) over belonging (+), or of parts (+) over elements (+), or of the state of the situation (+) over the situation (+), by reducing that excess to the minimum. - Constructivism is the ontological decision subjacent to any nominalist thought. ENQUIRY - An enquiry is a finite series of connections, or of non-connections, observed—within the context of a procedure of fidelity (+)—between the terms of the situation and the name ex, of the event (+) such as it is circulated by the intervention. - A minimal or atomic enquiry is a positive, y1 □ ex, or negative ~(y2 □ ex), connection. It will also be said that y1 has been positively investigated (written y1(+)), and y2 negatively (y2(-)). - It is said of an investigated term that it has been encountered by the procedure of fidelity. EVENT - An event—of a given evental site (+)—is the multiple composed of: on the one hand, elements of the site; and on the other hand, itself (the event). - Self-belonging is thus constitutive of the event. It is an element of the multiple which it is. - The event interposes itself between the void and itself. It will be said to be an ultra-one (relative to the situation). EVENTAL SITE - A multiple in a situation is an evental site if it is totally singular (+): it is presented, but none of its elements are presented. It belongs but it is radically not included. It is an element but in no way a part. It is totally ab-normal (+). - It is also said of such a multiple that it is on the edge of the void (+), or foundational. FIDELITY, PROCEDURE OF FIDELITY - The procedure by means of which one discerns, in a situation, the multiples whose existence is linked to the name of the event (+) that has been put into circulation by an intervention (+). - Fidelity distinguishes and gathers together the becoming of what is connected to the name of the event. it is a post-evental quasi-state. - There is always an operator of connection characteristic of the fidelity. It is written □. - For example, ontological fidelity (+) has deductive technique (+) as its operator of fidelity. FORCING, AS FUNDAMENTAL LAW OF THE SUBJECT - If a statement of the subject-language (+) is such that it will have been veridical (+) for a situation in which a truth has occurred, this is because there exists a term of the situation which belongs to this truth and which maintains, with the names at stake in the statement, a fixed relation that can be verified by knowledge (+), thus inscribed in the encyclopaedia (_). It is this relation which is termed forcing. it is said that the term forces the decision of veracity for the statement of the subject-language. - One can thus know, within the situation, whether a statement of the subject-language has a chance or not of being veridical when the truth will have occurred in its infinity. - However, the verification of the relation of forcing supposes that the forcing term has been encountered and investigated by the generic procedure of fidelity (+). Thus it depends on chance. GENERIC EXTENSION OF A QUASI-COMPLETE SITUATION - Take a quasi-complete situation (+), written S, and a generic part (+) of that situation, written ♀. We will term generic extension, and write as S(♀), the set constituted from the referential values (+), or ♀-referents, of all the names (+) which belong to S. - Observe that it is the names which create the thing GENERIC THOUGHT - The generic orientation of thought (+) assumes the errancy of excess (+), and admits unnamable or indiscernible (+) parts into being. It even sees in such parts the place of truth. For a truth (+) is a part indiscernible by language (against constructivism (+)), and yet it is not transcendent (+) (against onto-theology). - Generic thought is the ontological decision subjacent to any doctrine which attempts to think of truth as a hole in knowledge (+). There are traces of such from Plato to Lacan. - The ontological schema of such thought is Paul Cohen’s theory of generic extension (+). INTERVENTION - The procedure by which a multiple is recognised as event (+), and which decides the belonging of the event to the situation in which it has its site (+). - The intervention is shown to consist in making a name out of an unpresented element of the site in order to qualify the event whose site is this site. This nomination is both illegal (it doesn’t conform to any rule of representation) and anonymous (the name drawn from the void is indistinguishable precisely because it is drawn from the void). It is equivalent to ‘being an unpresented element of the site’. - The name of the event, which is indexed to the void, is thus supernumerary to the situation in which it will circulate the event. - Interventional capacity requires an event anterior to the one that it names. It is determined by a fidelity (+) to this initial event. KNOWLEDGE - Knowledge is the articulation of the language of the situation over multiple-being. Forever nominalist, it is the production of the constructivist orientation of thought (+). Its operations consist of discernment (this multiple has such a property) and classification (these multiples have the same property). These operations result in an encyclopaedia (+). - A judgment classified within the encyclopaedia is said to be veridical. ON THE EDGE OF THE VOID - Characteristic of the position of an evental site within a situation. Since none of the elements of the site are presented ‘underneath’ the site there is nothing—within the situation—apart from the void. In other words, the dissemination of such a multiple does not occur in the situation, despite the multiple being there. This is why the one of such a multiple is, in the situation, right on the edge of the void. SUBJECT - A subject is a finite local configuration of a generic procedure (+). A subject is thus: a) a finite series of enquiries (+); b) a finite part of a truth (+). It can thus be said that subject occurs or is revealed locally. - It can be shown that subject, finite instance of a truth, realizes an indiscernible (+), forces a decision, disqualifies the unequal and saves the singular. TRUTH - A truth is the gathering together of all the terms which will have been positively investigated (+) by a generic procedure of fidelity (+) supposed complete (thus infinite). It is thus, in the future, an infinite part of the situation. - A truth is indiscernible (+): it does not fall under any determinant (+) of the encyclopaedia. It bores a hole in knowledge. - It is truth of the entire situation, truth of the being of the situation. - It must be remarked that if veracity is a criteria for statements, truth is a type of being (a multiple. There is therefore no contrary to the true, whilst the contrary of the veridical is the erroneous. Strictly speaking the ‘false’ can solely designate what proves to be an obstacle to the pursuit of the generic procedure. VOID - The void of a situation is the suture to its being. Non-one of any count-as-one (except within the ontological situation (+)), the void is that unplaceable point which shows that the that-which-presents wanders throughout the presentation in the form of a subtraction from the count.
Posted on: Mon, 25 Nov 2013 07:00:45 +0000
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