Edit: "ZFC" makes no sense. Should be ZF.)
According to Slavoj Zizek, when we arrange symbols in a semiotic table, there are necessarily mismatches, however slight, between the signs and what they signify by way of symbol combinations that are allowed in our representation but which have no correspondence in factual reality. This signifies that we have jumbled at least two unrelated tables within a single frame of comparison. The quality that makes these signs be unrelated to each other is the Real. From page 100 in his book Absolute Recoil, with the surrounding context and the relevant text at the end bolded:
I'm not as familiar with Alain Badiou's conception of Being. As I understand it, Badiou's view is that language is incapable of expressing truth because it only ever deals with finite representations. Truth exists and it can be thought, but it cannot be expressed in language because truth is infinite and mathematical. What does that mean? Well, there was this dude called Paul Cohen who used a kind of mathematical object called a generic set (see generic filter on Wikipedia) to prove that the continuum hypothesis (CH) is independent of ZF. This is significant because ZF is supposed to be the foundation of math. What is CH then, not math?There is a further complication in Levi-Strauss' procedure which renders problematic the simple opposition of structure and history. His basic thesis is that human history consists in a series of catastrophes or falls: the invention of writing, the "Greek miracle," the rise of monotheism, Descartes and modern industrial-scientific civilization... Levi-Strauss insists on the contingency of these falls-there was no necessity to the "Greek miracle," which took place due to a thoroughly contingent intersection of multiple conditions. Such falls are thus not simply variations within an ahistorical structural matrix-they are cuts, contingent explosions of the New. Levi-Strauss' dream here is the idea of possible virtual alternative histories: not that nothing New would have emerged and that we would have remained in the old universe of la pensee sauvage, but that each new fall is accompanied by (or gives rise to) a virtual shadow of alternative possibilities: "Indeed, one invariant trait of Levi-Strauss' catastrophic history is that, at each turning point, at each bifurcation, there is the shadow of an alternative history, the phantom of what has never existed, but might have existed." These alternative possibilities are not simply variations within an eternal matrix; the point is rather that each historical event, each emergence of the New, each fall, is always split between what actually happened and its failed alternatives.
The key problem is thus that of the umbilical cord connecting a formal-transcendental structure to its contingent historical content: how is the Real of history inscribed into a structure? Let us approach this problem at its most abstract, apropos historiography itself. Hayden White defines historical work as a verbal structure in the form of a narrative prose discourse that classifies past structures and processes in order to explain them by representing them as models: a historian does not just find history; she takes events that have happened and makes a story out of them, that is, reorganizes them into a narrative prose discourse. She does this by arranging events in a certain order, deciding which to include and exclude, stressing some events and subordinating others, all this in order to answer the questions: What happened? When? How? Why? In her answers, the historian relies on three modes of explanation: Emplotment, Argument, and Ideological implication. For each of these three explanations, there are four types from which the historian can choose:
Emplotment-"every history, even the most 'synchronic' of them, will be emplotted in some way." The four types of emplotment are: Romance (the drama of self-identification, including a hero's triumph over evil); Satire (the opposite of romance: people are captives in the world until they die); Comedy (harmony between the natural and the social; causes for celebration); Tragedy (a hero, through a fall or test, learns through resignation to work within the limitations of the world, and the audience learns as well).
Argument-the four types of argument are: Formalist (identification of objects by classifying, labeling, categorizing: "any historiography in which the depiction of the variety, color, and vividness of the historical field is taken as the central aim of the work"); Organicist (the whole is more than the sum of its parts; goal-oriented, the principles are not laws but are an integral part of human freedom); Mechanistic (finding laws that govern the operations of human activities); Contextualist (events are explained by their relationships to similar events; threads are traced back to origins).
Ideology-reflects the ethics and assumptions the historian has about life, how past events affect the present, and how we ought to act in the present; claims the authority of "science" or "realism". There are again four types: Conservative (history evolves; we can hope for utopia, but change occurs slowly as part of the natural rhythm); Liberal (progress in social history is the result of changes in law and government); Radical (utopia is imminent and must be effected by revolutionary means); Anarchist (the state is corrupt and therefore must be destroyed and a new community inaugurated).
The historian also "prefigures" the act of writing history by writing within a particular trope-one of four deep poetic structures: metaphor, synecdoche, metonymy, and irony. Tropes "are especially useful for understanding the operations by which the contents of experience which resist description in unambiguous prose representations can be prefiguratively grasped and prepared for conscious apprehension." White glosses the four tropes as follows:
Metaphor-one phenomenon is compared or contrasted to another in the manner of an analogy or simile.
Synecdoche-using a part of something to symbolize the quality of the whole; for example, "He is all heart."
Metonymy-substitution of the name of a part for the whole, e.g., "sail" for "ship."
Irony-literal meaning that makes no sense figuratively; examples are paradox (oxymoron) or the "manifestly absurd expression" (catachresis).
Metaphor is representational, metonymy is reductionist, synecdoche is integrative, and irony is negational. The net result is a complex proto-Kantian a priori formal scheme represented in the table below:
Code: Select all
Emplotment Argument Ideology Poetic Structure ---------------------------------------------------------------- Romantic Formalist Anarchist Synecdoche Tragic Mechanistic Radical Metaphor Comic Organicist Conservative Metonymy Satirical Contextualist Liberal Irony
White himself denies being a relativist or postmodernist, asserting that the reality of events in the past is not contradicted by literary portrayals of those events. But he nonetheless remains within a Kantian space, opposing the formal-transcendental a priori of an atemporal scheme or matrix to the contingent reality which actualizes the possibilities prescribed by the scheme-the real for White is the contingent event which affects the scheme from outside. The model can go wrong in two ways: first, reality fails to fit it, to fill in all its places, all the options it allows, so that some remain blank, empty possibilities with no actualization. This is the Levi-Straussian position, asserting the deficit of reality with regard to the structural matrix. Second, the empiricist shift of perspective: there is too much reality, reality is too rich and will elude any matrix. This is the common-sense view: every conceptual network will be too rough and abstract to catch the fine texture of the reality out there.
The proper Hegelian path is the third alternative: an immanent structural inconsistency, such that the formal matrix is thwarted immanently, on account of an inherent antagonism rather than an excess of reality. What if the fact that some options remain blank, empty possibilities with no actualization indicates that the matrix proposed by White is an attempt to bring together two different matrices and obliterate their antagonism? It is here that we touch the Real: not as an external reality too rich to be captured by a formal matrix, but as the antagonism causing the formal split of matrices. We cannot locate it directly in reality but only in the deadlock of the structural formalization of reality. This Real (antagonism) is not relative, it is the "absolute" of a given historical constellation, its fixed impossibility or point of reference. This is how we can avoid relativism even while accepting that historical material is always organized into narratives that are partial and engaged: there is a conflict of narratives, and the Real is touched by this conflict that maintains the distance of the narratives from reality; the Real is inaccessible, and the Real is the very obstacle which makes it inaccessible-this is how the (narrative) form itself falls into its content.
Badiou says that mathematical truth is infinite because language contains structures like generic sets. These generic sets are finite linguistic constructs that restructure the domain of language from within by telling us truths about them, such as CH's independence from ZF. ZF is a finite language, but we used the generic set to establish that mathematics is larger than ZF. In this way, generic sets are like dark windows that exist within language looking out onto the infinity of mathematical truth. Badiou calls this infinity the "multiple", presumably because he's an idiot, and the generic set equivalent an "event" in the political sense because of his murderous Maoist inclinations. (He has also raised a poor, mentally handicapped child from a disadvantaged background. What a monster, huh?)
I see some interesting similarities between Zizek's and Badiou's conceptions of objectivity here, but this is where where Badiou starts to go wrong if I understood him right. I would like someone familiar with Badiou to correct my misconceptions. Badiou says that because CH is independent of ZF, we can choose whether CH is valid or not, which introduces a core of subjectivity within linguistic objectivity. This is where he is serious about introducing a role for chance, something I don't see Zizek mention much. The shitty internet pdf I'm cribbing this from puts it as follows:
"Source": https://www.academia.edu/29483612/After ... istic_TurnWhat is critical is that Badiou, in this way, acknowledges the force of finitude, so
to speak, and specifically the knot which binds language and thought. To elaborate
further, he accepts that thought is, in a certain sense, limited by language. There is a
norm of finitude at work in any situation, which is its fortification by a state and an
encyclopedia. This is why constructivism, according to which language marks the
limits of thought and accords with being seamlessly, constitutes a sort of default
orientation for thought. As is the case (in Badiou’s more recent work) with
democratic materialism, according to which there are only bodies and languages.
There are, for Badiou, nonetheless truths, or thought processes, which take place
“amidst discernible finitude” (BE, 399), employing only “the resources of the
situation … its multiples, its language” (398). It is not that thought takes place at
some remove from language (from rules, discursive norms or logical formulas, etc.)
but that when the finite combines with chance (by way of an event, an intervention,
and a randomised series of enquiries) it is able to touch on being in the very
rearrangement of the terms it provides. To revise this procedure: being, as multiple,
necessarily exceeds the grasp of language due to its recourse to a structuring or oneeffect
which places it on the side of representation and the state, rather than truth. As
is the case with knowledge, which essentially consists in what the situation’s language
carves up of its multiples. A situation’s knowledge never grasps the truth of the
situation as such. We could render this is Foucauldian terms: knowledge, for instance,
fails to account for its complicity in power relations; or in psychoanalytic terms, the
real resists symbolisation, due to the slippage of the signifier and the impossibility of
metalangauge. For an antiphilosopher, this gap between what can be said and known
and the real as such might be grasped in an heroic act of the philosopher, or a selfeffacing
gesture. For Badiou, it merely the space in which thought, in its properly
universal sense, takes place: an event opens the situation to this excess, to the hole in
its knowledge; the arbitrariness of a signifier latches onto this aleatory flicker of being
as the event is named; a subject proceeds to randomly inquire as to the connection of
the knowledge of the situation with the occurrence of the event, forging a generic set
which cannot be comprehended within the knowledge/language of the situation at
hand; and a subjective language forms which consists only of terminology available in
the situation’s own language, but whose sense is contingent upon the ‘will have been’
of a situation extended to incorporate this generic set. In this way, the “discernible
finitude” of a situation is exposed to the infinity of its being, and a truth comes to be.
Finally I'm in a position to ask my question: What the fuck is the connection between being free to choose between the truth and falsehood of CH and aleatory randomness playing a role in the domain of truth? Did I understand that connection correctly? If I did, does Badiou put it that way in BE, or is this the fault of the guy who wrote this thesis?