i got 99 problems but an axiom ain’t one

ATP on Problematic-Axiomatic

Axiomatics vs Problematics 1, p374 — Nomadology

Although safety is a fundamental element in the theoretical norms of the State, and of the political ideal, there is also something else at issue as well. Due to all their procedures, the ambulant sciences quickly overstep the possibility of calculation: they inhabit that “more” that exceeds the space of reproduction and soon run into problems that are insurmountable from that point of view; they eventually resolve those problems by means of a real-life operation. The solutions are supposed to come from a set of activities that constitute them as nonautonomous. Only royal science, in contrast, has at its disposal a metric power that can define a conceptual apparatus or an autonomy of science (including the autonomy of experimental science). That is why it is necessary to couple ambulant spaces with a space of homogeneity, without which the laws of physics would depend on particular points in space. But this is less a translation than a constitution: precisely that constitution the ambulant sciences did not undertake, and do not have the means to undertake. In the field of interaction of the two sciences, the ambulant sciences confine themselves to inventing problems whose solution is tied to a whole set of collective, nonscientific activities but whose scientific solution depends, on the contrary, on royal science and the way it has transformed the problem by introducing it into its theorematic apparatus and its organization of work. This is somewhat like intuition and intelligence in Bergson, where only intelligence has the scientific means to solve formally the problems posed by intuition, problems that intuition would be content to entrust to the qualitative activities of a humanity engaged in following matter.40

Axiomatic vs Problematics 2, p461 — Capture

Politics is by no means an apodictic science. It proceeds by experimentation, groping in the dark, injection, withdrawal, advances, retreats. The factors of decision and prediction are limited. It is an absurdity to postulate a world supergovernment that makes the final decisions. No one is even capable of predicting the growth in the money supply. Similarly, the States are affected by all kinds of coefficients of uncertainty and unpredictability. John Kenneth Galbraith and Francois Chatelet have formulated the concept of constant and decisive errors, which make the glory of men of State no less than their rare successful evaluations. But that is just one more reason to make a connection between politics and axiomatics. For in science an axiomatic is not at all a transcendent, autonomous, and decision-making power opposed to experimentation and intuition. On the one hand, it has its own gropings in the dark, experimentations, modes of intuition. Axioms being independent of each other, can they be added, and up to what point (a saturated system)? Can they be withdrawn (a “weakened” system)? On the other hand, it is of the nature of axiomatics to come up against so-called undecidable propositions, to confront necessarily higher powers that it cannot master.60 Finally, axiomatics does not constitute the cutting edge of science; it is much more a stopping point, a reordering that prevents decoded semiotic flows in physics and mathematics from escaping in all directions. The great axiomaticians are the men of State of science, who seal off the lines of flight that are so frequent in mathematics, who would impose a new nexum, if only a temporary one, and who lay down the official policies of science. They are the heirs of the theorematic conception of geometry. When intuitionism opposed axiomatics, it was not only in the name of intuition, of construction and creation, but also in the name of a calculus of problems, a problematic conception of science that was not less abstract but implied an entirely different abstract machine, one working in the undecidable and the fugitive.61 It is the real characteristics of axiomatics that lead us to say that capitalism and present-day politics are an axiomatic in the literal sense. But it is precisely for this reason that nothing is played out in advance. From this standpoint, we may present a summary sketch of the “givens.”

Axiomatics vs Diagrammatics p143-4 — Regime of Signs

Above all, diagrammaticism should not be confused with an operation of the axiomatic type. Far from drawing creative lines of flight and conjugating traits of positive deterritorialization, axiomatics blocks all lines, subordinates them to a punctual system, and halts the geometric and algebraic writing systems that had begun to run off in all directions. This happened in relation to the question of indeterminism in physics: a “reordering” was undertaken to reconcile it with physical determinism. Mathematical writing systems were axiomatized, in other words, restratified, resemiotized, and material flows were rephysicalized. It is as much a political as a scientific affair: science must not go crazy. Hilbert and de Broglie were as much politicians as scientists: they reestablished order. An axiomatization, a semiotization, a physicalization, is not a diagram but in fact the opposite of a diagram. The program of a stratum, against the diagram of the plane of consistency. This does not, however, preclude the diagram’s heading back down the road to escape and scattering new, singular abstract machines (the mathematical creation of improbable functions was carried out in opposition to axiomatization, and the material invention of unfindable particles in opposition to physicalization). Science as such is like everything else; madness is as intrinsic to it as reorderings. The same scientists may participate in both aspects, having their own madness, police, signifiances, or subjectifications, as well as their own abstract machines, all in their capacity as scientists. The phrase “the politics of science” is a good designation for these currents, which are internal to science and not simply circumstances and State factors that act upon it from the outside, leading it to make as atomic bomb here and embark upon a space program there. These political influences or determinations would not exist if science itself did not have its own poles, oscillations, strata, and destratifications, its own lines of flight and reorderings, in short, the more or less potential events of its own politics, its own particular “polemics,” its own internal war machine (of which thwarted, persecuted, or hindered scientists are historically a part). It is not enough to say that axiomatics does not take invention and creation into account: it possesses a deliberate will to halt or stabilize the diagram, to take its place by lodging itself on a level of coagulated abstraction too large for the concrete but too small for the real. We will see in what sense this is the “capitalist” level.

Other Important References:

“the State is not axiomatic” (but is an abstract machine) p223 — Micropolitics & Segmentarity

history of states as modes of realization of the (capitalist) axiomatic p434, 436 — Capture

*****Capitalism as a worldwide axiomatic, p453-6 — Capture

Subjectivation and the axiomatic, p457-9

*****7 Aspects of the axiomatic, 461-73 — Captures

Abstract Machines can Axiomatize – 513-4 — Conclusion/Abstract Machines

Also see: Daniel Smith on the maths of axioms/problems, badiou/deleuze: Badiou on Deleuze

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