Thought without premises thus encounters insurmountable difficulty in the process of appropriation. And the theorem that reveals it is perhaps the thought from which that thought hangs by imperceptible threads. But it is not certain that the construction of the formal system is directed primarily toward appropriating logical consistency. Even thought from which the gods are absent has its paradoxes. Indeed, what is immediately striking about the formal system is its power. Arithmetic, which is the formal system on which Gödel demonstrated his theorem, cannot affirm its own consistency. But arithmetic is effective. And a formal system that works is also a machine that produces and amplifies power. Let us return to the construction of the formal system: what are its characteristics in relation to the rest of the world of propositions? First, the absence of premises: the formal system regards everything outside it as equal to zero. Second, it is arbitrary: any statement can be taken as a first proposition of a theory in a formalized system, provided that every constituent element is defined without a remainder. (In reality, there is always a remainder: the proposition a=b is formed by the signs a,=, and b: “In the beginning was the sign,” said Hilbert, and the phrase—inadvertently?—pointed to the fact that arbitrary choice can make everything transparent, but not itself.) The reduction of the surrounding context to zero and the arbitrary manner of setting the signs of the propositions in the formal system are two procedures of enormous power. Their application is not limited to the ambit in which such procedures appear in their pure form, which is the logico-mathematical sphere. Without the subject knowing it, these procedures act in all areas where thought has no premises. They act in their least pure, and of course their least consistent, forms: each time they are always more or less subtle or elaborate simulations of formal systems. But their purpose is not consistency, which moreover the formal system is unable to possess internally. These simulations aim at power—and they achieve it. Often to an extent that goes far beyond what is expected (precisely because they are simulations, therefore their elements are mixed with empirical data, they are not transparent—even if it is pretended they are, so long as the simulation holds). The formal system can be an impressive system of control, even though, inevitably, at a certain point in its development, it encounters an element that is entirely uncontrollable. But the hope is that such an element doesn’t cause too much practical disturbance. Arithmetic has indeed continued to make its contribution after Gödel’s theorem. In simulated formal systems, uncontrollability appears in forms that are clearly much more drastic, even in terms of pure functioning. But the intoxication of power, up to that moment, is immense. In such intoxication, thought without premises finds its formulation in what is its own. Own is that which belongs to the area in which a form of power can be exerted. The power is gauged in terms of capacity to control. Control is produced by simulating pure formal systems, or by mixing simulations with pure formal systems. But are we ourselves the formal systems that act within us?