Formalization and Dialectics
If dialectics is to be reanimated, today, we must cross it at is point of greatest resistance, a blind spot formed by a resistance to mathematics: the idea, which Hegel resisted furiously despite the embryonic status in which his time retained it, of logical calculation. It was through this idea that history would give birth to another that is ultimately more profound: the idea of logico-mathematical formalisation, an idea that would liberate mathematical thought from the contingency of its objects, through an act of reflection that would make it itself a mathematical object — but a reflection subject to the essentially dialectical drama of escaping away from itself just when it tries to grasp itself as such, a refractory reflection that would generate antinomies, incompletions and subversions of meaning. Through a struggle to apprehend itself as such, mathematical logic would, quietly, and without attracting the attention of either of the two traditions that the nineteenth century began, rebuild the dialectic from the calculi Hegel rejected.
The purpose of this conference is, first and foremost, to draw philosophy’s attention to this reanimation of the dialectic from the ‘dead bones’ of calculus, to accelerate this reanimation through careful experiments in formalisation, and interrupt the servitude to ‘the understanding’ to which philosophers have, for the last century, indentured mathematical logic. If philosophy wishes to find in logic something other than a regimentation of the understanding’s prejudices, then the task of tapping the underground current of the dialectic in mathematical logic is one we can no longer ignore.