concrete rules and abstract machines

“ Why did God choose this world rather than another, when another was possible? Leibniz’s answer becomes splendid: it’s because it is the world that mathematically implicates the maximum of continuity, and it’s uniquely in this sense that it is the best of all possible worlds. A concept is always something very complex. We can situate today’s meeting under the sign of the concept of singularity. And the concept of singularity has all sorts of languages that intersect within it. A concept is always necessarily polyvocal. You can grasp the concept of singularity only through a minimum of mathematical apparatus: singular points in opposition to ordinary or regular points, on the level of thought experiences of a psychological type: what is dizziness, what is a murmur, what is a hum , etc. And on the level of philosophy, in Leibniz’s case, the construction of this relation of compossibility. It’s not a mathematical philosophy, no more than mathematics becomes philosophy, but in a philosophical concept, there are all sorts of different orders that necessarily symbolize. It has a philosophical heading, it has a mathematical heading, and it has a heading for thought experience. And it’s true of all concepts. It was a great day for philosophy when someone brought this odd couple to general attention, and that’s what I call a creation in philosophy. When Leibniz proposed this topic, the singular, there precisely is the act of creation; when Leibniz tells us that there is no reason for you simply to oppose the singular to the universal. It’s much more interesting if you listen to what mathematicians say, who for their own reasons think of “singular” not in relation to “universal,” but in relation to “ordinary” or “regular.” Leibniz isn’t doing mathematics at that point. I would say that his inspiration is mathematical, and he goes on to create a philosophical theory, notably a whole conception of truth that is radically new since it’s going to consist in saying: don’t pay too much attention to the matter of true and false, don’t ask in your thinking what is true and what is false, because what is true and what is false in your thinking always results from something that is much deeper. ”