concrete rules and abstract machines

“ Now, me, my answer to the question: but what is it exactly, this that Spinoza speaks to us of when he speaks of the relations of movement and rest, of proportions of movement and rest, and says: the infinitely small, a collection of the infinitely small belonging to such an individual under such a relation of movement and rest, what is this relation? I would not be able to say like Gueroult that it is a vibration which assimilates the individual to a pendulum: it is a differential relation. It is a differential relation such that it is manifested in the infinite sets, in the infinite sets of the infinitely small. And, in effect, if you take Spinoza‚s letter on blood, of which I have made great use, and the two components of blood, chyle and lymph, this now tells us what? It tells us that there are corpuscles of chyle, or better chyle is an infinite set of very simple bodies. Lymph is another infinite set of the very simple bodies. What distinguishes the two infinite sets? It is the differential relation! You have this time a dy/dx which is: the infinitely small parts of chyle over the infinitely small parts of lymph, and this differential relation tends towards a limit: the blood, that is to say: chyle and lymph compose blood.
If this is right, we could say why infinite ensembles are distinguished. It is because the infinite sets of very simple bodies don’t exist independently of the differential relations which they put into effect. Therefore it is by abstraction that I began by speaking of them. But they necessarily exist, they exist necessarily under such and such a variable relation, they cannot exist independently of a relation, since the notion even of the term infinitely small, or of vanishing quantity, cannot be defined independently of a differential relation. Once again, Œdx‚ has no sense in relation to Œx‚, Œdy‚ has no sense in relation to Œy‚, only the relation dx/dy has a sense. That’s to say that the infinitely small don’t exist independently of the differential relation. Good. Now, what permits me to distinguish one infinite set from another infinite set? I would say that the infinite sets have different powers [puissances], and that which appears quite obviously in this thought of the actual infinite is the idea of the power [puissance] of an set. Let’s understand here that I don’t at all mean, it would be abominable to make me mean that they have anticipated things which closely concern set theory in the mathematics of the beginning of the 20th century, I don’t mean that at all. I mean that in their conception, which is in absolute contrast with modern mathematics, which is completely different, which has nothing to do with modern mathematics, in their conception of the infinitely small and of the differential calculus interpreted from the perspective of the infinitely small, they necessarily brought out - and this is not peculiar to Leibniz, it is also true of Spinoza, and of Malebranche, all these philosophers of the second half of the 17th century ˜ brought out the idea of infinite sets which are distinguished, not by their numbers, an infinite set by definition, it can not be distinguished from another infinite set by the number of its parts, since all infinite sets excede all assignable number of parts - therefore, from the point of view of the number of parts, there cannot be one which has a greater number of parts than another. All these sets are infinite. Therefore under what aspect are they distinguished? Why is it that I can say: this infinite set and not that one? ”