Abstract

It is well known that the history of Calculus in the nineteenth century coincides with the process of substitution of infinitesimals by the notion of limit. But it is adviseable to keep in mind the ontological implications of that process.We can find a background for this ontological approach in Abraham Robinson’s Non-Standard AnaIysis and “The Metaphysics of the Calculus”. Indeed, by the choice of the word “metaphysics” and by the several recalls of the ontological nature of the arguments, Robinson claims for a filiation which is at the same time fruitful in the mathematical register and necessary for a true philosophical reflection about the infinite