undermining the contention that “this seems hardly compatible, etc.”

Edward Nelson demonstrated that infinitesimals can be found within the ordinary real line itself in the following sense. Nelson finds infinitesimals in the real line by means of enriching the language through the introduction of a unary predicate *standard* and an axiom schemata (of Idealization), one of most immediate instances of which implies the existence of infinitely large integers and hence nonzero infinitesimals; see [@Ne77]. This is closely parallel to the dichotomy of *assignable* vs *inassignable* in Leibniz, whereas Carnot spoke of *quantités désignées* [@Ca97], [@Ba89 p. 46]. Thus, we obtain infinitesimals as soon as we assume that (1) there are assignable (or standard) reals, that obey the same rules as all the reals, and (2) there are reals that not assignable.

In more detail, one considers the ordinary ZFC formulated in first order logic (here the term is used in a different sense from the rest of this article), adds to it the unary predicate and the axiom schemata, and obtains a framework where calculus and analysis can be done with infinitesimals. For further discussion see [@KK15].

The passage from Robinson cited above does indicate that second order theory may 