between first and second order does not only affect the ontology but also the epistemology of the historical agents involved.

In sum, a modern infinitesimal reconstruction of L deals with a first-order version of L, namely L1, and not with L. In line with his position on geometric algebra, [@Un76] could point out that L1 is a modern artefact, different from the “real” L. Therefore additional arguments are needed in favor of the hypothesis that L and L1 are epistemologically sufficiently similar, but this seems difficult. In any case, a purely ontological assumption does not suffice.

To respond to the L *vs* L1 distinction, note that the tools one needs are *almost* limited to first order logic, but not quite, since one needs the shadow principle and the relation of infinite proximity. Rather than arguing that $L=L1$, we are arguing that $L=L1+\epsilon$.

Now the difference between calculus and analysis is that in calculus one deals mostly with first order phenomena (with the proviso as in Section \[three\]), whereas in analysis one starts tackling phenomena that are essentially second order, such as the completeness property i.e., existence of the least upper bound for an arbitrary bounded set, etc. It seems reasonable 