cope with Leibniz?* this is of course possible in principle. However, we are interested here in the practical issue of modern commentators missing some compelling aspects of interpretation of Leibniz’s work because of a self-imposed limitation to a Weierstrassian interpretive framework.

A lid on ontology
=================

It could be objected that one cannot escape so easily with the general argument along the lines of “Let’s Ignore (ontological) Differences,” or LID for short (putting a *lid* on ontology, so to speak).

The LID proceeds as follows. We start with the ‘real’ L, i.e., the mathematician who lived, wrote, and argued in the 17th century. It seems plausible to assume that L based his reasoning on a mixture of first and second order arguments, without clearly differentiating between the two.

In a reconstruction of L’s arguments, one replaces the cognitive agent L by a substitute L1 who argues only in a first order framework. This entails, in particular, that L1 cannot distinguish between $\mathbb{N}$ and ${}^\ast\mathbb{N}$.

However, it seems likely that L could distinguish the two structures, simply because he did not distinguish between the first and second order levels. In other words, the LID recommendation does not help because the distinction 