of routine undergraduate mathematics, but not in the 19th century.

As far as Cassirer is concerned, Leibniz was indeed doing *analysis* as l’Hôpital called it. It is not even sure Cassirer was aware of the more advanced analysis. Leibnizian calculus only seems “trivial" from the standpoint of properly 20th century mathematics. It is an advance in understanding when we make a distinction between Leibnizian calculus and analysis. We don’t mean to diminish Leibniz’s greatness by this distinction, nor do we suggest that Cassirer was *wrong*. He was merely using the term *analysis* in its 17–19th century sense rather than the sense in which we use it today.

Edward Nelson
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As far as the passage from [@Ro66] is concerned, we find the following comment at the end of the paragraph:

> The following framework for higher order structures and higher order languages copes with these and similar cases. It is rather straightforward and suitable for our purposes. [@Ro66 section 2.6, p. 19]

Robinson then proceeds to develop a solution, which roughly corresponds to level (3) as outlined in Section \[FOL\]. The claim that we are dealing with first order logic plus *standard part* is in a sense a mathematical theorem, 