to assume that what they were doing in the 17th century was calculus rather than analysis.

As far as Unguru is concerned, he is unlikely to be impressed by interpretations of Leibnizian infinitesimals as quantified propositions or for that matter by reading Leibniz as if he had already read not only Weierstrass but also Russell à la Ishiguro, contrary to much textual evidence in Leibniz himself. We provide a rebuttal of the Ishiguro–Arthur *logical fiction* reading in [@Ba16] and [@Ba16b].

Robinson, Cassirer, Nelson
==========================

Robinson on second-order logic
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The following quote is from Robinson’s *Non-standard Analysis*:

> The axiomatic systems for many algebraic concepts such as groups or fields are formulated in a natural way within a first order language…, However, interesting parts of the *theory* of such a concept may well extend beyond the resources of a first order language. Thus, in the theory of groups statements regarding subgroups, or regarding the existence of subgroups of certain types will, in general, involve quantification with respect to sets of individuals… [@Ro66 section 2.6, p. 19]

This appears to amount to a claim that the local ontology may indeed be often formulated in first-order terms, while the global ontology is 