the ontology of mathematical entities such as numbers, and concentrate instead on the procedures, in line with Quine’s comment to the effect that

> Arithmetic is, in this sense, all there is to number: there is no saying absolutely what the numbers are; there is only arithmetic. [@Qu p. 198]

Related comments can be found in [@Be65]. If one could separate the “ontological questions" from the rest, then framework A would be more appropriate than framework B for interpreting the classical texts *if and only if* framework A provides better proxies for the procedural moves found in Leibnizian infinitesimal calculus than framework B does, and vice versa.

The tempting evidence in favor of the appropriateness of a modern framework B for interpreting Leibnizian infinitesimal calculus is the presence of infinitesimals and infinite numbers in both, as well as the availability of hyperreal proxies for guiding principles in Leibniz’s work such as the law of continuity as expressed in [@Le01c] and [@Le02a] as well as the transcendental law of homogeneity [@Le10b]; see [@KS2], [@KS1], [@SK], [@Gu]. To what extent Leibnizian infinitesimals can be implemented in differential geometry can be gauged from [@NK].

The question we seek to explore is whether the 