  Did Leibniz exploit infinitesimals and infinities `a la rigueur, or only as
shorthand for quantified propositions that refer to ordinary Archimedean
magnitudes? Chapter 5 in (Ishiguro 1990) is a defense of the latter position,
which she reformulates in terms of Russellian logical fictions. Ishiguro does
not explain how to reconcile this interpretation with Leibniz's repeated
assertions that infinitesimals violate the Archimedean property, viz., Euclid's
Elements, V.4. We present textual evidence from Leibniz, as well as historical
evidence from the early decades of the calculus, to undermine Ishiguro's
interpretation. Leibniz frequently writes that his infinitesimals are useful
fictions, and we agree; but we shall show that it is best not to understand
them as logical fictions; instead, they are better understood as pure fictions.
  Keywords: Archimedean property; infinitesimal; logical fiction; pure fiction;
quantified paraphrase; law of homogeneity
