  Leibniz used the term fiction in conjunction with infinitesimals. What kind
of fictions they were exactly is a subject of scholarly dispute. The position
of Bos and Mancosu contrasts with that of Ishiguro and Arthur. Leibniz's own
views, expressed in his published articles and correspondence, led Bos to
distinguish between two methods in Leibniz's work: (A) one exploiting classical
`exhaustion' arguments, and (B) one exploiting inassignable infinitesimals
together with a law of continuity. Of particular interest is evidence stemming
from Leibniz's work Nouveaux Essais sur l'Entendement Humain as well as from
his correspondence with Arnauld, Bignon, Dagincourt, Des Bosses, and Varignon.
A careful examination of the evidence leads us to the opposite conclusion from
Arthur's. We analyze a hitherto unnoticed objection of Rolle's concerning the
lack of justification for extending axioms and operations in geometry and
analysis from the ordinary domain to that of infinitesimal calculus, and
reactions to it by Saurin and Leibniz. A newly released 1705 manuscript by
Leibniz (Puisque des personnes...) currently in the process of digitalisation,
sheds light on the nature of Leibnizian inassignable infinitesimals. In a pair
of 1695 texts Leibniz made it clear that his incomparable magnitudes violate
Euclid's Definition V.4, a.k.a. the Archimedean property, corroborating the
non-Archimedean construal of the Leibnizian calculus.
  Keywords: Archimedean property; assignable vs inassignable quantity; Euclid's
Definition V.4; infinitesimal; law of continuity; law of homogeneity; logical
fiction; Nouveaux Essais; pure fiction; quantifier-assisted paraphrase;
syncategorematic; transfer principle; Arnauld; Bignon; Des Bosses; Rolle;
Saurin; Varignon
