Abstract
In this article, I address two different kinds of
equivocations in reading Leibniz’s fictional infinite and infinitesimal.
These equivocations form the background of a reductive reading of
infinite and infinitesimal fictions either as ultimately finite or as
something whose status can be taken together with any other
mathematical object as such. The first equivocation is the association of
a foundation of infinitesimals with their ontological status. I analyze this
equivocation by criticizing the logicist influence on 20th century
Anglophone reception of the syncategorematical infinite and
infinitesimal. The second equivocation is the association of the rigor of
mathematical demonstration with the problem of the admissibility of
infinite or infinitesimal terms. I analyze this by looking at Leibniz’s
constructive method and apagogic argument style in his quadrature
method. In treating these equivocations, I critique some assumptions
that underlie the reductive reading of Leibniz’s fictionalism concerning
infinite and infinitesimals. In turn, I suggest that these infinitesimal
“fictions” pointed to a problematic within Leibniz’s work that was
conceived and reconsidered in Leibniz’s work from a range of different
contexts and methods.