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.ĪB - In this article, I address two different kinds of equivocations in reading Leibniz’s fictional infinite and infinitesimal. In treating these equivocations, I critique some assumptions that underlie the reductive reading of Leibniz’s fictionalism concerning infinite and infinitesimals. I analyze this by looking at Leibniz’s constructive method and apagogic argument style in his quadrature method. 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 equivocation by criticizing the logicist influence on 20th century Anglophone reception of the syncategorematical infinite and infinitesimal.
The first equivocation is the association of a foundation of infinitesimals with their ontological status. 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. N2 - In this article, I address two different kinds of equivocations in reading Leibniz’s fictional infinite and infinitesimal. T1 - Equivocation in Leibniz’s infinitesimal fictionalism 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.Ībstract = "In this article, I address two different kinds of equivocations in reading Leibnizs work from a range of different contexts and methods.
In this article, I address two different kinds of equivocations in reading Leibniz’s fictional infinite and infinitesimal.
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