What Does God Know but can’t Say? Leibniz on Infinity, Fictitious Infinitesimals and a Possible Solution of the Labyrinth of Freedom

Lison, Elad

doi:10.1007/s11406-019-00086-4

Philosophia

2019

DOI: 10.1007/s11406-019-00086-4

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What Does God Know but can’t Say? Leibniz on Infinity, Fictitious Infinitesimals and a Possible Solution of the Labyrinth of Freedom

Elad Lison

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2021

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Fiction, possibility and impossibility: three kinds of mathematical fictions in Leibniz’s work

Esquisabel

Quintana

2021

Arch. Hist. Exact Sci.

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This paper is concerned with the status of mathematical fictions in Leibniz's work and especially with infinitary quantities as fictions. Thus, it is maintained that mathematical fictions constitute a kind of symbolic notion that implies various degrees of impossibility. With this framework, different kinds of notions of possibility and impossibility are proposed, reviewing the usual interpretation of both modal concepts, which appeals to the consistency property. Thus, three concepts of the possibility/impossibility pair are distinguished; they give rise, in turn, to three concepts of mathematical fictions. Moreover, such a distinction is the base for the claim that infinitesimal quantities, as mathematical fictions, do not imply an absolute impossibility, resulting from self-contradiction, but a relative impossibility, founded on irrepresentability and on the fact that it does not conform to architectonic principles. In conclusion, this "soft" impossibility of infinitesimals yields them, in Leibniz view, a presumptive or "conjectural" status.

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Fiction, possibility and impossibility: three kinds of mathematical fictions in Leibniz’s work

Esquisabel

Quintana

2021

Arch. Hist. Exact Sci.

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What Does God Know but can’t Say? Leibniz on Infinity, Fictitious Infinitesimals and a Possible Solution of the Labyrinth of Freedom

Cited by 1 publication

References 16 publications

Fiction, possibility and impossibility: three kinds of mathematical fictions in Leibniz’s work

Fiction, possibility and impossibility: three kinds of mathematical fictions in Leibniz’s work

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