Article ID: CBB813371353

Fiction, possibility and impossibility: three kinds of mathematical fictions in Leibniz’s work (2021)

unapi

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 architectural principles. In conclusion, this “soft” impossibility of infinitesimals yields them, in Leibniz view, a presumptive or “conjectural” status.

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Authors & Contributors
Katz, Mikhail G.
Mormann, Thomas
Arthur, Richard T. W.
Vrhovski, Jan
Bair, Jacques
Ely, Robert
Concepts
Infinitesimals
Calculus
Mathematics
Philosophy of mathematics
Mathematical analysis
Philosophy of science
Time Periods
17th century
18th century
20th century, early
20th century, late
Early modern
Modern
Places
China
Portugal
Germany
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