Two-track depictions of Leibniz's fictions

TL;DR

This paper explores Leibniz's perspective on imaginary roots, negatives, and infinitesimals, analyzing whether he considered them as mathematical entities or mere fictions, through a detailed review of current scholarship.

Contribution

It offers a new interpretation of Leibniz's views on mathematical fictions by critically examining contemporary scholarship and historical texts.

Findings

Leibniz viewed certain mathematical concepts as useful fictions.

Current scholarship presents diverse interpretations of Leibniz's stance.

The paper clarifies Leibniz's position on the ontological status of mathematical fictions.

Abstract

Leibniz described imaginary roots, negatives, and infinitesimals as useful fictions. But did he view such 'impossible' numbers as mathematical entities? Alice and Bob take on the labyrinth of the current Leibniz scholarship.