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Leibniz's Fictionalist Interpretation of Infinitesimals in the History of Calculus

A historiographical thesis, defended through close reading of Leibniz's texts, that Leibniz used genuine infinitesimals which he regarded as useful fictions, on a par with negative and imaginary numbers, rather than as self-contradictory or as mere shorthand for ordinary quantities. Distinguishes existence in nature from existence in mathematics and argues that non-Archimedean continua are compatible with Leibniz's notions of number, quantity, and magnitude.