Single Idea 13190

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite]

Full Idea

Notwithstanding my infinitesimal calculus, I do not admit any real infinite numbers, even though I confess that the multitude of things surpasses any finite number, or rather any number. ..I consider infinitesimal quantities to be useful fictions.

Clarification

[Leibniz was one of the inventors of calculus]

Gist of Idea

I don't admit infinite numbers, and consider infinitesimals to be useful fictions

Source

Gottfried Leibniz (Letters to Samuel Masson [1716], 1716)

Book Reference

Leibniz,Gottfried: 'Philosophical Essays', ed/tr. Arlew,R /Garber,D [Hackett 1989], p.229


A Reaction

With the phrase 'useful fictions' we seem to have jumped straight into Harty Field. I'm with Leibniz on this one. The history of mathematics is a series of ingenious inventions, whenever they seem to make further exciting proofs possible.