Single Idea 23026

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers]

Full Idea

It is by the natural light that the axioms of mathematics are recognised. If we take away the same quantity from two equal things, …a thing we can easily predict without having experienced it.

Gist of Idea

We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light

Source

Gottfried Leibniz (Letters to Queen Charlotte [1702], p.189)

Book Reference

Leibniz,Gottfried: 'Philosophical Essays', ed/tr. Arlew,R /Garber,D [Hackett 1989], p.189


A Reaction

He also says two equal weights will keep a balance level. Plato thinks his slave boy understands halving an area by the natural light, but that is just as likely to be experience. It is too easy to attribut thoughts to a 'natural light'.