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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 Ref
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'.
| 13189 | A necessary feature (such as air for humans) is not therefore part of the essence [Leibniz] |
| 19432 | Intelligible truth is independent of any external things or experiences [Leibniz] |
| 19430 | We know objects by perceptions, but their qualities don't reveal what it is we are perceiving [Leibniz] |
| 19431 | There is nothing in the understanding but experiences, plus the understanding itself, and the understander [Leibniz] |
| 23026 | We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz] |