more from Gottfried Leibniz

Single Idea 12956

[catalogued under 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units]

Full Idea

The definition of 'number' as a multitude of units is appropriate only for whole numbers.

Gist of Idea

Only whole numbers are multitudes of units

Source

Gottfried Leibniz (New Essays on Human Understanding [1704], 2.15)

Book Reference

Leibniz,Gottfried: 'New Essays on Human Understanding', ed/tr. Remnant/Bennett [CUP 1996], p.156


A Reaction

One can also define rational numbers by making use of units, but the strategy breaks down with irrational numbers like root-2 and pi. I still say the concept of a unit is the basis of numbers. Without whole numbers, we wouldn't call the real 'numbers'.