more from Baruch de Spinoza

Single Idea 4821

[catalogued under 26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature]

Full Idea

If an infinite line be measured out in feet, it will consist of an infinite number of such parts; it would equally consist of an infinite number of parts, if each part was only an inch; therefore, one infinity would be twelve times as great as the other.

Gist of Idea

An infinite line can be marked in feet or inches, so one infinity is twelve times the other


Baruch de Spinoza (The Ethics [1675], I Pr 15)

Book Reference

Spinoza,Benedict de: 'Ethics, Improvement of Understanding, Letters', ed/tr. Elwes,R [Dover 1955], p.56

A Reaction

This seems to anticipate Cantor. Spinoza's point seemed bewildering then, but is now accepted as a standard feature of the concept of infinity.