back to ideas for this text


Single Idea 9861

[from 'The Republic' by Plato, in 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism ]

Full Idea

We see the same thing to be both one and an unlimited number at the same time.

Gist of Idea

The same thing is both one and an unlimited number at the same time

Source

Plato (The Republic [c.374 BCE], 525a)

Book Reference

Plato: 'Complete Works', ed/tr. Cooper,John M. [Hackett 1997], p.1141


A Reaction

Frege makes the same point, that a pair of boots is both two and one. The point is at its strongest in opposition to empirical accounts of arithmetic. However, Mill observes that pebbles can be both 5 and 3+2, without contradiction.