Full Idea
Quantity, though philosophers seem to think it essential to mathematics, does not occur in pure mathematics, and does occur in many cases not amenable to mathematical treatment. The place of quantity is taken by order.
Gist of Idea
Quantity is not part of mathematics, where it is replaced by order
Source
Bertrand Russell (The Principles of Mathematics [1903], §405)
Book Reference
Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.419
A Reaction
He gives pain as an example of a quantity which cannot be treated mathematically.
Related Idea
Idea 17784 Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry]