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Single Idea 14158

[filed under theme 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / b. Quantity ]

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 Ref

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]

The 4 ideas with the same theme [specifying amounts of things numerically]:

14123 Some quantities can't be measured, and some non-quantities are measurable [Russell]
14158 Quantity is not part of mathematics, where it is replaced by order [Russell]
17782 Greek quantities were concrete, and ratio and proportion were their science [Mayberry]
17781 Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry]