Single Idea 14159

[catalogued under 2. Reason / D. Definition / 13. Against Definition]

Full Idea

The statement that a class is to be represented by a symbol is a definition in mathematics, and says nothing about mathematical entities. Any formula can be stated in terms of primitive ideas, so the definitions are superfluous.

Gist of Idea

In mathematics definitions are superfluous, as they name classes, and it all reduces to primitives

Source

Bertrand Russell (The Principles of Mathematics [1903], §412)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.429


A Reaction

[compressed wording] I'm not sure that everyone would agree with this (e.g. Kit Fine), as certain types of numbers seem to be introduced by stipulative definitions.