more from Richard Dedekind

Single Idea 14437

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts]

Full Idea

Dedekind set up the axiom that the gap in his 'cut' must always be filled …The method of 'postulating' what we want has many advantages; they are the same as the advantages of theft over honest toil. Let us leave them to others.

Gist of Idea

Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil


report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - Introduction to Mathematical Philosophy VII

Book Reference

Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.71

A Reaction

This remark of Russell's is famous, and much quoted in other contexts, but I have seen the modern comment that it is grossly unfair to Dedekind.

Related Idea

Idea 14436 A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum [Russell]