Full Idea
We want our numbers to be such as can be used for counting common objects, and this requires that our numbers should have a definite meaning, not merely that they should have certain formal properties.
Gist of Idea
Numbers are needed for counting, so they need a meaning, and not just formal properties
Source
Bertrand Russell (Introduction to Mathematical Philosophy [1919], I)
Book Reference
Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.10
A Reaction
Why would just having certain formal properties be insufficient for counting? You just need an ordered series of unique items. It isn't just that we 'want' this. If you define something that we can't count with, you haven't defined numbers.