Full Idea
Russell gives an argument that other minds exist, because if one is entitled to believe this, then one can rely on the testimony of others, which, jointly with one's own experience, will give powerful support to the view that there a real spatial world.
Gist of Idea
Other minds seem to exist, because their testimony supports realism about the world
Source
report of Bertrand Russell (Our Knowledge of the External World [1914], 3) by A.C. Grayling - Russell Ch.2
Book Reference
Grayling,A.C.: 'Russell' [OUP 1996], p.45
A Reaction
I rather like this argument. It is quite close to Wittgenstein's Private Language Argument, which also seems to refute scepticism about other minds. I think Russell's line, using testimony, knowledge and realism, may be better than Wittgenstein's.