Full Idea
When you do what a logician would call 'asserting not-p', you are saying 'p is false'.
Gist of Idea
Asserting not-p is saying p is false
Source
Bertrand Russell (An Inquiry into Meaning and Truth [1940], 5)
Book Reference
Russell,Bertrand: 'An Inquiry into Meaning and Truth' [Penguin 1967], p.77
A Reaction
This is presumably classical logic. If we could label p as 'undetermined' (a third truth value), then 'not-p' might equally mean 'undetermined'.