Full Idea
Moore's Paradox says it makes no sense to assert 'I believe that p, but p is false', even though it makes perfectly good sense to assert 'I used to believe p, but p is false' or 'You believe p, but p is false'.
Gist of Idea
Moore's Paradox: you can't assert 'I believe that p but p is false', but can assert 'You believe p but p is false'
Source
report of G.E. Moore (works [1905]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.10
Book Reference
Lowe,E.J.: 'Introduction to the Philosophy of Mind' [CUP 2000], p.292
A Reaction
I'm not sure if this really deserves the label of 'paradox'. I take it as drawing attention to the obvious fact that belief is commitment to truth. I think my assessment that p is true is correct, but your assessment is wrong. ('True' is not redundant!)