Full Idea
'Material implication' is a term introduced by Russell which is defined as 'the conjunction of p and not-q is false', but carries a strong implication that p implies q, and so there must be some kind of connection between them, which is misleading.
Gist of Idea
'Material implication' is defined as 'not(p and not-q)', but seems to imply a connection between p and q
Source
Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.270)
Book Reference
Mautner,Thomas: 'Dictionary of Philosophy' [Penguin 1997], p.270
A Reaction
Mautner says statements of the form 'if p then q' are better called 'conditionals' than 'material implications'. Clearly there is a need for more precise terminology here, as the underlying concepts seem simple enough.