Full Idea
If all truths are implied by a falsehood, then 'if there are no trees in the park then there is no shade' and 'if there are no trees in the park there is plenty of shade' both come out as true. Intuitively, though, the second one is false.
Gist of Idea
If all truths are implied by a falsehood, then not-p might imply both q and not-q
Source
Jennifer Fisher (On the Philosophy of Logic [2008], 08.I)
Book Reference
Fisher,Jennifer: 'On the Philosophy of Logic' [Thomson Wadsworth 2008], p.107
A Reaction
The rule that a falsehood implies all truths must be the weakest idea in classical logic, if it actually implies a contradiction. This means we must take an interest in relevance logics.